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Six Sigma

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Control Charts and Introduction to Six Sigma

Session 12: Control Charts and Introduction to Six Sigma concepts

Control Charts and Introduction to Six Sigma

Control Charts - Topics of Discussion
– – – – – Control Chart History Control Limits Individuals and Moving Range Charts X-bar and R Charts Subgrouping

Control Charts and Introduction to Six Sigma

Typical Process Metrics
• • • • • • • • • Cycle times Lead times Productivity Schedule variance Budget variance Employee satisfaction Customer satisfaction Safety incidents System users (# hits) • • • • • • • • • Days sales outstanding Customer service calls Request for quotes Proposal development Attrition/retention Bid win rate Transactional defects Sales orders Revenue dollars

What are some metrics associated with your projects? What are some metrics associated with your projects?

Control Charts and Introduction to Six Sigma

Control Charts
– “While every process displays Variation, some processes display controlled variation, while other processes display uncontrolled variation” (Walter Shewhart). – Controlled Variation is characterised by a stable and consistent pattern of variation over time. Associated with Common Causes. – Process A shows controlled variation.
X-Bar Chart for Process A X-Bar Chart for Process A
UCL=77.20 UCL=77.20 75

X a C a fo P ce B -B r h rt r ro ss
8 0 U L 7 .2 C= 7 7

Sample Mean

7 0

X= 0 8 7 .9 L L 6 .7 C= 4 0

6 0

5 0

Special Causes

0

5

1 0

1 5

2 0

2 5

SmleNme a p u br

Sample Mean Sample Mean

75

70

X=70.91 X=70.91 70

65

65 0 0 5 5 1 0 1 0 1 5 1 5 20 20 25

LCL=64.62 LCL=64.62

Sam N ber ple um Sam N ber ple um

25

– Uncontrolled Variation is characterised by variation that changes over time. Associated with Special Causes. – Process B shows uncontrolled variation.

Control Charts and Introduction to Six Sigma

In-Statistical-Control

• A process is said to be operating in a state of statistical control (or short in-statistical-control) when only sources of variation are from common causes.

Control Charts and Introduction to Six Sigma

Interpreting Data
“Specifications may be used to define when one is in trouble with regard to the voice of the customer, specifications do nothing to describe or define the voice of the process.”

– It was Walter Shewhart who first gave a simple and effective way to define the voice of the process --- he called it a Control Chart. UCL LCL Time – A Control Chart begins with a time series graph. – A central line (X-bar) is added as a visual reference for detecting shifts or trends. (Process location). – Control limits (UCL & LCL computed from the data) are placed equidistant on either side of the central line. (Process dispersion).

Control Charts and Introduction to Six Sigma

Types of Control Charts

Metric

Average

Control Limits

Time • Types of Charts: • Individuals & Moving Range Charts • X-Bar & R Charts • p Charts (& np Charts) • c Charts (& u Charts)

Control Charts and Introduction to Six Sigma

Individuals Charts
• Appropriate questions for Individuals and Moving Range (I and MR) Charts take the form of “How does the short term variation compare to long-term variation?”
• • • •• • •• • • •• • •• • • • • • •



• • •



• • • •



• • •

• • •• •



Time
We are interested in: - the average of the process - the “short-term” variation - the “long-term” variation

Control Charts and Introduction to Six Sigma

I and MR Chart Basics
I and MR Chart
39 UCL=38.76

Individual Value

38 Mean=37.38 37

UCLX = X + (3 × mR /d2)) UCLX = X + (3 × mR /d2 = 37.38 + (( 3 × 0.5195 // 1.128)= 38.76 = 37.38 + 3 × 0.5195 1.128)= 38.76

36 0 10 20 30 40

LCL=35.99

LCLX = X -- (3 × mR // d2)) LCLX = X (3 × mR d2 = 37.38 -- (3 × 0.5195 // 1.128) = 35.99 = 37.38 (3 × 0.5195 1.128) = 35.99

Subgroup

Difference between successive INDIVIDUAL VALUES is Range value
2 111

Moving Range

UCL=1.697

UCLR = 3.267 × mR UCLR = 3.267 × mR = 3.267 × 0.5195 = 1.697 = 3.267 × 0.5195 = 1.697

1 mR=0.5195 0 LCL=0

n = 2 (difference of two measures) then d2 =1.128 n = 2 (difference of two measures) then d2 =1.128

Control Charts and Introduction to Six Sigma

I and MR Chart
39 UCL=38.76

Individ ual Value

38 Mean=37.38 37

How are the control limits of the individual values derived? What comparison is being made on the Individual chart?

36 0 10 20 30 40

LCL=35.99

Subgroup

What does this indicate?
2 1 1 1 UCL=1.697

M o ving Ra nge

1 mR=0.5195 0 LCL=0

Control Charts and Introduction to Six Sigma

Drawing A Moving Range Chart
Solids content Moving Range 37.61 NA 37.95 0.34 37.63 0.32 37.50 0.13 37.20 0.30 37.60 0.40 36.10 1.50 37.94 1.84 36.11 1.83 37.88 1.77 37.47 0.41 38.24 0.77 37.78 0.46 37.29 0.49 36.43 0.86 37.15 0.72 37.16 0.01 37.83 0.67 37.30 0.53 37.42 0.12 37.74 0.32 37.50 0.24 37.90 0.40 37.70 0.20 36.80 0.90 37.28 0.48 37.88 0.60 37.41 0.52

Step 1: Calculate moving range. To calculate each moving range, subtract each measurement from the previous one. There will be no moving range for the first observation on the chart Moving range = Positive value of (Yn - Yn-1) Step 2: Calculate average of individuals data and average of moving range Step 3: Calculate the control limits UCLR = Upper Control Limit for Range = 3.267 × (mR) UCLX = Upper Control Limit for Individuals = X + (3 × mR / d2) LCLX = Lower Control Limit for Individuals = X - (3 × mR / d2) Where d2 = 1.128 (for 2 samples) Step 4: Plot the data, the averages and the control limits in 2 charts Step 5: Analyse the data Averages

X X

mR mR

Control Charts and Introduction to Six Sigma

Table of Constants for Control Charts
X-bar R Charts N 2 3 4 5 6 7 8 9 10 20 A2 1.880 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308 0.180 d2 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078 3.735 D3 0.076 0.136 0.184 0.223 0.415 D4 3.267 2.574 2.282 2.114 2.004 1.924 1.864 1.816 1.777 1.585 A3 2.659 1.954 1.628 1.427 1.287 1.182 1.099 1.032 0.975 0.680 X-bar s Charts c4 0.7979 0.8862 0.9213 0.9400 0.9515 0.9594 0.9650 0.9693 0.9727 0.9869 B3 0.030 0.118 0.185 0.239 0.284 0.510 B4 3.267 2.568 2.266 2.089 1.970 1.882 1.815 1.761 1.716 1.490

Control Charts and Introduction to Six Sigma

Formulas for Individuals Charts

Formulas:

UCLR = 3.267× mR

UCLX = X + 3 LCLX = X − 3

mR d2

mR d2

d2 = 1.128 when the moving range is based on the range between successive numbers.

Control Charts and Introduction to Six Sigma

Exercise - Moving Range Charts
Distance Moving Range

Step 1: Calculate moving range. To calculate each moving range, subtract each measurement from the previous one. There will be no moving range for the first observation on the chart Moving range = Positive value of (Yn - Yn-1) Step 2: Calculate average of individuals data and average of moving range Step 3: Calculate the control limits UCLR = Upper Control Limit for Range = 3.267 × (mR) UCLX = Upper Control Limit for Individuals = X + (3 × mR / d2) LCLX = Lower Control Limit for Individuals = X - (3 × mR / d2) Where d2 = 1.128 (for 2 samples) Step 4: Plot the data, the averages and the control limits in 2 charts Step 5: Analyse the data

X X

mR mR

Averages

Control Charts and Introduction to Six Sigma

Chart Your Results
Moving Range Individual Value

Control Charts and Introduction to Six Sigma

When to Use Individual Moving Range Charts
• Assist in understanding variable data when the subgroup size is one. (And in certain situations, attribute data.) Appropriate Usage Situations: I. A ‘natural’ subgroup is one. – When there are very few units produced relative to the opportunity for process variables (sources of variation) to change. – When there is little choice due to data scarcity. II.The variation within a ‘natural’ subgroup is of little concern. – When within subgroup variation is unimportant in a manufacturing or engineering sense (take one measurement per ‘natural’ subgroup unit). – When the relative magnitude of within ‘natural’ subgroup variation is small compared to between subgroup variation (as verified by a Multi-Vari study). III. When the state of process knowledge is of a meagre and unsatisfactory kind.



Control Charts and Introduction to Six Sigma

Individual Moving Range and Rational Subgrouping
• Individual moving range charts are applied for a variety of reasons. – The natural subgroup size is unknown. – The amount or pedigree of the data prevents clear picture of a rational subgroup. – Early in a design phase or when data is scarce, subgrouping is not yet practical. – The natural subgroup needing to be assessed is not defined yet. – HOWEVER, once we are able to subgroup, many new possibilities regarding insight into processes can be discovered.

Control Charts and Introduction to Six Sigma

Sub-grouping
– The concept of subgrouping is one of the most important components of the control chart method. – Shewhart’s principle is to organise (classify, stratify, group, etc.) data from the process in a way that ensures the greatest similarity among the data in each subgroup and the greatest difference among the data in different subgroups. – The aim of rational subgrouping is to include only common causes of variation within subgroups, with all special causes of variation occurring between subgroups. – The purpose of understanding the within and between variation is to determine where to work, i.e. we reduce the number of potential variables considerably when we determine the variation is within or between.

Control Charts and Introduction to Six Sigma

Analysing the X-Bar & R Chart
• R CHART – The R chart displays change in the “within” subgroup dispersion of the process – Asks “Is the variation in the measurements within subgroups consistent?” – Measurements within subgroup are consistent when the R Chart is in control – The R Chart must be in control to draw the X-bar Chart

Control Charts and Introduction to Six Sigma

Analysing the X-Bar & R Chart
• X-bar CHART – The X-bar Chart shows change in the average value of the process – Asks “Is the variation between the averages of the subgroups more than that predicted by the variation within subgroup?” – If the X-bar Chart is in control, the variation “between” is smaller than the variation “within” – If the X-bar Chart is not in control, the variation “between” is greater than the variation “within”

Control Charts and Introduction to Six Sigma

X-bar and R Chart - Terms
X Subgroup n X R R X UCL LCL One measurement Grouping of measurements (sample) Number of items in subgroup (sample size) Average of subgroup Range within subgroup Average Range of subgroups Average of all subgroups averages Upper Control Limit Lower Control Limit

Control Charts and Introduction to Six Sigma

Drawing an X bar & R Chart
1. Determine an appropriate sampling plan, sampling location, sampling frequency, and size of subgroup. 2. Take a set of readings at each specified interval of time and/or from each suspected source of variation. 3. Calculate the average and range for each subgroup. 4. Plot the data. (Both average and range) 5. After “20” or more sets of measurements, calculate the control limits for the Range chart. 6. If the range chart is not in control, take appropriate action. 7. If the Range chart is in control, calculate the control limits for the X-bar chart. 8. If the X-bar chart is not in control, take appropriate action. 9. If both charts are in control, take appropriate action.

Control Charts and Introduction to Six Sigma

Formulae X-bar and R Chart
• Central Line for Average and Range



Control Limits for Average and Range

x1 + x 2 + K + x k 1 k x = ∑ xi = k i =1 k R1 + R 2 + K + Rk 1 k R = ∑ Ri = k i =1 k UCL x = X + A 2 × R LCL x = X − A 2 × R

UCLR = D 4 × R

LCLR = D3 × R

where A2, D3 and D4 are constants based on subgroup size.

