Six Sigma Statistical Methods Using Minitab 13 Manual

SIX SIGMA QUALITY SIX SIGMA QUALITY TECHNIQUES...TECHNIQUES...

WHERE YOU NEED TO BE TO WHERE YOU NEED TO BE TO COMPETE IN THE NEW COMPETE IN THE NEW

MILLENNIUMMILLENNIUMMichael W. PiczakMichael W. Piczak

Dipl.T., B.Comm., MBADipl.T., B.Comm., MBA

THE MAIN ELEMENTSTHE MAIN ELEMENTSImprovement Process

Basic Components

Quality Initiatives

Enabling Initiatives and Tools

Improvement ToolsQuality Measurement

1 . D e fine P roduc ts and S e rv ices2 . Iden tify C us tom er R equ irem en ts3 . C om pare P roduc t w ith R equ irem en ts4 . D esc ribe the P rocess5 . Im prove the P rocess6 . M easure Q ua lity and P roduc tiv ity

1 . S e lf D irec ted W ork T eam s2 . S ho rt-cyc le M anu fac tu ring3 . D es ign fo r M anu fac tu re4 . B enchm ark ing5 . S ta tis tica l P rocess C on tro l6 . S upp lie r Q ua lifica tion

1 . O ld M etrics - p rocess m ean ( ) ands tandard dev ia tion ( )2 . C apab ility Index C p , C pk3 . N ew M e trics - de fec ts pe r un it (dpu ), de fec ts pe r m illion un its (dpm u)4 . C os t o f Q ua lity S tud ies

1 . Q ua lity F unc tion D ep loym en t2 . F low charts3 . P are to C harts4 . H is tog ram s5 . C ause-and-E ffec t D iag ram s6 . E xperim en ta l D es ign7 . G uage R & R

DE FACTO, 6 SIGMA IS: DE FACTO, 6 SIGMA IS:

The search for and control of The search for and control of X’X’ss

GOALS OF 6 SIGMAGOALS OF 6 SIGMA

Defect reductionDefect reductionYield improvementYield improvement Improved customer satisfactionImproved customer satisfactionHigher net incomeHigher net income

WHERE TO FOCUS?WHERE TO FOCUS?

For each product or process critical to quality For each product or process critical to quality (CTQ):(CTQ):

MeasureMeasure AnalyzeAnalyze ImproveImprove ControlControl

PRIMARY SOURCES OF VARIATIONPRIMARY SOURCES OF VARIATION

Inadequate design marginInadequate design margin Unstable parts and materialUnstable parts and material Insufficient process capabilityInsufficient process capability

WHO IS THE ENEMY?WHO IS THE ENEMY?

VARIATIONVARIATION

SELECTION OF RESPONSE VARIABLE (Y)

CHOICE OF FACTORS (Xi’s), LEVELS, RANGES

RECOGNITION OF & STATEMENT OF PROBLEM

CHOICE OF EXPERIMENTAL DESIGN

PERFORMING EXPERIMENT

STATISTICAL ANALYSIS OF DATA

CONCLUSIONS, RECOMMENDATIONS, NEXT STEPS

OUR BASIC RESEARCH PARADIGMOUR BASIC RESEARCH PARADIGM

Enter data and editing sameEnter data and editing same Verify data integrity via Verify data integrity via

Counts/DescribeCounts/Describe Run DescriptivesRun Descriptives Generate graphs & charts of dataGenerate graphs & charts of data Analyze ANOVAsAnalyze ANOVAs Run regressions, DOEs, GR&Rs Run regressions, DOEs, GR&Rs

PEDAGOGICAL APPROACHPEDAGOGICAL APPROACH

LectureLecture Discussion, debate and argumentDiscussion, debate and argument VideosVideos Hands-on exercises using general and Hands-on exercises using general and

company specific examplescompany specific examples

TERMINAL PERFORMANCE OBJECTIVESTERMINAL PERFORMANCE OBJECTIVES

As a result of taking this program, the participant As a result of taking this program, the participant will be able to:will be able to:

Appreciate the scope of 6 Sigma practices in Appreciate the scope of 6 Sigma practices in context of other company initiativescontext of other company initiatives

Apply a variety of tools to solve problemsApply a variety of tools to solve problems

T.P.O.s CONTINUED...T.P.O.s CONTINUED...

Participate as a contributing member of Participate as a contributing member of a continuous improvement or problem a continuous improvement or problem solving teamsolving team

Use Minitab as a data analysis toolUse Minitab as a data analysis tool

GENESIS OF 6 SIGMAGENESIS OF 6 SIGMA

DefineRequirements and

Set Targets

Measure ResultsAgainst Targets

AnalyzeDifferences

Between Targetsand Results

Recommend andImplement

Improvements

WHAT ARE WE REACHING FOR?WHAT ARE WE REACHING FOR?

