Chapter # 07 (Six Sigma)

8/19/2019 Chapter # 07 (Six Sigma)

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TOTAL QUALITYMANAGEMENT

BYDR. ASIF MAHMOOD

Institute of Business & Management

University of Engineering and Technology,

Lahore

Chapter 7: Six Sigma

[email protected]


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99.9% is already VERY GOOD But what could happen at a quality level of99.9% (i.e., 1000 ppm),

in our everyday lives (about 4.6 )?

•More than 3000 newborns accidentally falling from the hands of nurses or doctors each year

•4000 wrong medical prescriptions each year

•400 letters per hour which never arrive at their destination

•Two long or short landings at airports each day

HOW GOOD IS GOOD ENOUGH?

σ


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HOW CAN WE GET THESE RESULTS?

13 wrong drug prescriptions per year

10 newborn babies dropped bydoctors/nurses per year

Two short or long landingsper year.

One lost article of mail per hour


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THE ANSWER IS:

Six Sigma


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WHAT IS SIX SIGMA?

A statistical concept that measures aprocess in terms of defects – at the six

sigma level, there 3.4 defects per millionopportunities (DPMO).


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6

S t a t i s t i c s


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GOALS OF SIX SIGMA

o Improve Customer Satisfaction• Reduce variations

Oriented towards developing manufacturing/ service setupswhich has zero variations in both product and the process.

• Defect reductions Objective of six sigma is to eliminate or reduce the defectsand rejects to practically zero

o Standardize Business Development

o

Coordinate Metrics with Suppliers andCustomers

o Ensure Industry and Government Compliance

o Develop Career Growth Opportunities


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50 Publicly Traded Companies with Organizational-Wide 6σ Deployments

ource! ii"igma

*))%*C,


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WHAT IS SIGMA ?Sigma is the Greek letter usedin statistics to representstandard deviation from mean

value, an indicator of the degreeof variation in a set of a process.

μ

σ

Sigma measures how far a given processdeviates from perfection (the data spread).

STATISTICAL BACKGROUND


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STATISTICAL BACKGROUND

The Mean- measureof central tendency

Standard Deviation measures the amountof data dispersion

around mean

n

x

x

n

1i

i∑=

=

( )

1n

Xx

σ

n

1i

2

i

−

−

=

∑=


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MEASURING PROCESS PERFORMANCETHE PIZZA DELIVERY EXAMPLE. . .

Customers want their pizzadelivered fast!

Guarantee = “30 minutes or less”

What if we measured performance and foundan average delivery time of 23.5 minutes?On-time performance is great, right?Our customers must be happy with us, right?


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HOW OFTEN ARE WE DELIVERING ON TIME? ANSWER: LOOK AT

THE VARIATION!

Managing by the average doesn’t tell the whole story. The average

and the variationtogether show what’s happening.

s

x

30 min. or less

0 10 20 30 40 50


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REDUCE VARIATION TO IMPROVE PERFORMANCE HOW MANY STANDARD

DEVIATIONS CAN YOU

“FIT” WITHIN

CUSTOMER

EXPECTATIONS?

Sigma level measures how often we meet (or fail tomeet) the requirement(s) of our customer(s).

s

x

30 min. or less

0 10 20 30 40 50


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1 StandardDeviation

STATISTICAL BACKGROUNDTHE68-95-99.7 RULE OR THREE SIGMA RULE


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2 StandardDeviations

STATISTICAL BACKGROUNDTHE 68-95-99.7 RULE OR THREE SIGMA RULE


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3 StandardDeviations

STATISTICAL BACKGROUNDTHE 68-95-99.7 RULE OR THREE SIGMA RULE


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PROCESS CAPABILITY

Process capability is the ability of the processto meet the design specifications for a service orproduct.

Nominal value is a target for designspecifications.

Tolerance is an allowance above or below thenominal value.


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20 25 30

Upper

specification

Lower

specification

Nominalvalue

PROCESS CAPABILITY

Process distribution

Customer Requirement

OurProcess is capable


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OurProcess is not capable

20 25 30

Upper

specification

Lower

specification

Nominalvalue

Process distribution

PROCESS CAPABILITY

DefectsDefects Acceptable

Customer Requirement


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Process capability ratio, Cp, is the tolerance width

divided by 6 standard deviations (process variability).