Control Charts and Introduction to Six Sigma

X-bar & R Chart Example
Aged Release 1 week (g/inch) OP 45 47 48 43 36 45 42 42 48 47 45 40 36 43 38 37 42 45 36 38 OI 40 42 45 50 34 48 49 47 42 50 44 34 39 42 37 40 43 36 37 39 DI 45 46 47 48 38 50 46 41 47 48 44 34 36 43 36 37 41 38 41 40 DR 49 49 49 48 38 49 51 46 48 51 45 38 40 47 38 42 45 38 40 41 Average 44.75 46.00 47.25 47.25 36.50 48.00 47.00 44.00 46.25 49.00 44.50 36.50 37.75 43.75 37.25 39.00 42.75 39.25 38.50 39.50 42.74 Xbarbar Range 9 7 4 7 4 5 9 6 6 4 1 6 4 5 2 5 4 9 5 3 5.25 Rbar

AVERAGES

X

R

Control Charts and Introduction to Six Sigma

X-bar & R Chart for Aged Release
Average: The sum of all the values in the subgroup divided by size of the subgroup: e.g. n = 4
50

Sample Mean

1 45

1

1

1 1

BETWEEN BETWEEN

• What is your interpretation of these charts? • What would you do about
UCLX=46.56 X=42.74

40 1 0 10 1 1 1 1

LCLX=38.91

UCLX = X + A2 × R UCLX = X + A2 × R = 42.74 + 0.729 × 5.25 = 46.56 = 42.74 + 0.729 × 5.25 = 46.56

35 Subgroup

20

Range: the Highest value minus the lowest value WITHIN each subgroup
UCLR=11.98

LCLX = X -- A2 × R LCLX = X A2 × R = 42.74 -- 0.729 × 5.25 = 38.91 = 42.74 0.729 × 5.25 = 38.91 UCLR = D4 × R UCLR = D4 × R = 2.282 × 5.25 = 11.98 = 2.282 × 5.25 = 11.98

Sample Range

10

WITHIN WITHIN
R=5.250

5

n = 4: n = 4: A2 = 0.729 A2 = 0.729 D4 = 2.282 D4 = 2.282

0

Control Charts and Introduction to Six Sigma

X-bar & R Chart Transactional Example
Question:
Should I work within Business Unit or between Business Unit to improve system usage?
Organization No. Users/Day Sbgrp Xbar Sbgrp Range BU 1 189 BU 1 256 BU 1 178 209.8 78 BU 1 223 BU 1 198 BU 1 215 BU 2 179 BU 2 232 BU 2 189 192.3 55 BU 2 177 BU 2 187 BU 2 190 BU 3 230 BU 3 226 BU 3 239 244.2 105 BU 3 245 BU 3 210 BU 3 315 BU 4 177 BU 4 213 BU 4 199 191.7 41 BU 4 172 BU 4 186 BU 4 203 BU 5 245 BU 5 221 BU 5 236 224.7 34 BU 5 222 BU 5 211 BU 5 213

X

R

Control Charts and Introduction to Six Sigma

X-bar & R Chart for # Users/Day by Business Unit
Xbar/R for No. Users/Day
250 240 1

UCLX = X + A2 × R UCLX = X + A2 × R
UCL=242.8

= 212.4 + 0.483 × 62.6 = 242.8 = 212.4 + 0.483 × 62.6 = 242.8 LCLX = X -- A2 × R LCLX = X A2 × R = 212.5 -- 0.483 × 62.6 = 182.3 = 212.5 0.483 × 62.6 = 182.3

Sample M ean

230 220 210 200 190 180

BETWEEN BETWEEN

Mean=212.5

LCL=182.3 1 2 3 4 5

Subgroup

150

UCLR = D4 × R UCLR = D4 × R
UCL=125.4

Sample Rang e

100

WITHIN WITHIN
R=62.6 LCL=0

= 2.004 × 62.6 = 125.4 = 2.004 × 62.6 = 125.4

50

0

n = 6 so A2 = 0.483 and D4 = 2.004 n = 6 so A2 = 0.483 and D4 = 2.004

Control Charts and Introduction to Six Sigma

Interpreting X-bar and R Charts
• R Chart – Review this Chart first – If in control, then variation within subgroup is stable and predictable. Proceed to X-bar Chart. – If not in control, variation part to part is unstable and unpredictable. Stop and check rational subgrouping parameters and/or special causes. • X-bar Chart – If in control, then variation between subgroups is stable and predictable. Proceed to calculate capability, test hypotheses, etc. – If not in control, variation between subgroups is place to work.

Control Charts and Introduction to Six Sigma

Determining if Variation is Between or Within Subgroups

Between Group
X

Within Group Between Group

R

Within Group

Control Charts and Introduction to Six Sigma

R Chart: Within Group Variation

Is the Variation Within Subgroup Consistent?
In-Control ? Yes Out-Of-Control ? No

UCLR _ R LCLR

Control Charts and Introduction to Six Sigma

X-bar Chart: Between and Within Group Variation

Is Variation Between Subgroups greater than Within Subgroups?
In-Control ? No Out-Of-Control ? Yes

UCLX = X LCLX

Control Charts and Introduction to Six Sigma

Defining Variation from Control Chart
• What is ‘within’ variation? – Where is it found? – What is another name for ‘within variation’? • What is ‘between’ variation? – Where is it found? – What is another name for ‘between variation’? • What is the key measure that determines both the Range and X-bar control limits?

Control Charts and Introduction to Six Sigma

Exercise
– Based on the previous I and MR analysis, the team observes potential sources of variation in operator and round. Evaluating product performance has proved difficult with the large variation present. – The team decides they must first understand within and between variation for these sources before continuing with the evaluation. – How might your team change the way you are looking at the data to gain insight to differences in the sources of variation? Plan your experiment then run it and look at your data. Make it give up information related to these sources of variation.

Control Charts and Introduction to Six Sigma

Chart Your Results
Moving Range Individual Value

Control Charts and Introduction to Six Sigma

Sampling Plans
Sampling Plans: A Control Chart is only as useful as the sampling used to collect data. Consider a hypothetical process where all measurements on a key characteristic are available. The output from this hypothetical process is shown below.
• • • • • • • • •• • • • •• • • • • • •• • • • • • • • • • • • • • • • • •• • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • •

TIME
X Chart Range Chart Examines Variation Within Subgroups
Upper Control Limit

Examines Variation In Process
Upper Control Limit

Centre Line (X)

Centre Line (R)

Lower Control Limit

Control Charts and Introduction to Six Sigma

Sampling Strategies
– The purpose of sampling is to reduce the cost and time of checking every unit. The goal is to capture the voice of the process efficiently. – The charts on the following page are the output from a typical process. The goal is to make the output consistent, but you don’t know whether to work on x’s within time period or between time period. – You don’t know about the points you don’t measure, yet you need sampling to understand the state of the process. – Sketch the control charts for each sampling plan and subgrouping strategy. (Space is provided for you to suggest and draw charts for two sampling schemes.) – Which of the charts best displays the voice of the process?

Control Charts and Introduction to Six Sigma

Sampling Plans Case 1
Hour 0 Hour 2 Hour 4 Hour 6 Hour 8 Hour 0 Hour 2 Hour 4 Hour 6 Hour 8

• • • • • • • • • • • • • • • • • •• • • • •• • • • • • • • • • • • •• • • • • • • • • • •• • • • • • •• • • • • • • • • • • • • • • • • •• • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • •

• • • • • • • • • • • • • • •• • • • • • • •• • • • • • • • • • • • • • • • •• • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • •• • • •• • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • •

TIME

TIME

Create charts by subgrouping the first and last point of each time period.
Range Chart
Upper Control Limit

Create charts by subgrouping the first two and last two points of each time period.
Range Chart
Upper Control Limit

Centre Line(R)

Centre Line(R)

X Chart
Upper Control Limit

X Chart
Upper Control Limit

Centre Line(X)
Lower Control Limit

Centre Line(X)
Lower Control Limit

Control Charts and Introduction to Six Sigma

Sampling Plans Case 2
Shift 1

• • • • • • • • • • • • •• • • • • • • •

Shift 2 Shift 3 Shift 1
• • • • • • • •

Shift 1



Shift 2 Shift 3 Shift 1


• •

• •




• •

• •



• • • • • • • •

• •


• •




• •

• •



• • •






• • • •• • • • •


• • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • •








• • • •• • • • •


• • • • • • • • • • • • • • • • •

TIME

Create charts by randomly subgrouping three points each shift.
Range Chart
Upper Control Limit

Create charts by subgrouping the last two points and first two points of each shift (4 points total per group)
Range Chart
Upper Control Limit

Centre Line (R)

Centre Line (R)

X Chart
Upper Control Limit

X Chart
Upper Control Limit

Centre Line (X)

Centre Line (X)

Lower Control Limit

Lower Control Limit

Control Charts and Introduction to Six Sigma

Sampling Plans Case 3
• • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • •• • • • •• • • • • • • • • • •• • • • • • • • • • • • • • • • •• • • •• • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • •• • • • • • • • •• • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • •• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •


• • • •



• •



• • • •

• •




• •



TIME

TIME

Charts resulting from suggested sampling plan 1.
Range Chart
Upper Control Limit

Charts resulting from suggested sampling plan 2.
Range Chart
Upper Control Limit

Centre Line (R)

Centre Line (R)

X Chart
Upper Control Limit

X Chart
Upper Control Limit

Centre Line (X)

Centre Line (X)

Lower Control Limit

Lower Control Limit

Control Charts and Introduction to Six Sigma

Sampling Plans Case 4
• • • •• • • •


• •



• • • • ••




• • • •• • • •





• •

• • •• • • • • • • • • •







• ••




• • • • • • •• • • • • • • • • • • • • • • • • • • • • •• • • • •• • • • • • •

• • •

• •



• • • • • •
• • • • • • • ••






• • • •• • • •





• •

• • •• • • • • • • • • •







• ••




• • • • • • •• • • • • • • • • • • • • • • • • • • • • •• • • • •• • • • • • •

• • •

• •





• • ••

• • •

• • • • •



TIME

TIME

Charts resulting from suggested sampling plan 1.
Range Chart
Upper Control Limit

Charts resulting from suggested sampling plan 2.
Range Chart
Upper Control Limit

Centre Line (R)

Centre Line (R)

X Chart
Upper Control Limit

X Chart
Upper Control Limit

Centre Line (X)

Centre Line (X)

Lower Control Limit

Lower Control Limit

Control Charts and Introduction to Six Sigma

Expansion of Sub-grouping
Examine this output from a hypothetical process. The '•' indicate output from one machine. The '*' indicate output from another machine.

Time Assignment: Describe some sampling & graphing plans that might detect differences in machine.

*

* ** *

*** *

** * * * * ** * * **

* * ** ** * ** *** * *

* * ** * ** * ** * ** ** * *

*

**

• *** ** ** * * * **• • •** *• •*• • ** • • •• ••• • • •• •

*

* • * * * • • • * • • • • • • •* • • • • • • • ••

• • • • •• • • • • •* • • • • • • • • • ** • ** *• **

• • • • •• • •• • • •• • * • • • • • • ••*

Control Charts and Introduction to Six Sigma

Successful Sub-grouping Tips

– To aid in understanding a process, the intent of control charts on end-product parameters is to learn about sources of variation. The size and frequency of subgroups, the number of subgroups, and the sampling locations are a function of the state of process knowledge. – Subgroups are determined by the process variables identified on the process map and by cause and effect diagrams.

• Subgroup size, sampling frequency and time period are largely determined by considering the possible frequency of change of those process variables and causes. Sources of variation potentially causing systematic differences in product parameters are also large drivers of sampling and subgrouping plans.

Control Charts and Introduction to Six Sigma

Defect (Attribute) Data

• • • •

np-chart p-Chart C-chart U-chart

Control Charts and Introduction to Six Sigma

Control Charts Options (2)
• Attribute (discrete) data: – np (# of defective items; Constant sample size)

– p(# of defective items; Sample size is not constant) – c (# of defects; Constant sample size) – u(# of defects; Sample size is not constant)

Control Charts and Introduction to Six Sigma

Statistical Process Control Chart Selector
Determine “x” to Chart
Is the interest in non-conforming UNITS? Is the interest in non-conformities per unit?

Are the data variable?

Attribute

No

Yes
Is the sample size constant?

Yes No

Variable

p Chart

Is the sample size constant?

No

U Chart

Yes

Yes

np or p Chart
Does it make sense to subgroup for “Within” group variation analysis? No Yes Can subgroup averages No be conveniently calculated? Yes Subgroup size 9 or more? Yes Can sample standard deviation be calculated? Yes No No

C or U Chart

Me-R Chart

X-mR Chart
Examples: Batches, customer demand by request date, too little data, etc.