ELEMENT 1ELEMENT 1

PORTER’S 5 FORCES MODELPORTER’S 5 FORCES MODEL

PEST MODELPEST MODEL

‘‘BONUS’ MODELBONUS’ MODEL

A key elementA key element

VOICE OF THE CUSTOMERVOICE OF THE CUSTOMER

2 Brands of customers2 Brands of customersinternalinternalexternalexternal

ALL ON THE SAME PAGEALL ON THE SAME PAGE

Voice of the Voice of the customercustomer

DESCRIBE THE PROCESSDESCRIBE THE PROCESS

M1 R N

R efe r to phys ic iano rder OR respond to

ca ll be ll re : P R N

$2033 .05 A 121G et na rco tics keys ifnecessary and take

cart to room

$4062 .45 A 122W ake res iden t &

repos ition by e leva tinghead o f bed , ad jus ting

pos ition (e .g . fla t onback)

$10157 .95 A 123

P our m ed ica tion , se lec ttab le ts o r c rush in to

app lesauce & g ive tores iden t

$2033 .05 A 124 Low er head o f bed &repos ition com fo rtab ly

$10157 .95 A 125 D ocum ent rec iep t o r

re fusa l o f m ed ica tion inN urs ing N o tes , M A R SS hee t & R eport S hee t

$2033 .05 A 126

IdentifiedR x N eed

O bta inedK eys/C hart

P reparedR es ident

A dm in is teredM edication

R e-pos itionedR es ident

I1M onitored

R es ident

C1 P rofess iona l G u ide lines C2 H osp ita l P o lic ies & P rocedures

M2 R P N

O 1R esident C areP rov ided

O 2A dm in is teredM edication

IMPROVING THE PROCESSIMPROVING THE PROCESS

EliminationElimination SimplificationSimplification CombinationCombination ReuseReuse Parallel processingParallel processing SubcontractingSubcontracting

CRITICAL EXAMINATIONCRITICAL EXAMINATION

NO NEW PROBLEMS PLEASENO NEW PROBLEMS PLEASE

Poka Yoke techniquesPoka Yoke techniques• guide pinsguide pins

• templatestemplates

• limit switcheslimit switches

• limited computer screen fieldslimited computer screen fields

• checklistschecklists

• interconnectsinterconnects

GETTING BETTER?GETTING BETTER?

The need to measure in quantitative The need to measure in quantitative terms importantterms important

QS9000 demands it in terms of quality QS9000 demands it in terms of quality and effectivenessand effectiveness

• customer satisfactioncustomer satisfaction• quality levels (# non-conformances, dpu, dpmo)quality levels (# non-conformances, dpu, dpmo)• cycle timescycle times• die change timesdie change times

ELEMENT 2: MEASUREMENTELEMENT 2: MEASUREMENT

Quality Measurement

1 . O ld M etrics - p rocess m ean ( ) ands tandard dev ia tion ( )2 . C apab ility Index C p , C pk3 . N ew M e trics - de fec ts pe r un it (dpu ), de fec ts pe r m illion un its (dpm u)4 . C os t o f Q ua lity S tud ies

OLD METRICSOLD METRICS

Measures of central tendency or Measures of central tendency or typicality (mean, median, mode)typicality (mean, median, mode)

Measures of dispersion (range, variance, Measures of dispersion (range, variance, standard deviation)standard deviation)

THE NORMAL DISTRIBUTIONTHE NORMAL DISTRIBUTION

NORMAL CURVE CHARACTERISTICSNORMAL CURVE CHARACTERISTICS

ContinuousContinuous SymmetricalSymmetrical Tails asymptotic to zeroTails asymptotic to zero Bell shapedBell shaped Mean = median = modeMean = median = mode Total area under curve = 1Total area under curve = 1

A KEY FORMULAA KEY FORMULA

VARIATION IN PERSPECTIVEVARIATION IN PERSPECTIVE

± 1 Sigma± 1 Sigma ± 2 Sigma± 2 Sigma ± 3 Sigma± 3 Sigma ± 4 Sigma ± 4 Sigma ± 5 Sigma ± 5 Sigma ± 6 Sigma± 6 Sigma ± ? Sigma± ? Sigma

VISUALIZING VARIATIONVISUALIZING VARIATION

THE HUNT FOR XTHE HUNT FOR X

FIXING BELIEFFIXING BELIEF

Method of tenacityMethod of tenacity Method of authorityMethod of authority Method of reasoningMethod of reasoning Method of scienceMethod of science

THE SCIENTIFIC METHODTHE SCIENTIFIC METHOD

VISUALIZING VARIATIONVISUALIZING VARIATION

PROCESS CAPABILITYPROCESS CAPABILITY

PROCESS CAPABILITY IIPROCESS CAPABILITY II

THE JOURNEYTHE JOURNEY

Most companies presently at 3-4 sigmaMost companies presently at 3-4 sigma The move is toward 6 sigma (Cp = 2)The move is toward 6 sigma (Cp = 2) Literature has references to 12 sigma Literature has references to 12 sigma

(Cp = ?)(Cp = ?)