PROCESS CAPABILITYINDEX/RATIO, CP

Cp =Upper specification - Lower specification

6σ

Cp, upper =Upper specification - X

3σ

Cp, lower =

X - Lower specification

3σ


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INTENSIVE CARE LABEXAMPLE

Upper specification = 30 minutesLower specification = 20 minutes

Average service = 26.2 minutesσ = 1.35 minutes

The intensive care unit lab process has an averageturnaround time o !6.! minutes and a standarddeviation o ".3# minutes.

The nominal value or this service is !# minutes with an

upper speci$cation limit o 30 minutes and a lowerspeci$cation limit o !0 minutes.

The administrator o the lab wants to have three%sigmaperormance or her lab. &s the lab process capable othis level o perormance'


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Cp =pper speci$cation % ower speci$cation

6σ

Cp =30 % !0

6(".3#)* ".!3 Process Capability +atio

INTENSIVE CARE LAB ASSESSING PROCESS CAPABILITY

-ample


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PROCESS CAPABILITY INDEX—CP

Cp1

Cp=1

Poor Process

Just Ok

Good, Excellent

PROCESSCAPABILITY


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C pk * inimum o pper speci$cation / x

3σ

x / ower speci$cation

3σ

,

Process Capability &nde-, Cp, is an inde- that measuresthe potential or a process to generate deectiveoutputs relative to either upper or lower speci$cations.

PROCESS CAPABILITYINDEX, CPK

1e tae the minimum o the two ratios because it givesthe worst%case situation.

C GRASPINGTHE


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2

4peci$cationimit

4peci$cationimit

Cp *2 divided by

2 * 5istance rom process mean to closest spec limit * 3 4tandard 5eviations (also called 3 4igma7)

2 bigger Cp is better because ewer units will be beyond spec.(2 bigger 27 and a smaller 7 are better.)

CPK— GRASPING THE

CONCEPT

WHYC ISNEEDED?ISC NOT


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WHY CPK IS NEEDED? IS CP NOT

ENOUGH?

o Cp tells u only about the smartness of curve

o Cpk tells u about the positioning / location of the curve


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PROCESS CAPABILITY INDEX/RATIOSTANDARDS

The current process capability inde- standardsor Cp and Cp are8

Cp 9 ".33

Cp 9 ".33

&mportant :ote8Cp, lower* Cp, upper* Cp* Cp

(1hen the process is centered about the


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INTENSIVE CARE LABEXAMPLE—CONTINUED

Upper specification = 30 minutesLower specification = 20 minutes

Average service = 26.2 minutesσ = 1.35 minutes

The intensive care unit lab process has an averageturnaround time o !6.! minutes and a standarddeviation o ".3# minutes.

The nominal value or this service is !# minutes with an

upper speci$cation limit o 30 minutes and a lowerspeci$cation limit o !0 minutes.

The administrator o the lab wants to have three%sigmaperormance or her lab. &s the lab process capable othis level o perormance'


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C pk * inimum o pper speci$cation / x

3σ

x / ower speci$cation

3σ,

pper speci$cation * 30minutesower speci$cation * !0minutes2verage service * !6.!minutesσ * ".3# minutes


C pk =Minimum of

26.2 – 20.0

3(1.35) ,30.0 –26.2

3(1.35)

C pk = Minimum of 1.53, 0.94 = 0.94ProcessCapability &nde-

-ample


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Before Process ModificationUpper specification = 30.0 minutes Lower specification = 20.0

minutes Average service = 26.2 minutesσ = 1.35 minutes Cpk=0.94 Cp=1.23


Does not meet 3σ (1.00 Cpk) target due to a shift in mean

(Note variability is ok sinceCpis over 1.0)

-ample


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% 6σ −5σ −4σ %3 σ −2σ −1σ 0 +1σ +2σ +3σ +4σ +5σ +6σ

6σ to LSL 6σ to USL

Cp=2 Cpk=1.5Cp=2 Cpk=1.5

Cp=Cpk = 2

±1.5σLSL

12.5% 12.5%

75%

3.4 DPMO 3.4 DPMO

USL

SIGMA


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DEFECTS PER MILLION OPPORTUNITIES

Six Sigma allows managers to readily

describe process performance using acommon metric: Defects Per MillionOpportunities (DPMO)

1,000,00x

unitsof No . xunit

pererrorfor

iesopportunit of Nu mber

defectsof Number

= DPMO


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Example of Defects Per Million

Opportunities (DPMO) calculation.Suppose we observe 200 lettersdelivered incorrectly to the wrongaddresses in a small city during asingle day when a total of 200,000

letters were delivered. What is theDPMO in this situation?