Xbar-R Chart

Xbar-R Chart

Assumptions: Rational Subgrouping performed if using subgroups. The measurement system has been assessed and is appropriate. Adapted from AIAG SPC Manual

Xbar-s Chart

Control Charts and Introduction to Six Sigma

np-Chart
• Charts number of items in a sample having an attribute • Each subgroup is the same size • Purposes
– Find the average number having the attribute – Find subgroups where the number is out of control relative to other subgroups
30

NP Chart for Rejects
1

Sample Count

20

1

1 UCL=19.96

10

NP=12

LCL=4.043 0 0 10 20

Sample Number

• An example is inspection
– Attribute is nonconformance to some requirement – Periodic samples are checked – Sample size is always the same – Assume nonconforming

• Assumptions
– Items in a subgroup are distinct – Each item either has or does not have the attribute

Control Charts and Introduction to Six Sigma

p-Chart
• Charts proportion of items having an attribute - the number having the attribute divided by the number of items • Each subgroup can be a different size • Purposes
– Find the average probability of having the attribute – Find subgroups where the proportion is out of control relative to other subgroups
P Chart for Rejects
UCL=0.3324 0.3

Proportion

0.2 P=0.1685 0.1

0.0 0 10 20

LCL=0.004728

Sample Number

Caution: All proportions are ratios, but not all ratios are proportions

• Incorrect uses:

• Same assumptions as

– Today’s rework divided by today’s production – Number of defects on all invoices divided by the number of invoices

Control Charts and Introduction to Six Sigma

Example p-Chart
• Each month, the company receives a different number of complaints • Each complaint requires a report be written within 15 days • For some number of the complaints, the reports are not finished by 15 days • P-Chart shows the proportion of each month’s complaints where the report was not completed on time • Conclusion – Overall, 16% of the reports were not finished on time – Process improvements seem to have reduced the proportion, continue to monitor Unusually high – action is necessary to uncover the cause
P Chart for Unfinished Reports
0.4

0.3

UCL=0.2950

Proportion

0.2 P=0.1565 0.1 LCL=0.01809

0.0 0 5 10

Sample Number

Process improvement was made here – continue to monitor progress

Control Charts and Introduction to Six Sigma

C-Chart
• Charts the number of events within a constant area of opportunity C Chart for Blemish • Purposes – Find the average number of events 8 3.0SL=7.677 7 – Find subgroups where the number is 6 out of control relative to other subgroups 5 4 • Assumptions 3 C=2.725 – Count the number of discrete events 2 – The discrete events occur within some 1 well-defined region of space or time or 0 LB=0 product – The events occur independently of 0 10 20 30 40 Sample Number each other, and in proportion to the size of the area of opportunity (it • Example: Number of blemishes doesn’t matter which portion of the continuum is chosen to be the area of – A roll of material is 1 meter wide opportunity) – A 2 meter section is taken from the – The size of the area of opportunity is end of each roll the same for all samples – For each section, the number of – ALL the events are counted; as opposed to inspection, where things blemishes is counted and charted might be rejected upon encountering the first event, terminating the count
Sample Count

Control Charts and Introduction to Six Sigma

U-Chart
U Chart for NumLeaks
0.4







0.3 UCL=0.2955 Charts the number of events per unit sampled in each sub0.2 group (uneven subgroup sizes) U=0.1379 0.1 Same assumptions as C0.0 LCL=0 Chart, except: 0 10 20 – The area of opportunity can Sample Number varying in size • Example: Leaks per radiator – The sizes don’t vary – Number of radiators varies each day randomly, but vary – All leaks are counted on all radiators • Some radiators might have zero deliberately or inherently leaks Chart the average number of • Area of opportunity represents all events per area the surface area of radiators that

Sample Count

were produced that day – Chart shows the average number of leaks per radiator by day

Control Charts and Introduction to Six Sigma

Control Charts Options (1)
• Variable (continuous) data: – X bar-R (Average and Range: measurements in subgroups) – X bar-s (Average and standard deviation: measurements in subgroups) – I-mR (also called X-mR) (Individual and moving Range: individual measurements)

Control Charts and Introduction to Six Sigma

Action - Action - Action
• • • • Don’t MEASURE it if you are not going to RECORD it

Don’t RECORD it if you are not going to GRAPH it Don’t GRAPH it if you are not going to ANALYSE it Don’t ANALYSE it if you are not going to take ACTION

Forms of action from Control Charts: 1. Proactive tool – Real time tool for process control. Anticipate trends before they become a problem. 2. Predictive tool – Process or product designers will know how to specify new products or processes. 3. Reactive tool – When rejects or failures occur try to understand why and focus problem solving on the right sources of variation.

Why measure it, if you are not going to take ACTION?

Control Charts and Introduction to Six Sigma

A Case Study Sales Process

Control Charts and Introduction to Six Sigma

The Job of Management
• When should you take action? – Something has changed and you need to adapt • When should you “Stay the Course”? – Keep your resources focused on the Imperatives • Decisions need to be made in the context of Variation

Control Charts and Introduction to Six Sigma

Case Study
• Reference :
– “How To Teach Others To Apply Statistical Thinking”, By Roger Hoerl, Galen Britz, Don Emerling, Lynne Hare, Janice Shade

• Objective: Analyse the Case Study as if you were the VP of Sales • What’s Going On Here?

Control Charts and Introduction to Six Sigma

Sample of Sales Data ...

Time

NEast 765 1008 1038 952 1041 1020 976 1148

SWest 1352 1353 1466 1196 1330 1003 1197 1337

NWest 883 851 997 878 939 834 688 806

NCentral 466 536 551 670 588 699 743 702

MAtlantic 691 723 701 802 749 762 807 781

SCentral 445 455 363 462 420 454 447 359

1995_Q1 1995_Q2 1995_Q3 1995_Q4 1996_Q1 1996_Q2 1996_Q3 1996_Q4

Values In Columns = Sales In Thousands

Control Charts and Introduction to Six Sigma

Managerial Statistical Thinking in Sales (1)
• Suppose that Ron Hagler, the vice president of sales for Selit Corp., had just gotten a report on the past five years of quarterly sales data for the regions under his authority. Not happy with the results, he got on the phone to his secretary. “Marsha, tell the regional managers I need to speak with them this afternoon. Everyone must attend !” Marsha had been Hagler’s secretary for almost a decade. She knew by the tone in his voice that he meant business, so she contacted the regional managers about the impromptu meeting at 2 pm. At 1:55 pm, the regional managers filed into the room. The only time they were called into a meeting together was when Hagler was unhappy. Hagler wasted no time. “I just received the quarterly sales report. Northeast sales were fantastic. Steve, you not only improved 17.6% in the fourth quarter, but you also increased sales a whopping 20.6% over the previous year. I don’t know how you do it !”. Steve smiled. His philosophy to end the year with a bang by getting customers to stockpile units paid off again. Hagler had failed to notice that Steve’s first quarter sales were always sluggish.





Control Charts and Introduction to Six Sigma

Managerial Statistical Thinking in Sales (2)
• Hagler continued: “Terry, Southwest sales were also super. You showed an 11.7% increase in the fourth quarter and an 11.8% increase over the previous year”. Terry also smiled. She wasn’t sure how she did so well, but she sure wasn’t going to change anything. Jan, Northwest sales were up 17.2% in the fourth quarter, but down 8.2% from the previous year,” said Hagler. “You need to find out what you did previously to make your sales go through the roof. Even so, your performance in the fourth quarter was good.” Jan tried to hide his puzzlement. Although he had received a big order in November, it was the first big order he had received in a long time. Overall, sales for the Northwest were declining. Hagler was now ready to deal with the “problem” regions. “Leslie, North Central sales were down 5.5% in the fourth quarter, but up 4.7% from the previous year. I don’t understand how your sales vary so much. Do you need more incentive?” Leslie looked down. She had been working very hard the past five years and had acquired numerous new accounts. In fact, she received a bonus for acquiring the most new business in 1994.





Control Charts and Introduction to Six Sigma

Managerial Statistical Thinking in Sales (3)
• “Kim, Mid-Atlantic sales were down 3.2% in the fourth quarter and down 2.6% from the previous year. I’m very disappointed in your performance. You were once my best sales representative. I had high expectations for you. Now, I can only hope that our first quarter results show some sign of life.” Kim felt her face get red. She knew she sold more units in 1996 than in 1995. “What does Hagler know anyway,” she thought to herself. “He’s just an empty suit.” Hagler turned to Dave, who felt a surge of adrenaline. “Dave, South Central sales were the worst of all! Sales were down 19.7% in the fourth quarter and down 22.3% from the previous year. How can you explain this? Do you value your job? I want to see a dramatic improvement in this quarter’s results or else!”. Dave felt numb. This was a tough region, with a lot of competition. Sure, accounts were lost over the years, but those lost were always replaced with new ones. How could he be doing so badly?



“How To Teach Others To Apply Statistical Thinking” by Roger Hoerl (GE), Galen Britz, Don Emerling, Lynne Hare, Janice Shade in Quality Progress - June 1997

Control Charts and Introduction to Six Sigma

The REAL Story
SW has no idea how they look good -PURE NOISE NE Stockpiling sales causes large swings in volume
I and MR Chart for Northeast
1400 1300 1200 1100 1000 900 800 700 600 0

I and MR Chart for Southwest
3.0SL=1368
1600 1500 1400 1300 1200 1100 1000 900 800 0 10 3.0SL=1535

Individual Value

X=1000

Individual Value

Q4 1992
10

X=1196

1996
-3.0SL=632.4

-3.0SL=857.3

Subgroup 600

GLORY
1

20

Subgroup

GLORY

20

Moving Range

400 300 200 100 0

3.0SL=451.6

Moving Range

500

1

400 300 200 100 0

3.0SL=416.0

R=138.2 -3.0SL=0.00E+

R=127.3 -3.0SL=0.00E+

NW has been dropping for years
I and MR Chart for Northwest
1500 1400 1300 1200 1100 1000 900 800 700 600 0 1

N Central chastised despite excellent growth
I and MR Chart for N. Central
750 1 1 1 3.0SL=669.7

Individual Value

Individual Value

3.0SL=1298 X=1026 -3.0SL=753.8 1 10

650 550 450 350

1

X=519.5

-3.0SL=369.4 0 10

Subgroup

GLORY

20

Subgroup 200

BLASTED

20

Moving Range

200 100 0 R=102.3 -3.0SL=0.00E+

Moving Range

300

3.0SL=334.3

3.0SL=184.5

100 R=56.47 0 -3.0SL=0.00E+

Control Charts and Introduction to Six Sigma

The REAL Story
Mid Atlantic chastised despite excellent growth
I and MR Chart for Mid-Atlantic
800 1 1 1

S Central has been holding even - PURE NOISE
I and MR Chart for S. Central
550 3.0SL=534.2

Individual Value

Individual Value

1 3.0SL=750.2 X=656.7

500 450 400 350 300 0 10 -3.0SL=306.4 X=420.3

700 600 500 1 0 1 1 -3.0SL=563.2 1 10

Subgroup

BLASTED

20

Subgroup 150

BLASTED

20

3.0SL=114.9

3.0SL=140.0

Moving Range

Moving Range

100

100 50 0

50 R=35.16 0 -3.0SL=0.00E+

R=42.84 -3.0SL=0.00E+



The VP gave GLORY for selling into the next quarter’s demand, no improvement, and loss of market share. The VP BLASTED two regions for excellent year over year growth, and one region for holding even in a tough competitive situation. This will drive terrible behaviours in the sales force. The best performers may look elsewhere for work. The marginal performers have been reinforced to sell into next month, continue mediocre performance, and hope for luck.



Control Charts and Introduction to Six Sigma

Final Thoughts
“Failure to use Control Charts to analyse data is “Failure to use Control Charts to analyse data is one of the best ways known to mankind to one of the best ways known to mankind to increase costs, waste effort, and lower morale.” increase costs, waste effort, and lower morale.” --Dr. Donald J. Wheeler Dr. Donald J. Wheeler

• • • •

People respond to the way they are measured. Using data correctly can drive GREAT results. Using data incorrectly drives CHAOS. Don’t be part of the PROBLEM - Be part of the SOLUTION

Control Charts and Introduction to Six Sigma

Summary
– We evaluate metrics to look for major sources of variation – Concept of Within & Between variation is crucial. – Control charting helps with this investigation. R Chart is used to display Within Variation X-bar Chart displays the Between Variation – Subgrouping is a key concept. – I mR chart can be used anytime. – There are specific charts for attribute data.



Control Charts and Introduction to Six Sigma

Quiz – True or False? (1)
1. Six Sigma focuses on SPC for continuous improvement more than monitoring. 2. Common cause variation is the random chance-like variation in a process. 3. Special cause variation creates an unusual deviation. 4. Control limits and Specification Limits are the same thing. 5. Nearly all of the variation of a stable process will lie between the upper and lower control limits. 6. One question the X-bar and R Chart asks is: ”What’s Changing Within Subgroups”.