CpkCpk

HYDRAULIC LIFT COMPANYHYDRAULIC LIFT COMPANY

See case on Page 37See case on Page 37

CAPABILITY ST & LTCAPABILITY ST & LT

Cp LONG TERM (LT)Cp LONG TERM (LT)

ST to LTST to LT

NEW METRICSNEW METRICS

dpudpu dmpodmpo

THE CAVEATTHE CAVEAT

Dpmo, Cp and SigmaDpmo, Cp and Sigma

using page 608 Lindsay and Evans, using page 608 Lindsay and Evans, derive figures shownderive figures shown

using page 48 Piczak, derive figures using page 48 Piczak, derive figures shownshown

2 ROADS TO PROFITABILITY2 ROADS TO PROFITABILITY

COSTS OF QUALITY COSTS OF QUALITY

Prevention Appraisal

D iscre tionary C os ts

InternalNon-conform ance

ExternalNon-conform ance

C onsequentia l C os ts

C osts O f Q ua lity

ELEMENT 3: QUALITY INITIATIVESELEMENT 3: QUALITY INITIATIVES

Quality Initiatives

1 . S e lf D irec ted W ork T eam s2 . S ho rt-cyc le M anu fac tu ring3 . D es ign fo r M anu fac tu re4 . B enchm ark ing5 . S ta tis tica l P rocess C on tro l6 . S upp lie r Q ua lifica tion

SDWT’sSDWT’s

See Appendix GSee Appendix G

LITERATURE IDENTIFIED BENEFITSLITERATURE IDENTIFIED BENEFITS

Productivity Productivity 15% -250% 15% -250%

All employees can perform all tasksAll employees can perform all tasks

Costs Costs 30% 30%

Cycle time Cycle time 50%-90% 50%-90%

Inventory Inventory 66% 66%

Rework due to engineering flaws Rework due to engineering flaws 50% 50%

BENEFITS CONT’DBENEFITS CONT’D

Late jobs Late jobs 1000% 1000%

Quality Quality

Recurring defective product problems Recurring defective product problems 10% 10%

Return on investment/sales Return on investment/sales

BENEFITS CONT’DBENEFITS CONT’D

Sales Sales 830% 830%

Operating statistics improved by 25-40%Operating statistics improved by 25-40%

Accounts receivable Accounts receivable from 66 days to 51 from 66 days to 51 daysdays

Corporate overhead Corporate overhead from $100M to from $100M to $24M$24M

Accidents Accidents 72% 72%

SHORT CYCLE MFG.SHORT CYCLE MFG.

SMEDSMEDautomated & computerized inspectionautomated & computerized inspection X and moving range control chartsX and moving range control charts automated systems automated systems

(MAPs/CAD/CAM/flexible mfg., etc.)(MAPs/CAD/CAM/flexible mfg., etc.) flexible, self directed work forceflexible, self directed work force

DFMDFM

Group technologyGroup technology accessibility of different parts & areasaccessibility of different parts & areas ease of workpiece handlingease of workpiece handling ergonomic principlesergonomic principles safety requirementssafety requirements appearanceappearance QFDQFD

BENCHMARKINGBENCHMARKING

more than just organized tourismmore than just organized tourism more than just a nice walk over at a more than just a nice walk over at a

friend’s plantfriend’s plant not industrial espionagenot industrial espionage not a one way channel of communicationnot a one way channel of communication

THE ALCOA SEQUENCETHE ALCOA SEQUENCE

SPCSPC

using numbers to describe absence or using numbers to describe absence or presence of a phenomenonpresence of a phenomenon

systematic gathering of datasystematic gathering of data using a collection of analytics that using a collection of analytics that

promote common understandingpromote common understanding emphasis is on measurementemphasis is on measurement

STATISTICSSTATISTICS

CollectingCollecting OrganizingOrganizing SummarizingSummarizing AnalyzingAnalyzing PresentingPresenting

