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Introduction to Six Sigma
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Page 1: SIX SIGMA

Introduction to

Six Sigma

Page 2: SIX SIGMA

Six Sigma: An overviewWhat is Sigma and Six Sigma?Why Six Sigma?Six Sigma LevelsSix Sigma Methodology and ManagementKey Roles for Six SigmaTools for Six SigmaTrainings and CertificationsConclusion

• Genesis• Six Sigma: An overview• What is Six Sigma• Six Sigma focus• Six Sigma Scale• Six Sigma Companies• Six Sigma – The statistical background• DMAIC/DMADV• Benefits

Page 3: SIX SIGMA

GENESIS• Motorola in early 80s• Mikel Harry formalized the process for targeting the

inputs to the quality problems rather than the outputs of the those problems

• Input oriented approach leads to: A problem solving methodology and a set of tools to manage the problems

• Adapted gradually by other Fortune 500 Co.• Another very famous proponent – Jack Welch (GE)• Its had evolved to mean different things to different

people, sometimes any QI improvement process is also termed as SS

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Six Sigma Companies

Page 5: SIX SIGMA

Six Sigma and Financial Services

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6

Six Sigma

• A term (Greek) used in statistics to representstandard deviation from mean value, an indicator of the degree of variation in a set of a process.

• Six Sigma - A highly disciplined process that enables organizations deliver nearly perfect products and services.

• A rigorous, data based problems solving approach to improving the performance of an organization

• DMAIC / DMADV Cycle

Page 7: SIX SIGMA

Six Sigma• A performance goal, representing 3.4 defects for

every million opportunities to make one.• A series of tools and methods used to improve or

design products, processes, and/or services.• A statistical measure indicating the number of

standard deviations within customer expectations.• A disciplined, fact-based approach to managing a

business and its processes.• A means to promote greater awareness of customer

needs, performance measurement, and business improvement.

Page 8: SIX SIGMA

Six Sigma

Six Sigma can be defined as a specific methodology to

develop and implement quality improvements in an

organization’s critical processes by rigorously measuring

and analyzing and identifying variations from customer

specifications in those processes and improving them or

designing entirely new processes to keep variations at an

acceptable level and sustaining and institutionalizing or

verifying the improvements for future as well.

Page 9: SIX SIGMA

Six Sigma• CTQ/CTC/CTD: Attributes which are important to

customers• Defect: Failing to deliver what the customers wants• Process Capability: What your process can deliver• Variation: What the customers see and feels • Stable Operations: Ensuring consistent, stable

processes• DFSS: Designing to meet customers needs and

process capability

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10

Six Sigma Focus is on

• Defining users requirements• Aligning processes to meet those requirements• Using metrics to minimize the variations• Rapidly and permanently improve the process

(Try and incorporate the best of the options in process)• Sustain and hold on to the improvement achieved

(Check the design for its use, usability & performance)

Page 11: SIX SIGMA

Sigma ScaleIn a world at 3 Sigma

• There are 964 U.S. flight cancellations per day.

• The police make 7 false arrests every 4 minutes.

• In MA, 5,390 newborns are dropped each year.

• In one hour, 47,283 international long distance calls are accidentally disconnected.

In a world at 6 Sigma

• 1 U.S. flight is cancelled every 3 weeks.

• There are fewer than 4 false arrests per month.

• 1 newborn is dropped every 4 years in MA.

• It would take more than 2 years to see the same number of dropped international calls.

Page 12: SIX SIGMA

Statistical Background

Target = m

Some Key measure

Page 13: SIX SIGMA

+/ - 3s

Statistical Background

Target = m

‘Control’ limits

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+/ - 3s

LSL USL

Statistical Background

Required Tolerance

Target = m

Page 15: SIX SIGMA

+/ - 3s

+/ - 6s

LSL USL

Statistical Background

Tolerance

Target = m

Six-Sigma

Page 16: SIX SIGMA

+/ - 3s

+/ - 6s

LSL USL

ppm1350

ppm1350

Statistical Background

Tolerance

Target = m

Page 17: SIX SIGMA

+/ - 3s

+/ - 6s

LSL USL

ppm0.001

ppm1350

ppm1350

ppm0.001

Statistical Background

Tolerance

Target = m

Page 18: SIX SIGMA
Page 19: SIX SIGMA

LSL

0 ppm ppm3.4

1.5s USL

ppm3.4ppm

66803

m

+/ - 6s

Statistical Background

Tolerance

Page 20: SIX SIGMA

Statistical Background

• Six-Sigma allows for un-foreseen ‘problems’ and longer term issues when calculating failure error or re-work rates