Control Charts and Introduction to Six Sigma

Quiz – True or False? (2)
7. How we sample and subgroup determines the control limits for the X-bar Chart. 8. If we capture a lot of X’s and noise in the process our control limits will tend to be larger. 9. If an X can not be measured using variables data, it can not be plotted on a Control Chart. 10. Being “in-control” is how we learn more about our process. 11. Keep the charts in the lab to prevent losing them.

Control Charts and Introduction to Six Sigma

Introduction to Six Sigma Concepts
Subhash Dixit

Control Charts and Introduction to Six Sigma

History of Six Sigma
I

1999-2003

Enters finance, education, government

1996-98
1994-96

Enters chemicals, healthcare, services
GE and Allied Signal results popularize the methodology for manufacturing

1988
1985-87

Helps Motorola win Baldrige Award
Developed and deployed at Motorola

Control Charts and Introduction to Six Sigma

Six Sigma in Other Companies
Source: "Six Sigma - The pragmatic Approach" by Kjell Magnusson, Dag Kroslid and Bo Bergman

Mr Jack Welch, GE: "Six Sigma is the most important concept we have ever adopted, and it will bring us 70 to 110 MUSD savings in the coming 5 years."

Motorola 1987

IBM DEC 1989 1991

ABB Kodak Allied Signal TI General Electric 1993 1995

Air Products American Express Ford Motor Johnson Control Johnson & Johnson J.P Morgan Chase LG Group Ericsson Maytag Compaq Navistar Dow Chemical DuPont NCR Deere Nokia Lockheed Martin Philips Raytheon NEC Praxair PACCAR Seagate Tech Samsung Electronics Siemens Solectron Sony Sumitomo Toshiba United Technologies Whirlpool US Postal Service 1997 1999

Amazon.com Black & Decker Bosch Canon Caterpiller Compac Daimler Chrysler Dell Computor Delphi Aut. Syst. Eaton Corp. Flextronix Int Heller Financial ITT Internat. Johnson Controls Pilkington Polaroid Rexam Beverage Roche Diagno Samsung Sear Sun Microsystem Textron + +

I

2000

Control Charts and Introduction to Six Sigma

Six Sigma Vision
• Statistical literacy is the key to our industrial competitiveness - Craig Barrett, Senior Vice President, Intel • “ Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write ” H.G.Wells • The next leader of this company will know this stuff, Being web savvy will become like reading and writing. So, there is never a choice between the two as a career enhancement -Six Sigma training is the career enhancer.” - Jack Welch • The problems that exist in the world of today cannot be solved by the level of thinking that created them - Albert Einstein

Control Charts and Introduction to Six Sigma

Benchmarking Sigma 6 5 4 3 2 1 PPMO 3.4 233 6210 66,807 COPQ < 10% 10-15% TYPE World Class

15-20% Averag e 20-30% Poor

308,537 30-40% 690,000 >40%

Control Charts and Introduction to Six Sigma

Accept 99.9% Quality ?
I

• You get . . • One hour of unsafe drinking water every month. • Two unsafe plane landings per day at O’Hare International Airport in Chicago. • 16,000 pieces of mail lost by the U.S. Postal Service every hour. • 500 incorrect surgical operations each week. • 50 newborn babies dropped at birth by doctors each day. • 22,000 checks deducted from the wrong bank accounts each hour.

Control Charts and Introduction to Six Sigma

I

Six Sigma Evolution
Dr Mikel Harry, Richard Schroeder Bob Galvin of Motorola Larry Bossidy of Allied Signal Jack Welch of GE Charles Holliday of DuPont

Control Charts and Introduction to Six Sigma

Evolution towards Six Sigma
High Six Sigma Quality Marking Customers Winners : GE Tool - Kit Intensity of change Key Strategic Initiatives : QMI*, NPI*, OTR*, SP*, Productivity, Globalization Change Acceleration Process : Increase success and accelerate change Process Improvement : Continuous improvement, re-engineering Productivity / Best Practices looking outside GE Work- Out / Town Meetings : Low Continuous improvement, re-engineering
Time

Action Work-Outs Customized Work-Outs

Control Charts and Introduction to Six Sigma

Evolution of Six Sigma

Unconscious incompetence

Conscious incompetence

Conscious competence

Unconscious competence

We didn’t know what we didn’t know

Six Sigma The way we work

96-98 “ Industrial Quality Initiatives

97-99 Design for Six Sigma

99 -00 Customer Impact

00Customer Centricity

Control Charts and Introduction to Six Sigma

Six Sigma as a GOAL

Sigma Rating
2 3 4 5 6 Process Capability

PPM

308,537 66,807 6,210 233 3.4 Defects per Million Opportunities

The Sigma scale of measure is perfectly correlated to such characteristics as defects-per-unit, parts-per-million defective, and the probability of a failure/error.

Control Charts and Introduction to Six Sigma

Scenario
Organization: Motorola Turnover Locations : $ 4000 million : 30 Man Power : 1 lakh
I

1979 : Quality was poor Stiff competition especially from Japanese Companies. To become world leaders in manufacturing of communication products such as pagers, mobile phones etc.

Control Charts and Introduction to Six Sigma

Six Sigma Philosophy Science
* We don’t know what we don’t know * If we can’t measure it, we really don’t know much about it

Six Sigma

Art
* If we don’t know much about it, we can’t control it. Magic * If we can’t control it, we are at the mercy of chance

Control Charts and Introduction to Six Sigma

What is special about Six Sigma Cultural Change & High Energy level
• The conventional Quality efforts are implemented by & large through the normal organizational Hierarchy • In 6 Sigma Approach Black Belts, Green Belts are trained who cut across Departments & Managerial Hierarchy. This brings up high energy individual in the forefront irrespective of their Seniority • These ‘Belted Boys’ become change Agents • Routine work is not affected so nobody can crib

Control Charts and Introduction to Six Sigma

Facilitators of Six Sigma
1. Master Black Belt : First and foremost teachers. They also review and mentor Black Belts. Selection criteria for Master Black Betls are quantitative Skills and the ability to teach and mentor. Master Black Belts are full-time positions. 2. Black Belt : Leaders of team responsible for measuring, analysing, improving and controlling key process that influence customer satisfaction and / or productivity growth. Black Belts are fulltime positions. 3. Green Belt:Similar to Black Belt but not a full-time position. 4. Ultimately --All Employees

Control Charts and Introduction to Six Sigma

Six Sigma People
GM Global Quality & Six Sigma Full Time

Master Champions
• Help choose projects • Interview Black Belt candidates • Tie project DPU to business needs. • Remove barriers, drive Six Sigma in to the culture of their functions.

Greenbelts
Apply Six Sigma tools and methodology in everyday work

Black Belts Full Time
Develop tools, and teaching material. Conduct all training and communication sessions. Mentor Black Belts and their projects.

Six Sigma Black Belts Full Time
• Full-time project work • Change agents • Expert application of tools.

Mean
SIX SIGMA
THE WAY WE WORK

Six Sigma Fundamentals
Specification Limit
Some chance of failure

Control Charts and Introduction to Six Sigma

1

Zst 2 3 4 5 6

DPMO 308,537 66,807 6,210 233 3.4
Zst ( distribution Shifted 1.5

The higher the number (Z) in front of the sigma symbol, the lower the chance of producing a defect

μ

Yields through Multiple Steps/ Parts/ Processes

3

Much Less chance of failure

# of parts, Steps, or Processes 1 5 10 20 50 100 200 500 1000 2000 5000 10000 20000 50000

3

4

5

6

93.32% 70.77% 50.09% 25.09% 3.15% ,10%

99.38% 96.33% 93.96% 88.29% 73.24% 53.64% 28.77% 4.44% 0.20%

99.9767% 99.88% 99.77% 99.54% 98.84% 97.70% 95.45% 89.00% 79.21% 62.75% 31.19% 9.73% 95%

99.99966% 99.9983% 99.997% 99.993% 99.983% 99.966% 99.932% 99.830% 99.661% 99.932% 98.314% 96.657% 93.426% 84.366%

1

6
THE 3 TENETS:
1. PROCESS SIMPLIFICATION - Rolled Throughput 2. IMPROVING THE MEAN 3. CONTROLIING VARIATION - Customers feel variation, not averages - the hidden factory

Control Charts and Introduction to Six Sigma

Aligning the orgnanization
Business Strategy for Growth & Competitiveness Performance Management Career Management Flow Up E & E 9 Blockers
‘Y” Flow Down to Functions & Divisions Sub Ys Evolved The Big Ys : Organization Level Goals & Objectives

Score Score Cards Cards

Monthly Reviews

Set Effectiveness & Engagement 9 Blocker

6 Sigma Project Execution & Tracking
Create 6 Sigma Project Funnel Mapping Projects to Sub Ys Prioritize & Sequence Projects

Select, Align, Train People - MBB, BB. GB

Control Charts and Introduction to Six Sigma

Shooting for the target
BB, MBB, & Biz Team Brainstorms to fit in Big Picture & Arrive at Relative Priority

Maps Organization’s G&O? Current Sigma Too Low ?

Customer Benefits ? Well Bounded Problem ? Maps to My Daily Job

Financial Benefits ?

Green Belt Pitches Idea

All Stakeholders Sign Off

Control Charts and Introduction to Six Sigma

Six Sigma Methodolgies : DMAIC
The 5-Step Methodology
GUIDE POSTS D I R E C T I O N

Define

Measure

Analyze

Improve

Control

What are the Customer’s Needs & Key Processes ?

What is the Frequency of Defects

When and Where do Defects Occur ?

How can we fix the process ?

How can we ensure process Remains Fixed ?

TOOLS
TRANS- Surveys PORT Interviews Inquiries Process Map Measurement Statistical Analysis DOE Error Proofing Sigma Score Pareto SOP Process Monitoring Cost of Poor Quality FMEA Risk Analysis Action Planning

Control Charts and Introduction to Six Sigma

Six Sigma Methodolgies : DMADV
The 5-Step Methodology
GUIDE POSTS D I R E C T I O N

Define

Measure

Analyze

Improve

Control

Understand Initiate, Scope, Customer Needs and and Plan the Specify Project CTQs

Develop Design C oncepts And High Level Design

Develop Detailed Design and Control / Test Plan

Test Design and Implement Full - Scale Processes

TOOLS
TRANSPORT •MGP •Project Management Customer Research QFD Benchmarking FMEA / Error Proofing Process Simulation Design Scorecards

Control Charts and Introduction to Six Sigma

Brain Storming Fishbone Pareto Analysis ANOVA T,F, χ2 Tests Box & Matrix Plots Regression

Summary of Methodology
ANALYZE : Y= f (x ) ( Statistical Definition )

Process Mapping Process Modeling Process Simulation DOE FMEA Score Cards Tolerance Models

DESIGN ( Statitiscal Solution )
QFD Control Charts Capability Charts • MTTR, MTBF • SPAN

CONTROL & VERIFY Pilot Changes in Process & Technology Optimize ( Poka Yoke ) Control Charts

MEASURE Current Capability ( Process & Product ) DEFINE Where am I ? Where do I want to Go ?