THE ANALYST’S DUTYTHE ANALYST’S DUTY

Start with a regularity, uniformity or Start with a regularity, uniformity or curiositycuriosity

identify all previously significant identify all previously significant predictors of phemon in questionpredictors of phemon in question

theorize as to why independent variables theorize as to why independent variables (X’s) should be predictive of dependent (X’s) should be predictive of dependent variables (Y)variables (Y)

construct conceptual model of construct conceptual model of hypothesized relationshipshypothesized relationships

set out research question(s) clearlyset out research question(s) clearly gather datagather data organize same into spread/worksheetorganize same into spread/worksheet run full model followed by reduced formrun full model followed by reduced form draw conclusions/rec’s and share samedraw conclusions/rec’s and share same

3 KINDS OF STATISTICS3 KINDS OF STATISTICS

Descriptive (p. 71)Descriptive (p. 71) InferentialInferential PredictivePredictive

NASA DATA & REGRESSION LINENASA DATA & REGRESSION LINE

'O' RING EROSION x TEMPERATURE

-20-10

0102030405060

0 25 50 75 100

Launch Temperature (F.)

Ero

sio

n D

epth

(t

ho

usa

nd

ths)

SPACE SHUTTLE '0' RING DEFORMATION EMPIRICAL DATA FOR 22 FLIGHTS

0 RING ACTUAL TEMPERATURE EROSION OF Predicted Y

AT LAUNCH RINGS66 0 13.4570 53 7.80 SUMMARY OUTPUT69 0 9.21

68 0 10.63 Regression Statistics67 0 12.04 Multiple R 0.55517733572 0 4.97 R Square 0.30822187373 0 3.56 Adjusted R Square 0.27363296770 0 7.80 Standard Error 5.7498439657 40 26.18 Observations 22

63 0 17.7070 28 7.80 ANOVA

78 0 -3.51 df SS MS F Significance F67 0 12.04 Regression 1 1910.597 1910.597 8.911003727 0.00731659953 48 31.84 Residual 20 4288.175 214.40967 0 12.04 Total 21 6198.77375 0 0.73

70 0 7.80 Coefficients Standard Error t Stat P-value81 0 -7.76 Intercept 106.778 33.343 3.202 0.00476 0 -0.69 X Variable 1 -1.414 0.474 -2.985 0.007

79 0 -4.9375 0 0.7376 0 -0.69

DATA TYPESDATA TYPES

DiscreteDiscrete ContinuousContinuous

CHART TYPESCHART TYPES

CHART TYPESCHART TYPES

X Bar and R chartsX Bar and R charts X and Moving Range chartsX and Moving Range charts p chartsp charts c charts and c charts and u chartsu charts

CONTROL LIMITS FOR X BAR & R CHARTSCONTROL LIMITS FOR X BAR & R CHARTS

Upper control limit (UCLUpper control limit (UCL )= x double )= x double

bar + Zbar + Z

Lower control limit (LCLLower control limit (LCL )) = x double = x double

bar - Zbar - Z

OROR

FOR RFOR R

X & MOVING RANGE CHARTSX & MOVING RANGE CHARTS

PLOTTING RPLOTTING R

PLOTTING XPLOTTING X

P CHARTSP CHARTS

AN EXAMPLE P. 102AN EXAMPLE P. 102

A SUMMARY TABLE OF FORMULASA SUMMARY TABLE OF FORMULAS

INTERPRETING CHARTSINTERPRETING CHARTS

Examining patterns to make rational Examining patterns to make rational decisionsdecisions

Using patterns puts the odds of making a Using patterns puts the odds of making a good decision on your sidegood decision on your side

Can make two good decisions and two Can make two good decisions and two bad decisions bad decisions

U CAN BE RIGHT, U CAN BE WRONGU CAN BE RIGHT, U CAN BE WRONG

PATTERN ANALYSIS FIG. 41PATTERN ANALYSIS FIG. 41

CHANGE OR JUMP IN LEVELCHANGE OR JUMP IN LEVEL

RECURRING CYCLES F. 43RECURRING CYCLES F. 43

TREND OR STEADY CHANGE IN LEVELTREND OR STEADY CHANGE IN LEVEL

NO BRAINERSNO BRAINERS

50% ABOVE/BELOW MEAN50% ABOVE/BELOW MEAN

6 POINT RUN6 POINT RUN

CYCLICAL PATTERNCYCLICAL PATTERN

CYCLICAL PATTERNCYCLICAL PATTERN

SHORT TERM TREND WITH ADJUSTMENTSHORT TERM TREND WITH ADJUSTMENT

68% WITHIN 1 SIGMA68% WITHIN 1 SIGMA

SYSTEMATIC CAUSES OF VARIATIONSYSTEMATIC CAUSES OF VARIATION

Lack of preventative maintenanceLack of preventative maintenance Worn toolsWorn tools Operator performanceOperator performance DifferentialsDifferentials Environmental changesEnvironmental changes Sorting practicesSorting practices