• Allows for a process ‘shift’• So what constitutes an acceptable level of

quality for any business?• While a 4 sigma is acceptable for restaurants

but then for a hospital medication process this seems to be too low

Page 21: SIX SIGMA

DPMO or PPM Table

Page 22: SIX SIGMA

Managing Up the Sigma Scale

Sigma % Good % Bad DPMO

1 30.9% 69.1% 691,462

2 69.1% 30.9% 308,538

3 93.3% 6.7% 66,807

4 99.38% 0.62% 6,210

5 99.977% 0.023% 233

6 99.9997% 0.00034% 3.4

Page 23: SIX SIGMA

Performance Standards

23456

30853766807

62102333.4

PPM

69.1%93.3%99.38%99.977%99.9997%

Yield

Processperformance

Processperformance

Defects permillion

Defects permillion

Long term yield

Long term yield

Current standardCurrent standard

World ClassWorld Class

Page 24: SIX SIGMA

24

WHAT IS DMAICDefine,Measure,Analyse,Improve,Control

• A logical and structured approach to problem solving and process improvement.

• An iterative process (continuous improvement)

• A quality tool which focus on change management style.

Page 25: SIX SIGMA

DMAIC

Define Determine purpose and scope of project

Measure Collect info which indicates process perf.

Analyze R’ship betn key process input variables

Improve Expt. inputs variables to get right outputs

Control Std. & sustain change for improvements

Six-Sigma - A Roadmap for Improvement

Page 26: SIX SIGMA

DMAIC – The Improvement Methodology

Objective:DEFINE the

opportunity

Objective:MEASURE current performance

Objective:ANALYZE the root causes of problems

Objective:IMPROVE the process to eliminate root causes

Objective:CONTROL the process to sustain the gains.

Key Define Tools:• Cost of Poor

Quality (COPQ)• Voice of the

Stakeholder (VOS)

• Project Charter• As-Is Process

Map(s)• Primary Metric

(Y)

Key Measure Tools:

• Critical to Quality Requirements (CTQs)

• Sample Plan• Capability

Analysis• Failure Modes

and Effect Analysis (FMEA)

Key Analyze Tools:

• Histograms, Boxplots, Multi-Vari Charts, etc.

• Hypothesis Tests• Regression

Analysis

Key Improve Tools:

• Solution Selection Matrix

• To-Be Process Map(s)

Key Control Tools:

• Control Charts• Contingency

and/or Action Plan(s)

Define Measure Analyze Improve Control

Page 27: SIX SIGMA

Define – DMAIC ProjectWhat is the project?

• What is the problem? The “problem” is the Output (a “Y” in a math equation Y = f(x1,x2,x3) etc).

• What is the cost of this problem• Who are the stake holders / decision makers• Align resources and expectations

Six Sigma

Project Charter

Voice of the

Stakeholder

S takeho lders

$

Cost of Poor

Quality

Page 28: SIX SIGMA

Define – Customer RequirementsWhat are the CTQs? What motivates the customer?

Voice of the Customer Key Customer Issue Critical to QualitySECONDARY RESEARCH

PRIMARY RESEARCH

Surveys

Surveys

OTM

Market Data

Ind

ust

ry

Inte

lLi

sten

ing

Po

sts

Industry Benchmarking

Focus Groups

Customer Service

Customer Correspondence

Obser-vations

Page 29: SIX SIGMA

Measure – Baselines and CapabilityWhat is our current level of performance?

50403020100

95% Confidence Interval for Mu

26.525.524.523.522.521.520.519.5

95% Confidence Interval for Median

Variable: 2003 Output

19.7313

8.9690

21.1423

Maximum3rd QuartileMedian1st QuartileMinimum

NKurtosisSkewnessVarianceStDevMean

P-Value:A-Squared:

26.0572

11.8667

25.1961

55.290729.610023.147516.4134 0.2156

1000.2407710.238483

104.34910.215223.1692

0.8540.211

95% Confidence Interval for Median

95% Confidence Interval for Sigma

95% Confidence Interval for Mu

Anderson-Darling Normality Test

Descriptive Statistics

• Sample some data / not all data• Current Process actuals measured

against the Customer expectation• What is the chance that we will succeed

at this level every time?

OthersAmount

Late

41779 4.017.079.0

100.0 96.0 79.0

100

50

0

100

80

60

40

20

0

Defect

CountPercentCum %

Pe

rce

nt

Co

unt

Pareto Chart for Txfr Defects

Page 30: SIX SIGMA

Six Sigma

Analyze – Potential Root CausesWhat affects our process?

y = f (x1, x2, x3 . . . xn)

Ishikawa Diagram

(Fishbone)

Page 31: SIX SIGMA

Analyze – Validated Root CausesWhat are the key root causes?