So, for every oe!"##"o #etter$

e#"vere t&"$'"ty($ po$t)#!))*er$ ')e+pe't to &)ve1,000 #etter$"'orre't#y $et

to t&e ro*)re$$.

Co$t of -)#"ty/ &)t !"*&t t&)t DPMO !e) " ter!$ of overt"!ee!p#oy!et to 'orre't t&e error$

DEFECTS PER MILLION OPPORTUNITIES

[ ]

000,1== 1,000,000x200,000 x1

200 DPMO

SIGMALEVELS


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SIGMA LEVELS

Spec.

Range/

Sigma

Level

Sigma

(with

1.5σ

shift)

(DPMO) %

Defective

%

Yield

Short

-term

Cpk

Long

-term

Cpk

1 -0.5 691,462 69% 31% 0.33 –0.17

2 0.5 308,538 31% 69% 0.67 0.17

3 1.5 66,807 6.7% 93.3% 1.00 0.5

4 2.5 6,210 0.62% 99.38% 1.33 0.83

5 3.5 233 0.023% 99.977% 1.67 1.17

6 4.5 3.4 0.00034% 99.99966% 2.00 1.5

7 5.5 0.019 0.0000019

%

99.9999981

%2.33 1.83


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SIX SIGMA TEAM

Executive Leader

Champion/Sponsor

Master Black Belt

Black Belt

Green Belt Yellow Belt White Belt


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EXECUTIVE LEADER

High Level Executive committed to Six

Sigma SuccessKnowledgeable in Six Sigma Process Assign key individuals to theChampion/Sponsor Position.

SIX SIGMA TEAM


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SIX SIGMA TEAM

Promote awareness and execution of SixSigma within lines of business and/or

functionsIdentify potential Six Sigma projects tobe executed by Black Belts and GreenBelts

Identify, select, and support Black Beltand Green Belt candidates

Participate in 2-3 days of workshoptraining

Champion (Sponsor)


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Master Black BeltTeacher and mentor for Black BeltsResource for the Black Belts-experts on

the mathematical theory of statisticalmethods

Experts on the Six Sigma process

Works with the Champion/Sponsor toselect projects.

SIX SIGMA TEAM


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Use Six Sigma methodologies and advancedtools (to execute business improvementprojects

Are dedicated full-time (100%) to Six Sigma

Serve as Six Sigma knowledge leaders withinBusiness Unit(s)

Undergo 5 weeks of training over 5-10 months

Black Belt (project leader)

SIX SIGMA TEAM


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Use Six Sigma DMAIC methodology and basictools to execute improvements within theirexisting job function(s)

May lead smaller improvement projects withinBusiness Unit(s)

Bring knowledge of Six Sigma concepts & tools totheir respective job function(s)

Undergo 8-11 days of training over 3-6 months

Yellow and White Belts…

Green Belt (project team member)

SIX SIGMA TEAM

DMAIC–THEIMPROVEMENT


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Def"e

Me)$re

)#ye

!prove

Cotro#

)"isting Processes

DMAIC THE IMPROVEMENTMETHODOLOGY


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DEFINE – DMAIC PROJECTWHAT IS THE PROJECT?

ProjectCharter

6o"'e of t&eSt)ke&o#er

Co$t of

Poor-)#"ty

Define the Customer, their Critical to Quality (CTQ) issues, and the

Core Business Process involved.

Define project boundaries (scope) the stop and start of the process

Define the process to be improved by mapping the process flow

•Cost of Poor Quality (COPQ)

• Voice of the Stakeholder (VOS)

•Project Charter

• As-Is Process Map(s)

KeyDefine Tools

S t ) k e & o # % e r $


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MEASURE – BASELINES AND CAPABILITYWHAT IS OUR CURRENT LEVEL OF PERFORMANCE?