INSTITUTIONALIZE Document, Train AAA Across the Organisation

Control Charts and Introduction to Six Sigma

Six Sigma People

GM Global Quality & Six SIGMA Full Time

Champions

Greenbelts
Apply Six Sigma tools and methodology in everyday work

Master Black Belts Full Time

• Help choose projects • Interview Black Belt candidates • Tie project DPU to business needs • Remove barriers, drive Six Sigma into the culture of their functions

Develop tools, and teaching material Conduct all training and communication sessions

Six Sigma Black Belts Full Time
Full-time project work • Change Agents • Expert application tools •

Mentor Black Belts and their projects

Control Charts and Introduction to Six Sigma

Six Sigma Execution
QUALITY FOCUS AREAS
FUNCTIONAL CHAMPIONS

ORGANIZATION : ACCOUNTABILITY
PRIORITIES CHAMPIONS

1. Clinical Excellence & Value 2. Fulfilment 3. Six Sigma with Customers 4. Global Products Company 5. Systems & Support 6. Proactive Risk Management

EXECUTION
Master Black Belt Black Belt / Green Belt

REVIEW & CONTROL
CLOSING THE LOOP

Project Team PROJECT

….FOR OUR COMPETITIVE EDGE

Focus Customer Impact
Clinical Excellence & Value
•New Clinical Capability

Control Charts and Introduction to Six Sigma

Operational Excellence
Global Product Company
• Supply Chain Excellence

Fulfillment • Reliable products & service delivery Six Sigma with Customers
• Help customers succeed ( ACFC)

Systems & Support
• Quality Systems & Processes

Proactive Risk Management
• Success in Global Complexity

Redefined value chain, Focused on Critical links

Control Charts and Introduction to Six Sigma

Systems & Support

• Capability, Stability, Predictability of Internal Processes • Information Systems Quality • Organization Development & Retention • Pricing & Margins • Acquisition Integration

Control Charts and Introduction to Six Sigma

Proactive Risk Management

• Finance Portfolio • Regulatory Compliance • Due Diligence - Potential Business Acquisitions • Government Relations • Environmental Health & Safety

Success in Global Complexity

Control Charts and Introduction to Six Sigma

What is special about 6 Sigma Sharper Tools
TQM ‘PDCA’ approach • Plan • Do • Check • Act 6 Sigma DMAIC approach • Define • Analyze • Measure • Improve • Control TQM is like Flood Light Six Sigma is like a Laser beam

Control Charts and Introduction to Six Sigma

Process Yield
What’s the yield of this process?
1000 Pcs

Step 1 Step 2 Step 3 Step 4

990 Pcs & 10 Rwk 985 Pcs & 15 Rwk 970 Pcs & 30 Rwk 950 Pcs & 50 Rwk

990 Pcs & 10 scrap

Final Test Step 6 Step 5

980 Pcs & 20 Rwk 960 Pcs & 40 Rwk

Pieces Out Pieces In

=

990 1000

=

Traditional Yield = 99%

First Pass Yield = 82.5% Traditional yield assessments mask the hidden factory!

Control Charts and Introduction to Six Sigma

Variation
Traditional View
Final Test

“The Hidden Factory” Rolled Throughput Yield is the probability that a product will pass through the entire process without rework and without any defects.It is the true yield for a product at the completion of all the individual processes. Six Sigma View:

Rework buried in the hidden factory increases costs and reduces throughput. Rework buried in the hidden factory increases costs and reduces throughput.

Control Charts and Introduction to Six Sigma

Computing Throughput Yield, DPO, DPMO and Sigma
– What is First Time Yield? – What is Throughput Yield? – What is Rolled Throughput Yield? – How can Yield be converted into a Sigma Value and how can this value be used?

D5

Control Charts and Introduction to Six Sigma

Integrating Lean into Six Sigma
D
Material and Information Flow

D
Product

M

A

I

C

Product & Information Flow (VSM) Change Over Pull Systems Workplace Redesign Activity Waste Analysis Performance Measures Visual Controls

D

M
SCOR

A

Baseline Assessment Product Family Analysis

Productivity

Supply Chain (VSM)

People

Standard Work
SAP / APO , Kaizen Six Sigma, Empowered Workforce

Enablers

Foundational Elements
5S (Workplace Organization) , Total Productive Maintenance, Mistake Proofing, Stable/Reliable/Capable Processes, & Flexible Workforce

Slide 96 D5 APO - Automated Purchase orders
Dixit, 16-12-2007

Control Charts and Introduction to Six Sigma

First Time Yield – FTY
• First Time Yield = Non-defective units from a process – Note: Does not offer a possibility to estimate the probability of a defect opportunity that may “Escape to the Customer” • First Time Yield (unit-based) is simply the number of good (nondefective) units produced divided by the number of total units going into the process, i.e. the proportion of units containing exactly zero defects. • FTY = units out / units in

Control Charts and Introduction to Six Sigma

Throughput Yield
• Throughput Yield (First Time Through Yield) = Non-defective opportunities from a process step. – Defect Opportunities = number of potential defects within one product or service. One product may have multiple defects and thus increase probability of defectives. • Throughput Yield (defect-based) is the probability that all defect opportunities produced at a particular step in the process will conform to their respective performance standards.

Control Charts and Introduction to Six Sigma

Rolled Throughput Yield – RTY
• Rolled Throughput Yield (RTY) is the probability that a single unit can pass through a series of process steps free of defects. •
RTY = e-TDPU

• Rolled Throughput Yield provides a possibility to estimate: probability of creating a defect opportunity.

Use the Poisson assumptions* to translate between the proportion of units without defects and defects per unit (DPU).

"Implementing Six Sigma" by Forrest W. Breyfogle III (2003)

Control Charts and Introduction to Six Sigma

Definitions (1)
• Unit (U) The number of parts, sub-assemblies, assemblies, or systems inspected or tested. – Example: 1 unit = 1 square • Opportunity (OP) A characteristic you inspect or test. – Example: 1 opportunity = 1 circle (5 per unit) • Defect (D) Anything that results in customer dissatisfaction. Anything that results in a non-conformance. – Example: 1 defect = 1 red circle (total: 9 defects in all 4 units)

Control Charts and Introduction to Six Sigma

Definitions (2)
• Defects per Unit (DPU) DPU = D/U = 9/4 = 2.25 • Total Opportunities (TOP) TOP = U × OP = 4 × 5 = 20 • Defects per Opportunity (DPO): a Probability DPO = D/TOP = 9/20 = 0.45 • Defects per Million Opportunities (DPMO): a Probability in ppm DPMO = DPO × 1,000,000 = 0.45 × 1,000,000 = 450,000

Control Charts and Introduction to Six Sigma

Summary DPMO Calculation

Type Description

Defects Units D U

Opportunities OP

Total Opportunities

Defects per Defects per Million Total OpportOpportDefects per unities unities Unit DPO = D / TOP DPMO = DPO × 106

TOP = U × OP DPU = D / U

Control Charts and Introduction to Six Sigma

The Calculation Simplified

DPMO =

Defects in Sample (1,000,000 ) (Defect Opportunit ies per Unit )(Number of Units in Sample )

Control Charts and Introduction to Six Sigma

Calculate Throughput Yield Example
– 100 Units processed in a step. – 5 Defect Opportunities are possible (4 CTQs and 1 more for all other potential defect types). – 10 Defects found in 100 Units. – Given there are 5 Opportunities per Unit. – Defects per Opportunity (DPO) = 10/(5 × 100) = 0.02 – Therefore, the probability of creating a defective opportunity= 2%. – DPMO = DPO × 1,000,000 = 0.02 × 106 = 20,000 – DPU = D / U = 10 / 100 = 0.1 – Sigma approximately 3.55 – Throughput Yield = e-DPU = e(- 0.1) = 90.5%

Control Charts and Introduction to Six Sigma

Calculating Rolled Throughput Yield



RTY = (Throughput Yield1 × Throughput Yield2 × Throughput Yield3 × ... × Throughput Yieldn)

So, simply multiply the Throughput Yields calculated for each process step

Control Charts and Introduction to Six Sigma

Rolled Throughput Yield vs. Final Quality Audit
1 2

Process

3

4

Final Audit/Test

90% FTTY 90 %

90% FTTY
Times

90% FTTY

90% FTTY
Times

=

90% FTTY

=
81 %

Times

=
73 %

=

66%

Rolled Throughput Yield

Using Final Test or FQA ignores the hidden factory. Improve First Time Through Yield (FTTY) to improve the quality of Y’s and achieve Six Sigma! RTY estimates the probability of failure using probability theory

Control Charts and Introduction to Six Sigma

What’s the Rolled Throughput Yield of this Process?
1000 Pcs

Step 1 Step 2 Step 3 Step 4

990 Pcs & 10 Rwk 985 Pcs & 15 Rwk 970 Pcs & 30 Rwk 950 Pcs & 50 Rwk

990 Pcs & 10 Rwk

Final Test Step 6 Step 5

980 Pcs & 20 Rwk 960 Pcs & 40 Rwk

Rolled Throughput Yield (RTY) = 990 x 985 x 970 x 950 x 960 x 980 x 990 1000 1000 1000 1000 1000 1000 1000 or RTY= e-TDU

Control Charts and Introduction to Six Sigma

Lean Six Sigma Project Selection
Specific Six Specific Six Sigma projects Sigma projects

Y
Delivery Service

Improved quality

Y1

Y2

Reduced cost

Y3

Profitable Growth

Y4

Yn

Y2,1

Y2,2

Y2,3

Y2,4

Reduced Cycle time Reduced Cycle time for Time to Market for Time to Market

Reduce Cycle Time Reduce Cycle Time from idea conception from idea conception to new product to new product

Y2,3,1 Y2,3,2

Reduce Cycle Time Reduce Cycle Time for marketing of for marketing of new product new product

Root Causes Root Causes

X2,3,2,1

X2,3,2,2

X2,3,2,3

Control Charts and Introduction to Six Sigma

The Focus of Improvement
Given a distribution function which approximates the histogram of a process which displays a reasonable degree of statistical control: * The parameter which will be used to characterize “process location” is called the mean (μ) of f(x). * The parameter which will be used to characterize “process dispersion” is called standard deviation (σ) of f(x).

Leverage variables which control the Mean

Y =f(

X 1 , ... , μ σ

XN )

Leverage variables which control the Standard Deviation

Scale of Y

The Focus of Lean Six Sigma — Understand the relationship of inputs to the response— Y = f(x)

Control Charts and Introduction to Six Sigma

Insight through Variance …
Baseline Improved? What 12 27 Delivery cycle time (days) seewe Cp 24 7 13 15 Cpk 7 4 Sigma Level 16 18 8 6 20 23 25 6 14 2 11.2 15.8 10 24 11 2 What customers feel 30 6 16 5 Using mean-based thinking, we improve Mean 15.8 11.2

•Std Dev 7.0

•9.0

average performance by 29%, and break out the champagne ... But our customer only feels the variance and cancels the next order!

Control Charts and Introduction to Six Sigma

Variation and Defects

Lower spec

Upper spec.

1st distribution 2nd distribution 3rd distribution

Defects

As the standard deviation increases, the number of defects increases.

Control Charts and Introduction to Six Sigma

Understanding Variation..

LSL

USL

Distribution Has moved to The right

Control Charts and Introduction to Six Sigma

Understanding Variation..

LSL

USL

New Mean

Old Mean

To reduce defects…

push the mean back

Control Charts and Introduction to Six Sigma

Understanding Variation..

And also …. Reduce the Variation

LSL

USL

Control Charts and Introduction to Six Sigma

Understanding Variation..
• • •
Higher σ = less variation = fewer defects = better performance 6 σ process Lower Specification Limit (LSL) Upper Specification Limit (USL)

Control Charts and Introduction to Six Sigma

Understanding Variation..
No Defects As long as Process Capability is Between USL & LSL

LSL

USL

Tolerance “T” = USL-LSL

Control Charts and Introduction to Six Sigma

Definition of a Six Sigma Process

If six standard deviations “fit” between our mean and the customer’s requirements . . . then: 99.99999975% of the products are included within the customer requirements. 6 5 4 3 2 1 1 2 3 4 5 6

Control Charts and Introduction to Six Sigma

Understanding Variation..
A 6 σ process has 6 standard deviations between the target and the nearest specification limit
Lower Spec Target Upper Spec

Process Centre
6 Standard Deviations

6 Sigma

Control Charts and Introduction to Six Sigma

Types of Variation
I

Expected variation (common cause) Unexpected variation (special cause) normal random systematic chance expected stable predictable in statistical control abnormal non-random local assignable cause unexpected unstable unpredictable not in statistical control

Immediate Goal: Eliminate unexpected variation Long-term Goal: Continuously reduce variation

Control Charts and Introduction to Six Sigma Six Sigma Breakthrough Roadmap
Define

Define
• Business Priorities • Measurable Goals • Selection Criteria • SIPOC

Analyze
• Problem Solving Teams • Capability Studies • Concepts of DOE • DOE Strategies & Analysis • Design for Six Sigma (DFSS)

Measure

Breakthrough Breakthrough business results rely business results rely on aa rigorous, on rigorous, structured structured methodology methodology The focus of Six Sigma

Y

Measure
• Economic Consideration of Quality • Quality Metrics • Thought Process Mapping • Process Mapping • FMEA • MSE •NEM •Statistical Tolerancing

Capability OK ? N Analyze Change

Y=

f (X)

Improvement
• DOE • Advanced Statistical Tools • Employee Involvement • Confirm Causal Variables • Establish Operating Limits • Verify Performance Improvements

Need A Change ? N Improve

Y

Define Define
Organizational Accountability

Control
• Control Strategies • Control Charts • Revised Standard Operating Procedures • Validate Control Systems • Implement Control System • Audit Control System • Monitor Performance Metrics

Measure Measure Analyze Analyze Improve Improve Control Control

N

Capability OK? Y Control

®

Process Excellence Six Sigma (DMAIC) Road Map

Define
Project Charter
Problem Statement: Goal: Business Case: Scope: Cost Benefit Projection: Milestones:

Control Charts and Introduction to Six Sigma
Business Case
Explain why it is important to work on this project.