OthersAmount

Late

41779 4.017.079.0

100.0 96.0 79.0

100

50

0

100

80

60

40

20

0

Defect

CountPercentCum %

Pe

rce

nt

Co

unt

Pareto Chart for Txfr Defects

OtherClerical

Currency

2 31211.817.670.6

100.0 88.2 70.6

15

10

5

0

100

80

60

40

20

0

Defect

CountPercentCum %

Pe

rce

nt

Co

unt

Pareto Chart for Amt Defects

Six Sigma

y = f (x1, x2, x3 . . . xn)Critical Xs

Process Simulatio

n

Data Stratificatio

n

Regression Analysis

Experim ental Design

Page 32: SIX SIGMA

Improve – Potential SolutionsHow can we address the root causes we identified?

• Address the causes, not the symptoms.

y = f (x1, x2, x3 . . . xn)

Critical Xs

Decision

Evaluat

e

Clarify

Generat

e

Divergent | Convergent

Page 33: SIX SIGMA

Improve – Solution SelectionHow do we choose the best solution?

Solution Sigma Time CBA Other Score

Time

Quality

Cost

Six Sigma

Solution Implementatio

n Plan

Solution Selection Matrix

☺ Nice Try

Nice Idea X

Solution Right Wrong

Imp

lem

enta

tion

Bad

G

ood

Page 34: SIX SIGMA

Control – Sustainable BenefitsHow do we ”hold the gains” of our new process?

0 10 20 30

15

25

35

Observation Number

Indi

vidu

al V

alue

Mean=24.35

UCL=33.48

LCL=15.21

• Some variation is normal and OK• How High and Low can an “X” go yet not materially impact the “Y”• Pre-plan approach for control exceptions

Process Owner: Date:Process Description: CCR:

Measuring and Monitoring

Key Measurements

Specs &/or

Targets

Measures (Tools)

Where & Frequency

Responsibility (Who)

Contingency (Quick Fix)

Remarks

P1 - activity duration, min.

P2 - # of incomplete loan applications

Process Control System (Business Process Framework)

Direct Process Customer:

Flowchart

Custom er Sales Branch ManagerProcessingLoan Service

Manager

1.1

Ap

plic

atio

n &

Re

vie

w1

.2P

roce

ssin

g1

.3C

red

it re

vie

w1

.4R

evi

ew

1.5

Dis

clo

sure

Apply forloan

Reviewappliation for

com pleteness

ApplicationCom plete?

Com pletem eeting

inform ationNo

Page 35: SIX SIGMA

Six Sigma

Six Sigma can be defined as a specific methodology to

develop and implement quality improvements in an

organization’s critical processes by rigorously measuring

and analyzing and identifying variations from customer

specifications in those processes and improving them or

designing entirely new processes to keep variations at an

acceptable level and sustaining and institutionalizing or

verifying the improvements for future as well (control).

Page 36: SIX SIGMA

36

BENEFITS OF SIX SIGMA

• Generates sustained success• Sets performance goal for everyone• Enhances value for customers• Accelerates rate of improvement• Promotes learning across boundaries• Executes strategic change

Page 37: SIX SIGMA

SIX SIGMA – PERFORMANCE MEASURES

TOP: Total number Of Opportunities

DPU: Defect Per Unit

DPO: Defect Per Opportunity

DPMO: Defects Per Million Opportunities

PPM: Parts Per Million

RTY/FPY: Rolled Throughput Yield or First Pass Yield

Page 38: SIX SIGMA

TOP• TOP: Total number Of Opportunity: In any given product or

service, this refers to the total number of defect opportunities possible.

• TOP = TOTAL NUMBER OF OPPORTUNITY = NUMBER OF SAMPLE UNITS INSPECTED * OPPORTUNITY PER UNIT

• For example: If there are 10 columns/spaces in a form to be filled then, we can say in each form there the TOP = 10 per form, so if we are inspecting 100 forms then the

• TOP = 10 * 100 = 1000 number of opportunities.

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DPU• DPU: Defect Per Unit: Average number of defects per unit.

Numerically it is the ratio between the total number of defects found in a sample to the total number of samples inspected.

• DPU = DEFECT PER UNIT = NUMBER OF DEFECTS IN A SAMPLE / NUMBER OF SAMPLE INSPECTED

• For example: If we had inspecting 100 forms and found that there are 140 defects (mistakes) in all the forms inspected then the

• DPU = 140/100 = 1.4 defects per unit

Page 40: SIX SIGMA

DPO• DPO: Defect Per Opportunity: Average number of defects per opportunity.

This is the ratio of total number of defects found in a sample with the total number of defect opportunities available in the sample.