Measure the performance of theCore Business Process involved.

Develop a data collection plan forthe process

Collect data from many sources todetermine types of defects andmetrics

Compare with customer surveyresults to determine shortfall

•Critical to Quality Requirements

(CTQs)•Sample Plan

•Capability Analysis

•Failure Modes and Effect Analysis(FMEA)

•Etc…

KeyMeasure Tools

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)r#"*


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ANALYZE – POTENTIAL ROOT CAUSES

&shiawa5iagram

(;ishbone)

Analyze the data collectedand process map to

determine root causes ofdefects and opportunities forimprovement.

Identify gaps between

current performance andgoal performance

Prioritize opportunities toimprove

Identify sources of variation

•Histograms, Boxplots, Multi-VariCharts, etc.

•Hypothesis Tests

•Regression Analysis

KeyMeasure Tools

IMPROVE SOLUTIONSELECTION


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IMPROVE – SOLUTION SELECTION

Time

Quality

Cost

Solution

Sigma

Time

C!

"t#er

Score

SolutionImplementation Plan

SolutionSelection Matrix

$ NiceTr% Nice

&dea '

4olution+ight 1rong

& m p l e m e n t a t i o n

3

a d

< o o d

Improve the targetprocess by designingcreative solutions to fixand prevent problems.

Create innovatesolutions using

technology anddiscipline

Develop and deployimplementation plan

•Solution Selection Matrix

•To-Be Process Map(s)

•

QFD/House of Quality

KeyImprove Tools

CONTROL SUSTAINABLEBENEFITS


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CONTROL – SUSTAINABLE BENEFITS

Control the improvements to keep the process on the new course.

Prevent reverting back to the "old way"

Require the development, documentation and implementation ofan ongoing monitoring plan

Institutionalize the improvements through the modification ofsystems and structures (staffing, training, incentives)

•Control C#arts

•Contingenc% and(or !ction )lan*s+

KeyControl Tools

0 10 20 30

15

25

35

O:$erv) t"o


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DFSS – THE DESIGN METHODOLOGY D ESIGN FORS IXS IGMA

UsesDesign new processes, products, and/or services from scratchReplace old processes where improvement will not suffice

Differences between DFSS and DMAICProjects typically longer than 4-6 monthsExtensive definition of Customer Requirements (CTQs)Heavy emphasis on benchmarking and simulation; less emphasis onbaselining

Key ToolsMulti-Generational Planning (MGP)

Quality Function Deployment (QFD)

Define Measure AnalyzeDesign Verify

DMADV


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48

Def"e

Me)$re

)#ye

De$"*

6er"fy Def"e

Me)$re

)#ye

!prove

Cotro#

&ew Processes )"isting Processes

DMADV - DMAIC


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49

COMPUTING THE CP VALUE AT COCOA FIZZ:3 BOTTLING MACHINES AREBEING EVALUATED FOR POSSIBLE USE AT THE FIZZ PLANT. THE MACHINESMUST BE CAPABLE OF MEETING THE DESIGN SPECIFICATION OF 15.8-16.2 OZ. WITH AT LEAST APROCESS CAPABILITY INDEX OF 1.0 (CP≥1)

The table below shows the informationgathered from production runs on eachmachine. Are they all acceptable?

Solution:Machine A

Machine B

Cp=

Machine C

Cp=

Machin

e

σ USL-

LSL

6σ

2 .0# .= .3

." .= .6

C .! .= ".!

1.336(.05)

.4

6σ

LSLUSLCp ==

−

COMPUTING THE CPK VALUE AT COCOA


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50

FIZZ

Design specifications call for a

target value of16.0 ±0.2 OZ.

(USL = 16.2 & LSL = 15.8)

Observed process output has nowshifted and has aµ of 15.9 and a

σ of 0.1 oz.

Cpk is less than 1, revealing thatthe processis not capable

.33.3

.1Cpk

3(.1)

15.815.9,

3(.1)

15.916.2minCpk

==

−−=

Documents

Chapter # 07 (Six Sigma)