Measure
Funneling*

Measures
I P O

I

Develop measures based on CTQ’s and SIPOC map.

Input Measures

Process Measures

Output Measures

Develop charter to include project description, baseline measures, business results, team members and schedule. Use Benchmarking as appropriate to establish some of the initial targets.

O1 O2 I1 I2 I3 I4

O3 O4

FMEA

Determine the critical few measures.

Data Collection Plan
What questions do you want to answer? Operational Definition and Procedures Data What Measure type/ How Related SamplingHow/ Data type measured conditionsnotes where

Data Collection Plan

Control
Innovative Improvement

Define

S U P P L I E R S

SIPOC*
Inputs Process Outputs

Measure

Yield: 60% Yield: 90% Yield: 45% Yield: 98%

C U S T O M E R S

Process Door
VA NVA

Develop a data collection plan.

How will you ensure What is your plan for consistency and stability?starting data collection? How will the data be displayed?

Gage R&R
Col # 1 2 Inspector A Sample # 1st Trial 2nd Trial 1 2.0 1.0 2.0 3.0 2 3 1.5 1.0 4 3.0 3.0 2.0 1.5 5 10.5 9.5 Totals Averages 2.1 1.9 3 Diff 1.0 1.0 0.5 0.0 0.5 3.0 0.6 R A 4 5 B 1st Trial 2nd Trial 1.5 1.5 2.5 2.5 2.0 1.5 2.0 2.5 1.5 0.5 9.5 8.5 1.9 1.7 Sum XB 3.6 1.8 6 Diff 0.0 0.0 0.5 0.5 1.0 2.0 0.4 R B

Analyze

Complete high-level “as is” process map and analyze yield to identify the process step with the highest impact.

Validate your measurement system.

Perform a detailed process analysis to identify problems.

Sum XA

4.0 2.0

VOC

Data Display
Gather / display data verifying customer needs and requirements. Display the data in graphic form to show current variation and other patterns.
UCL 1000 0 -1000 X LCL

Delighters More Is Better

VOC

Key Issue CTQ

10

20

30

Process Capability and Process Sigma*
Cp= 0.4 σ = 2.7
LSL USL

D B F A C E Other

Must Be

Calculate current process capability and sigma.

V7
* Not all tools in this area will be covered in as much depth during training for the Non-Technical Environment

Analyze
Data Door and Stratification*
22 21 20 19 18 17 16 15 14 13 12
O O O X O X O X X X X X X O X X O O O O

Innovative Improvement
Cost-Benefit Analysis
1 2 3 4 5 6 7 8 9 10

Control Charts and Introduction to Six Sigma

Generating Solutions
A B C D 4 1 3 2

Control
Develop and deploy a plan for how to respond to process changes.
Flowchart 1 2

I

Product Name Process Name Process Code #

QC Process Chart
Date of Issue: Revision Date Issued by: Reason

Approved by: Signature

Control/Check Points Response to Abnormality Work Control Permanent Notes InstructionsCode # Charac- Method Immediate Who Fix teristics Limits Fix Who

Use Multi-Vari Analysis, Stratification, and other techniques to identify potential causes.

Perform cost-benefit analysis for the preferred solution.

Generate solutions including Benchmarking and select best approach based on screening criteria.

Before

Process Change Management
After Improvement } A2 A1 A3 A4

12

Qualification, Validation, and Revalidation.

A1 A2 A3 A4

Before

After

Good

} Improvement

Selecting the Solution

Step 4 changes implemented

} Remaining Gap Target

Document new process, using training manuals and other tools to ensure standardization

Documentation & Standardization
Training Op Curriculum erating Pro Training ced Maures Manual nua l

Cause & Effect
Display your theories about root causes using a cause & effect diagram.

Fill to here

Assessing Risks

Recommend a solution involving key stakeholders.

Monitoring
UCL

Monitor the process using control charts to ensure process stays in control and conforms to specification.

LCL

Hypothesis-Testing*
Chi-Square χ²
Y

Regression Analysis*

Evaluating Results*
Use FMEA to identify risks associated with the solution and take preventive actions. LSL USL σ = 2.7 Cp = 0.4

Piloting
Original Test Full scale Recalculate process capability, process sigma, and financial results based on improvements.

t-test ANOVA Verify Root causes through statistical tools.
X1

Regression

Design of Experiments* Implementation Planning
Use hypothesis testing to identify differences.
1 2 3
A B C
G E

Key Learnings Results
Learnings

σ = Cp =

3.7 1.4

4

5 6 7 8 9 10

D F H G I J

Pilot the solution on a small scale and evaluate the results.

• • •

Recommendations next Document results and summarize key learnings. Identify potential future projects.

Use DOE and response surface optimization to quantify relationships.

Develop a full plan for implementation and change management.

Hand off the improved process to the process owner for on-going process management. Reward the improvement team.

Closure

Control Charts and Introduction to Six Sigma

Six Sigma Team Roles & Responsibilities
Champion / Sponsor Define Project Select MBB, BB and team members Determine needed resources Orient teams Review Progress Master Black Belt Help Plan meetings Observe team performance Coach the team if required Green Belt / Black Belt Help champion or guidance team select team members Plan team meetings Lead meetings Handle meeting logistics Make recommendation or changes Six Sigma Team Participate in the meeting Help with administrative tasks Meet with Champion for reviews Make recommendations or changes

Control Charts and Introduction to Six Sigma

SUMMING UP
• Six sigma is not a cure for everything • It cannot compensate for a bad management strategy • It cannot substitute for subject matter expertise (Remember: Garbage in, is garbage out) • It is not a resource item like capital • It is a tool that if properly deployed will bring positive results for the business

Control Charts and Introduction to Six Sigma

The Change Effectiveness Equation
I

QXA=E
TEC L HNI CAL ITY STR ATE GY

QU A

CHANGE

AC TURAL S L
CU

NCE PTTAATEGY CE R

TARGET

EFFECT

Control Charts and Introduction to Six Sigma

Approach ..Summary
6s For Cultural Change
I

1. 2. 3. 4. 5. 6.

Get Your Mind Around It Ingrain The Customer In Your Process Institutionalize It Involve Everyone… REALLY!! Have The Right Focus

} } }

Customer

Customer
Quality Is “Completely Satisfying Customer Needs Profitably”

Process

Commit To Do It

Em pl oy ee

Employee

s s s es es es oc oc oc Pr Pr Pr

Control Charts and Introduction to Six Sigma

Extension of Best Practices to Suppliers & Customers

Customers

Suppliers

Control Charts and Introduction to Six Sigma

6-sigma is not something else that you do…

It is what you should do.

Control Charts and Introduction to Six Sigma

Control Charts and Introduction to Six Sigma

Session 13 : Lean Six Sigma concepts

Subhash Dixit

Control Charts and Introduction to Six Sigma

Fulfillment
Input GE Process Output

Voice of the Customer
This is the date on which : I don’t care what happens in here - that’s your problem I wanted to use the equipment I wanted the part to arrive I wanted the repair to be comp I actually started using it I received the part I got my system repaired This is the date on which:

My Metric

= Outputs versus Input = Days Early / Late versus Request

My Expectation

= Zero for e very transaction

Fulfillment
5th Percentile 8.45 AM Median Time : 9.00 AM 50% cases, I arrive Before 9.00 AM

Control Charts and Introduction to Six Sigma

95th Percentile 9.45 AM

5% of the days I come to work within 8.45 AM Or 95% of the days I would be at work only after 8.45 AM

95% of the days I come to work within 9.45 AM Or at least 5% of the days I won’t be at wok even at 9.45 AM 5th Percentile 8.55 AM 95th Percentile 9.10 AM

This 1 Hr is Unpredictability or SPAN

I have now minimized the ‘ SPAN’ to 15 Minutes ( 10+5 ) Note that My Median or ‘ Performance’ is 9.00 A.M, Which is the ‘ Customer required ’ time.

Global Product Company

Control Charts and Introduction to Six Sigma

Strategy for Competitiveness : Transfer Manufacturing and Sourcing from HCC to LCC C O S T T I M
10% Material Cost Reduction

Process Structure Tools Training
Zst Catcher > Zst Pitcher

LCC I CV 25-30% Down 4 - 5 Years
On-going Material Cost Reduction in LCC

Six Sigma Transfers : The Phase Review Discipline

E

• Lowest Cost, Highest Quality - Worldwide Made in GE ! Drive Competitiveness through Six Sigma

Control Charts and Introduction to Six Sigma

How The Tools Complement Each Other
VALUE STREAM OPPORTUNITY
Lean Method
Baseline Assessment Product Families Value Stream Map / Product Flow Employee Activity Set-up Time Standard Work Material Replenishment Cell Design / Implementation Cell Performance Metrics Continuous Improvement

VARIATION OPPORTUNITY
Six Sigma Methods
VOC SIPOC

Six Sigma Focus Areas
Performance Evaluation Routing Standardization Process and Product Variation Cycle time Variation Method Variation Process Variation Method Variation Demand Variation Implementation PMAP & FMEA Common vs. special causes Six Sigma Tools

Lean Methods
Process Groups Value Stream Mapping SMED Process Flow Analysis Waste Analysis

Define Define

Measure Measure
Analyze Analyze

MSA FMEA
Capability Hypothesis

Improve Improve

DOE Control Control SPC

Standardization 5S Performance Measurements Visual Controls Mistake Proofing

“Five Minute” Lean Six Sigma
Number Of Invoices Lean Project

Control Charts and Introduction to Six Sigma

Six Sigma Project Eliminates Penalties

1% Penalty for Over 35 Days

0

5

10

15

20

25

30

35

Number of Days to Pay Invoice
Lean On Original Process Not Practical

1. Current State – Invoices are being processed on and average of 30 Days. 2. Supplier contract requires 1% Penalty for late Payments >35 days. 3. Six Sigma Project completed to Eliminate Penalties. 4. Supplier Offers 3% Discount if Invoices paid in less than 15 Days. 5. Lean Or Six Sigma Alone Could Not Accomplish

Control Charts and Introduction to Six Sigma

Lean Six Sigma Review
Original Process Lean Project Increased Speed
Lean Project Six Sigma Project Less Variation Eliminates Penalties

1% Penalty for Over 35 Days

0 Lean On Original Process Not Practical

10

15

20

25

30

35

Number of Days to Pay Invoice

1.Six Sigma – Reduction in Variation 2.Lean - Increased Flow/Speed

Control Charts and Introduction to Six Sigma

Lean Six Sigma
Faster, More, Cheaper and More Accurate
Controllable Inputs

X1
Inputs: Raw Materials, components, etc.