• DPO = DEFECT PER OPPORTUNITY = TOTAL NUMBER OF DEFECTS DETECTED IN A SAMPLE / TOTAL NUMBER OF DEFECT OPPORTUNITIES IN THE SAMPLE

• DPO = TOTAL NUMBER OF DEFECTS DETECTED IN A SAMPLE / (SAMPLE INSPECTED * NUMBER OF DEFECT OPPORTUNITIES PER UNIT IN THE SAMPLE)

• DPO = TOTAL NUMEBR OF DEFECTS DETECTED IN A SAMPLE / TOP

• For example: If we had inspecting 100 forms and there are 10 fields of information i.e. opportunities to make errors. If only 15 forms are sampled/inspected and 25 defects are found, then the

• DPO = 25 / (10*15) = 25/150 = 0.166667 defects per opportunity

Page 41: SIX SIGMA

DPMO• DPMO: Defects Per Million Opportunities: Ratio of total number of defects in one million

opportunities when an item can contain more than one defect. (This pertains to defects). This is the ratio of total number of defects found in a sample in one million opportunities.

• DPMO = DEFECT PER MILLION OPPORTUNITIES = TOTAL NUMBER OF DEFECTS DETECTED IN A SAMPLE * ONE MILLION / TOTAL NUMBER OF DEFECT OPPORTUNITIES

• DPMO = TOTAL NUMBER OF DEFECTS DETECTED IN A SAMPLE * ONE MILLION / (SAMPLE INSPECTED * NUMBER OF DEFECT OPPORTUNITIES PER UNIT IN THE SAMPLE)

• DPMO = TOTAL NUMEBR OF DEFECTS DETECTED IN A SAMPLE * 10,00,000 / TOP

• For example: If in a form, there are 10 fields of information i.e. opportunities to make errors. If only 15 forms are sampled/inspected and 25 defects are found, then the

• DPMO = 25 * 1000000 / (10*15) = 25 * 1000000 /150 = 166666.7 defect per million opportunity

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PPM• PPM: Parts Per Million: The number of defective units in one million

units. Usually, preferred when the fraction defective figures are too small to consider in normal circumstances. (This pertains to defectives).

• PPM = PARTS PER MILLION = TOTAL NUMBER OF DEFECTIVE UNITS DETECTED IN SAMPLE * 10,00,000/ NUMBER OF SAMPLES INSPECTED

• For example: If we had inspected 100 forms and there was 100% inspection done and 25 forms were found to be unacceptable, then the

• PPM = 25 * 1000000 / 100 = 250000 parts per million defective

Page 43: SIX SIGMA

RTY/FPY• RTY/FPY: Rolled Throughput Yield or First Pass Yield: It is the probability (or the

percentage chances) that a process will complete all required steps without any failures. The computations of RTY is based on reliability principle.

• Reliability of a system in series with n steps in the process = R1*R2*R3….Rn• Where, R is the reliability of each process from 1 to n.

• Similarly, yield of any process is the product of yield at every stage when quality is the performance metric: RTY = FPY = Y1 * Y2 * Y3 *….Yn ,Where, Y is the yield (proportion accepted/good) for each step in a n step process

• For example: In a three step process, the yield rate of different step is as: Step 1=0.97, Step 2=0.92 and Step 3=0.95. Then the RTY = 0.97 * 0.92 * 0.95 = 0.8478 It means that only 84.78% of the units completed through all this three step process will make it through without needing any repair work.

Page 44: SIX SIGMA

RTY & DPU

• RTY = e –DPU = e - 0.01666667 = 0.9835 = 98.35%

• The yield of a certain process is known and is around 0.836. Find DPU.

• RTY = 0.836 • RTY = e –DPU

• Therefore, DPU = - Logn (RTY) = - Logn (0.836) = 0.179127

Page 45: SIX SIGMA

DEFECTS OR

REJECTS

UNITS OF

PRODUCTION

OPPORTUNITIES/UNIT

OF PRODUCTION

DPU = DEFECTS PER UNITS

DPO = DEFECTS/(UNITS*OPPORTUNIT

Y/UNIT)

DPMO = DPO

* MILLIO

N

SIGMA SHORT TERM = ABS(NORMSINV(DPO))

SIGMA LONG

TERM = SSST +

1.5

RTY = E TO THE POWER MINUS

DPU

DPU FROM RTY =

MINUS LN

(RTY)

10 200 5

15 50 10

80 50 8

Page 46: SIX SIGMA

DEFECTS OR

REJECTS

UNITS OF

PRODUCTION

OPPORTUNITIES/UNIT

OF PRODUCTION

DPU = DEFECTS PER UNITS

DPO = DEFECTS/(UNITS*OPPORTUNIT

Y/UNIT)

DPMO = DPO

* MILLIO

N

SIGMA SHORT TERM = ABS(NORMSINV(DPO))

SIGMA LONG

TERM = SSST +

1.5

RTY = E TO THE POWER MINUS

DPU

DPU FROM RTY =

MINUS LN

(RTY)

10 200 5 0.05 0.01 10000 2.326 3.826 0.9512 0.05

15 50 10 0.3 0.03 30000 1.880 3.380 0.7408 0.3

80 50 8 1.6 0.2 200000 0.841 2.341 0.2018 1.6

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THANK YOU