X2

X3

Quality Characteristics: Outputs

LSL

USL

Y1, Y2, etc. The Process

Uncontrollable Inputs, we have to live with

Z1

Z2

Z3

Control Charts and Introduction to Six Sigma
Logical Steps
DEFINE .Identify Process CTQ's and CTF's . Create Strategy . Fill Up Project Charter .Define SMART goals . Complete SIPOC . Understand Customer / Supplier Requirement

DMAIC - METHODOLOGY

DMAIC - Deliverables:
Key Deliverables: . DI: CTQ'S aligned with Business Strategy .D2: SMART Goals must be established . Project Sponsor/ resources including YB's / BB's identified .D3: Project Charter scoped and signed off by Champion/ Sponsor . Hard Savings / Soft savings estimated . Financial Controller briefed about the project . D4:Establish Y=F(X)

D EFINE s Project Charter Thought Map SIPOC Survey Methods 7 management tools

MEASURE . Establish and measure Process and Performance gaps (Y's) . Identify a data collection plan . Perform Measurement System Evaluation

M EASURE

VSM, 5S, Standard work Swimlane Process Map MSE Thought Map Data collection worksheet

Key Deliverables: . (Y) must be identified and measurable . M1: Measure Baseline Sigma and waste. . M2: Identify "As-IS" and "To-BE" states X's as quantitative or . M3: Identify all possible qualitative and provide data collection plan . M4: Identify Hidden Factory . M5: Do the MSA . M6: Validate Y=F(X)

ANALYZE . Identify variation and Waste . Identify Cause and Effects . Perform Failure Mode Analysis . Perform Hypothesis Testing

A NALYZE
Hypothesis testing FMEA, VSM, Takt time C&E Regression Thought Map

Key Deliverables: .A1: Perform FMEA and C& E .A2: Identify Vital Few X's that are statistically significant for variation/waste .A3: Test the hypothesis . Significant X's must bear relation with Y or Validate Y=F(X)

IMPROVE . Identify the crucial causes for waste and variation . Design for robustness and reliability .Establish New Operating tolerances or specifications . Prove effectiveness . Execute and Implement

I MPROVE
Regression DOE VSM - Future state Standard work Kaizen Thought Map DFSS DFL or DFF

Key Deliverables: .I1: Proposed Solution .I2: Optimal setting for X's .I3: Separate Signal from Noise .I4: Operating specifications for X's confirmed .I5: Shift and trend in process towards "ToBe" State .I6: Validate Y=F(X)

C ONTROL
CONTROL . Develop Control Mechanisms . Document Standard Operating Procedures . Determine Process Capability . Develop RAIL . Implement Mistake Proofing and Visual Controls

Control Charts Process Maps Project Charter Sign off RAIL FMEA - Post RPN SOP KANBAN Mistake Proofing

Key Deliverables: .C1: List the Post RPN in FMEA .C2: RAIL- Responsibilities for next 3 months .C3: Mistake Proofing must be implemented as part of process .C4: Make up SOP's .C5: Process control Plan (SPC) .C6: Project sign off from Champion, financial controller, and AIT. C7: Prepare a transition plan for Project owner/ sponsor . Measure Y and control X

Indicates the number of potential X's

Control Charts and Introduction to Six Sigma

Lean Six Sigma Synergy
Six Sigma Lean
Y= f (X μ σ 1

, ... , XN )

Supply Chain

• Speed in the value chain • Waste elimination • Value stream redesign • Pull vs. Push

• Speed of improvement • Variation reduction • “How” Problems are Solved • Continuous Improvement

• Optimization of Process, Policy, Organization, and Systems

Integrated Approach Maximizes Results!

D3

Control Charts and Introduction to Six Sigma

Integrating Lean into Six Sigma
D D M A I
Material and Information Flow

C

Product

Product & Information Flow (VSM) Change Over Pull Systems Workplace Redesign Activity Waste Analysis Performance Measures Visual Controls

D

M
SCOR

A

Baseline Assessment Product Family Analysis

Productivity

Supply Chain (VSM)

People

Standard Work
SAP / APO , Kaizen Six Sigma, Empowered Workforce

Enablers

Foundational Elements
5S (Workplace Organization) , Total Productive Maintenance, Mistake Proofing, Stable/Reliable/Capable Processes, & Flexible Workforce

Slide 140 D3 APO - Automated Purchase orders
Dixit, 16-12-2007

Control Charts and Introduction to Six Sigma

Integrating Lean into Six Sigma
Define Value stream Mapping Charter – problem statement Voice of Customer Communicatio n Plan CTQ issues Business Results Benchmarking Measure Prioritization Matrix MSA Studies Analyze Regression analysis 5 Whys Improve DOE Control SPC

Kaizen events Visual Control

Capability Studies Videotaping Time studies SIPOC

Cause-effect Diagram Root cause analysis ANOVA Multi-vari Analysis Hypothesis testing

TOC Pull System SMED /SUD 5S or 6S

Control Plans TPM Standard Work Procedures and work Instructions Training requirements

Collecting data

Work flow improvement

Control Charts and Introduction to Six Sigma

Integrating Lean and Six Sigma Deliverables
Key Deliverables: . D1: CTQ'S aligned with Business Strategy . D2: SMART Goals must be established . D3: Project Charter scoped and signed off by Champion/ Sponsor . D4:Establish Y=F(X)

Define

VOC

Key Deliverables •V1: CTF's must be aligned with Strategic Business Objectives •V2: Leadership and Team Identification •V3: Completed Project Charter with estimated Savings

Key Deliverables: • M1: Measure Baseline Sigma and waste. • M2: Identify "As-IS" and "To-BE" states • M3: Identify all possible X's as quantitative or qualitative and provide data collection plan • M4: Identify Hidden Factory • M5: Do the MSA • M6: Validate Y=F(X)

Key Deliverables

Measure

Value

•VA1: Baseline assessment (Cpk) •VA2: Identify Gaps •VA3: Current VSM •VA4: Future VSM

Key Deliverables: • A1:Perform FMEA and C& E • A2: Identify Vital Few X's that are statistically significant for variation/waste • A3: Test the hypothesis

Analyze

Flow

Key Deliverables •F1: WorkStream Organization / Cell Design •F2: SMED /IMED •F3: Standard Operating Procedures •F4: Dynamic Line Balancing •F5: Single Piece Flow

Key Deliverables: •I1: Proposed Solution •I2: Optimal setting for X's •I3: Separate Signal from Noise •I4: Operating specifications for X's confirmed •I5:Shift and trend in process towards "ToBe" State •I6: Validate Y=F(X) Key Deliverables: •C1:List the Post RPN in FMEA •C2:RAIL- Responsibilities for next 3 months •C3: Mistake Proofing •C4: Make up SOP's •C5: Process control Plan (SPC) •C6: Project sign off •C7: Prepare a transition plan

Improve

Pull

Key Deliverables •P1: Volume-variability Analysis •P2: Mixed Model Scheduling •P3: Kanban bin calculation •P4: Make Supermarkets •P5: Achieve pull material replenishment

Control

Perfection

Key Deliverables •PE1: Visual / Electronic Dashboards •PE2: Lean Daily Management Systems (LDMS) •PE3: Team Recognition •PE4: Continual Organization Learning

Control Charts and Introduction to Six Sigma

Six Sigma Vs. Lean
• • • • • • • • • • Process Orientation Customer Focus Y=f(X) Data and Metric Driven Variation Reduction Statistical Rigor Project Orientation Dedicated Personnel Bottom Line Results Data Driven Culture
• • • • • • • • • Value Stream Orientation Customer Focus Flow Based Waste Elimination Velocity and Speed Driven Gemba (at the place where work done) Just in Time – Surfacing of Issues Improvement at Lowest Possible Level Behavior Based Culture

Leveraging Tools

An Integrated Lean Six Sigma Approach
Optimized Processes
Six Sigma Methodology and Roadmap for Common Tool Usage

Control Charts and Introduction to Six Sigma

I

Define

Measure

Analyse

Improve

Control

Lean Six Sigma Define (Value Stream Approach)
Acme Stamp And Others
46 orders per Day

Project Charter Process Map Rolled Throughput Yield Voice of Customer (QFD) Value Stream Map Cause & Effect Matrix Potential Failure Mode and Effects Analysis Measurement Systems Analysis Data Collection & Sampling Statistical Process Control Capability Study Multi-Vari Study Hypothesis Testing/Confidence Intervals Design of Experiments Control Plan Celebrate

Confirmation and Schedule

MRP
Customer # Type Quantity Requested Delivery

Production Schedule Shipping Schedule

Fax
4h

Takt = 10 Min.

IN

Order Entry Computer

2d

Credit Check OUT Computer C/T = 2 min Batch = 2 day Reject = 10% Rework = 5%

2d

Reconcile IN Paper C/T = 5 min Batch = 2 day Reject = 0% Rework = 5%

4h

Finalize for output run at night Finalized batch waits

MRP C/T 1 min Batch 4 hr Reject = 0% Rework = 0%

C/T = 5 min Batch = 4 hr Reject = 0% Rework = 15%

Remaining Issues
16 hr 120 hr 13 min

4 hr 5 min 46 X 230 M.

48 hr 2 min

48 hr 5 min 92 M. All

4 hr 1 min

Mono Flow Information flows with material

push 230 M. process

46 M. 598 M.

Value Stream Map Lean Quick Hits Lean Value Streams

Synergies of an Integrated Approach

Control Charts and Introduction to Six Sigma

•A value stream state approach for identifying opportunities coupled with a powerful data driven approach for prioritizing then addressing the opportunities •The knowledge of how and when to apply the right methodology and tools to the right opportunity

Synergies of an Integrated Approach

Control Charts and Introduction to Six Sigma

• The lasting organizational benefits of a culturally driven, behavior based approach, augmented with the data driven discipline • A value stream approach to run the entire business with a sophisticated problem solving

Control Charts and Introduction to Six Sigma

“Five Minute” Lean Six Sigma
Number Of Invoices Six Sigma Project Eliminates Penalties

Lean Project

1% Penalty for Over 35 Days

0

5

10

15

20

25

30

35

Number of Days to Pay Invoice
Lean On Original Process Not Practical

1. Current State – Invoices are being processed on and average of 30 Days. 2. Supplier contract requires 1% Penalty for late Payments >35 days. 3. Six Sigma Project completed to Eliminate Penalties. 4. Supplier Offers 3% Discount if Invoices paid in less than 15 Days. 5. Lean Or Six Sigma Alone Could Not Accomplish

Control Charts and Introduction to Six Sigma

Lean Six Sigma Review
Original Process Lean Project Increased Speed
Lean Project Six Sigma Project Less Variation Eliminates Penalties

1% Penalty for Over 35 Days

0 Lean On Original Process Not Practical

10

15

20

25

30

35

Number of Days to Pay Invoice

1.Six Sigma – Reduction in Variation 2.Lean - Increased Flow/Speed

Control Charts and Introduction to Six Sigma

Lean Six Sigma Flow vs. Variation Exercise Why do we need to integrate Lean and Six Sigma?

Control Charts and Introduction to Six Sigma

Review of Definitions of Yield
• The Classical Definition of Yield • Yield = Total # of good parts produced at the end of the process / Total # of parts manufactured • Rolled Throughput Yield • RTY = Yield1 * Yield2 * Yield3 * etc.

Control Charts and Introduction to Six Sigma

The Ten Principles for Improvement
• Throw out all fixed ideas about how to do things • Say how the new method will work - not how won’t it work • Don’t accept excuses • Don’t seek perfection • Correct mistakes when they are found - not months later • Don’t spend a lot of money on improvements • The problems encountered give us a chance to use our brain • Use the 5 Why’s to find the root cause • Ten peoples’ ideas are better than one person’s • Improvement knows no limit

I

Control Charts and Introduction to Six Sigma

Transformation to Lean Six Sigma
Companies deploying some form of Lean Six Sigma
• • • • • • • • Xerox TRW Ford Motor Co. Caterpillar Honeywell Ingersoll-Rand The Stanley Works Bank of America • • • • • • • • Starwood Hotels & Resorts Sunbeam Visteon Corporation United Technologies Washington Mutual Colgate-Palmolive Siemens Business Services St. John Health Systems

And many more…… Virtually all organizations who have deployed Six Sigma are now investigating how to integrate Lean

Control Charts and Introduction to Six Sigma

Industries in Lean Six Sigma
Industries deploying some form of Lean Six Sigma
• Advertising • Banking • Computer services & outsourcing • Document management • Energy services • Field & technical services • Financial services • Hotels & hospitality • Insurance • Logistics and distribution services • Professional services • Sales & Marketing • Transportation • Manufacturing

Implementation of Lean Six Sigma has transcended traditional manufacturing

Control Charts and Introduction to Six Sigma…...

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...The methodology of Six Sigma can be traced all the way back to the eighteenth century in Industrial Europe. Carl Frederick Gauss introduced a conceptual normal curve metric which was later built on when Walther Stewhart showed how three deviations from the mean required some type of process solution. Finally in the late 1980s Six Sigma became closer to what we know it as today. A Motorola Engineer, Bill Smith, developed Six Sigma as a process for quality management. They came up with the idea or simply pointed out that the lesser number of mishaps at each stage of production would result in less defects. While this seems logical it had not been addressed before this point. At that time Six Sigma in its basic form was born, it included four stages; Measure, Analyze, Improve and Control. What is Six Sigma? Six Sigma is a methodology used by engineers and statisticians to limit the number of defects or errors in a process. However, today this method is being applied across all fields and it is no longer just for engineers and statisticians. Most people know the term as the process to achieve near-perfect results as far as customer requirements and efficiency are concerned. This is true because if a company truly achieves Six Sigma they have fewer than 3.4 defects per million potential defects or 99.997% precision. Motorola defines it as a “management drive, scientific methodology for product and process improvement which creates breakthroughs in financial performance and...

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...Vol. 3, No. 1, 2011 19 Implementation of Six Sigma in Indian industries – a Delphi study R.K. Padhy and S. Sahu* Department of Industrial Engg. & Mgmt., Indian Institute of Technology, Kharagpur-721302, India E-mail: rkpadhy@iem.iitkgp.ernet.in E-mail: sahus@mech.iitkgp.ernet.in *Corresponding author R.K. Das Department of Mechanical Engg., College of Engg. & Technology, Bhubaneswar-751003, India E-mail: ranjitdas@gmail.com Abstract: A Delphi study was carried out to review and analyse the critical issues that affect Six Sigma initiatives in Indian context. This research is aimed at assisting Six Sigma management professionals, researchers and organisations to gain a better understanding of the critical factors that affect the successful implementation of the programme in India, and its future evolution. Consensus among experts has been arrived upon various issues related to implementation of Six Sigma. The expert opinions invited on various issues have been discussed in the context of present scenario. The main consensual issues as prioritised by the experts are top management commitment, developing an effective system for project selection, monitoring and selection of right people, with strong emphasis on training. The experts’ priorities also focus on effective resource management and communication system. Based on the conclusion drawn from the study and literature reviewed, the effective implementation of Six Sigma also warrants the identification of the risk......

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...UNLV Theses/Dissertations/Professional Papers/Capstones 10-1-2011 Lean and Six Sigma in Hospitality Organizations: Benefits, Challenges, and Implementation Justin M. Lancaster University of Nevada, Las Vegas Follow this and additional works at: http://digitalscholarship.unlv.edu/thesesdissertations Part of the Business Administration, Management, and Operations Commons, Hospitality Administration and Management Commons, and the Strategic Management Policy Commons Repository Citation Lancaster, Justin M., "Lean and Six Sigma in Hospitality Organizations: Benefits, Challenges, and Implementation" (2011). UNLV Theses/Dissertations/Professional Papers/Capstones. Paper 1150. This Professional Paper is brought to you for free and open access by Digital Scholarship@UNLV. It has been accepted for inclusion in UNLV Theses/ Dissertations/Professional Papers/Capstones by an authorized administrator of Digital Scholarship@UNLV. For more information, please contact marianne.buehler@unlv.edu. 1 Lean and Six Sigma in Hospitality Organizations: Benefits, Challenges, and Implementation. By Justin M. Lancaster Masters of Science University of Nevada Las Vegas 2011 A professional paper submitted in partial fulfillment of the requirements for the Master of Science Hotel Administration William F. Harrah College of Hotel Administration Graduate College University of Nevada, Las Vegas December 2011 Chair: Dr. Robert Woods 2 PART ONE Introduction The......

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...Six Sigma and TQM/CQI Impact on U.S. Healthcare Regla Perez Keiser University Dr. Mary Granoff HSM691-G3 August 23, 2014 Introduction The concept of Six Sigma can be traced as far back as the late 1700’s when Carl Frederick Gauss introduced the normal curve. It wasn’t until the 1920’s when Walter Schewart was able to pinpoint the distance from the mean where a process which shows evidence of a defect or negative result, can be changed or corrected. However, it was Motorola’s Chairman Bob Galvin in the early 1980’s who after trying the traditional ways to measure defects realized they did not provide sufficient details that would identify the true effects of the defects within the manufacturer’s organization. It was at this at this time he introduced the concept of Six Sigma and helped the company’s bottom line which had not been a profitable one. Once the application of the Six Sigma concept became public, and the positive impact it had on Motorola’s bottom line, many other businesses wanted to learn about this concept. The impact of this concept was such that many of the executives of some of the largest companies have applied Six Sigma’s methodology to refocus their business on the road to profitability. What is Six Sigma? The concept of Six Sigma can be defined as an efficient methodology to problem solving which contributes to the improvement of performance of an organization or business. ......

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...this essay I am going to critically analyse Six Sigma concepts in relation to contemporary software development projects. To do this I am going to research different topics of the Six Sigma focused on software development project. To begin with I am going to give an overview of the history of Six Sigma focusing on explaining aspects of its methodological development and give a detailed description of contemporary Six Sigma methodology. Finally I am going to analyse the central concepts of contemporary Six Sigma methodology and then conclude all of my work together and discuss the principal arguments. Six sigma is a methodology used to focus an organization on reducing variations and errors in processes and driving quality improvement. Developed by Motorola Inc in the USA in 1986, it became well known in the 90’s, when GE CEO Jack Welch evangelized it. Six sigma is now according to many business development and quality improvement experts, the most popular management methodology in history. Six sigma aims to maximise customer satisfaction and minimise defects. In statistical terms, the purpose of six sigma is to reduce the process variation so that virtually all the products or services provided meet exceeded customer expectations. The standard metric for Six Sigma is 3.4 defects per million opportunities. For example for every 1 million transactions that go through a system, there will be 3.4 errors and still achieve six sigmas. Therefore this process has so few defects......

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...Six Sigma Six Sigma Introduction Six Sigma is a quality improvement method that is being used more frequently in healthcare. This tool was developed and used in industry since around 1980 and began to be used in healthcare in the 1990's (Powell, Rushmer, & Davies, 2009). According to Lighter (2011) "This lean process management system provides quality improvement professionals with the ability to remove non-value added work and improve process efficiency" (p. 287). The healthcare industry needs to find a way to get rid of errors. Today's society demands a lot from the healthcare providers and will not tolerate unnecessary errors, no matter how small they may seem. Six Sigma works to recognize errors as soon as they occur so they will be corrected before the error is carried out. If the process is fully reliable, appropriate healthcare will be delivered in the same way to all patients every time. If the care is evidence-based, then every patient receives optimal care regardless of who actually delivers the care, when it is delivered or where it is delivered (Powell, Rushmer, & Davies, 2009). Six Sigma uses the DMAIC (Define, Measure, Analyze, Improve, Control) approach. This approach first defines the problem, measures the defects, analyzes the cause of the defects, improves the process to remove the defects, and controls the process to ensure that the defects do not recur (Powell, Rushmer, & Davies, 2009). These steps need to take place to avoid......

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...Six Sigma Desmond Studstill Keller University Six Sigma Six Sigma is a strategy that measures the degree that a business process deviates from its goal (Harry, 1998). Six Sigma is a rigorous and systematic methodology that uses information gathered from all company departments and statistical analysis to measure and improve operational performance, practices and systems of the organization by identifying and preventing defects in the manufacturing or service providing processes. Six Sigma provides a yield (return) on investment. Companies like General Electric have achieved profit growth of 2 billion U.S. dollars in 1999 in comparison to 1998 growth and profits of 2.4 billion U.S. dollars in 2000 compared to 1999. Statistical representation of Six Sigma approach describes quantitatively how a process works. To perform Six Sigma in the company means to achieve such progress in all parts of the process of creation or product / service, which means that the process and product are realized without any defects. To achieve Six Sigma, a process must produce less than 3.4 defects per million opportunities (DPMO). Six Sigma is focused on the client, the sigma improvement process is an important quality improvement standard as a five-stage model: Define, Measure, Analyze, Improve, Control, which is called the DMAIC process (Kwak & Anbari, 2006; Jones, Parast, & Adams, 2010). The main goal here is to allow the users to focus on applying the data to resolve the problems...

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...archive of this journal is available at www.emeraldinsight.com/0954-478X.htm TQM 19,1 6 Dynamics of organizational learning and continuous improvement in six sigma implementation Taina Savolainen Department of Business and Economics, University of Joensuu, Joensuu, Finland, and Arto Haikonen Genworth Financial, Helsinki, Finland Abstract Purpose – The purpose of this paper is to examine the dynamics of organizational learning and continuous improvement (CI) in the context six sigma implementation in business organizations operating in multicultural environments. Design/methodology/approach – A specific research question is: does learning mechanisms and continuous improvement practices support each other and how, and what type of learning can be identified in the improvement of business processes. The question is linked to one of the fundamental issues currently discussed in the field of organizational learning; how do organizations get “from here to there”, in other words, what is the dynamics of the processes of learning and how progressive learning is achieved. A case study of a few Finnish companies is made and a procedural implementation model is applied. Findings – The findings suggest that the learning process is characterized by measurement, detection and correction of errors, and cost reduction. In six sigma implementation, learning is a single-loop type of learning. It is an incremental change process which reminds a technical variant of the learning......

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...Six Sigma is a revolutionary business process geared toward dramatically reducing organizational inefficiencies that trans- lates into bottom-line profitability. It started in the 1980s at Motorola; then, organizations such as GE, Allied Signal, and Seagate worked with the initiative during the 1990s and made it the most successful business initiative of the era. Key to the Six Sigma methodology of the 1990s is a five- step process—Define, Measure, Analyze, Improve, and Control (DMAIC). By systematically applying these steps (with the appropriate tools), practitioners of this approach have been able to save substantial dollars. The basis of Six Sigma is measuring a process in terms of defects. The statistical concept of six sigma means our processes are working nearly perfectly, delivering only 3.4 defects per million opportunities (DPMO). Sigma (the Greek letter σ) is a statistical term that measures standard deviation. In the context of management, it’s used to measure defects in the outputs of a process and show how far the process deviates from perfection. A one-sigma process produces 691462.5 defects per million opportunities, which translates to a percentage of satisfactory outputs of only 30.854%. That’s obviously really poor perform- ance. If we have processes functioning at a three sigma level, this means we’re producing 66807.2 errors per million. Figure 1-1. DPMO at sigma levels nities, delivering 93.319% satisfactory......

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...Six Sigma -takes what has worked from TQM and improves on what has not. - Quality management has it’s roots in Shewhart’s work at Bell Labs and Western Electric. He was first to use statistical methods to reduce variation in Manufacturing process and improve product quality. - TQM approach emphasizes on involving those closest to the process as the key to improving the process. It has it’s roots in Japan’s Total Quality Control. Differences between TQM and Six Sigma Main differences are between specific goals of these techniques and the execution of the technique. TQM was developed by a technical personnel where as Six sigma is developed by CEOs. This difference is also visible in the strategy. TQM sets unclear/vague goals of customer satisfaction and highest quality at low price, where , Six sigma sets a specific goal of 3.4 defects per million. Six sigma also focuses on bottom line expense reductions with measurable as well as documented results. To stress on it further, TQM is for incremental and continual change where as Six sigma represents rapid, and radical change via innovation. Regarding execution, TQM is owned by quality department, thus making it difficult to integrate throughout the business, where as, Six sigma is a business strategy supported by a quality management strategy( an integrated approach). Effectively making it as a functional speciality. Furthermore, Six sigma is a business strategy, supported by a quality improvement......

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...for many companies. The implementation of programs such as Total Quality Management (TQM) and Six Sigma help companies increase production and quality control, evaluate employee performance, and receive customer feedback. The Internet is also a magnificent tool that allows businesses and customers to communicate and help improve the performance of the company. The goal of most companies is to provide products and services that meet the quality expectations of their customers. Programs such as Six Sigma and TQM are essential for companies to compete with one another. Meeting the standards of customers is critical for businesses to succeed, and companies must continually improve on their products and services to meet the increasing demand of consumers. “Quality is the most important aspect of products and services, and the basis for the purchase of consumers. It has been reported that the quality movement has one core idea, and that is, goods and services must achieve the highest attainable quality, or nothing else will do. Thus, the past decade or so has seen the rise of a philosophy aimed at maximizing organizational quality and understanding it” (Connor, 1997). While there are other considerations, such as price, delivery, and flexibility, quality is still of utmost importance. This paper will discuss the advantages and disadvantages of implementing such practices as Six Sigma and Total Quality Management. Is one more beneficial than the other is, or is it best to......

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...TABLE OF CONTENTS History of Six Sigma………….……………………………….…………...3 What is Six Sigma………..……..………………………………………….4 DMAIC……………………..……………………………………………...4 Importance of Six Sigma..…..……………………………………………...6 Roles and Responsibilities of Six Sigma.…………………………………..6 Six Sigma Structure……..………………………………………………….8 Conclusion……………………………………………………………….…9 References…………………………………………………………………10 History of Six Sigma The roots of Six Sigma can be traced back to the early industrial era, during the eighteenth century in Europe. Carl Frederick Gauss introduced it as a conceptual normal curve metric. The evolution of Six Sigma took one step ahead with Walter Shewhart showing how three sigma deviations from the mean required a process correction. Later in 1980, it got a definitive form when a Motorola engineer coined the term Six Sigma for this quality management process. Motorola not only implemented this system in their organization, but they copyrighted it as well (Jocowski, 2009). This powerful process improvement technique has changed the way companies all over the world set objectives, and prepare for long term growth and stability. Motorola realized that they were losing a large portion of their business and productivity through the cost of non-quality. Motorola was having 2,600 parts per million losses in manufacturing and also were losing business due to defective parts and support of systems in the field that were not reliable. Motorola,...

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