six sigma statistical methods using minitab 13 manual

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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 MILLENNIUM MILLENNIUM Michael W. Piczak Michael W. Piczak Dipl.T., B.Comm., Dipl.T., B.Comm., MBA MBA

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Page 1: 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

Page 2: Six Sigma Statistical Methods Using Minitab 13 Manual
Page 3: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 4: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 5: Six Sigma Statistical Methods Using Minitab 13 Manual

GOALS OF 6 SIGMAGOALS OF 6 SIGMA

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

Page 6: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 7: Six Sigma Statistical Methods Using Minitab 13 Manual

PRIMARY SOURCES OF VARIATIONPRIMARY SOURCES OF VARIATION

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

Page 8: Six Sigma Statistical Methods Using Minitab 13 Manual

WHO IS THE ENEMY?WHO IS THE ENEMY?

VARIATIONVARIATION

Page 9: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 10: Six Sigma Statistical Methods Using Minitab 13 Manual
Page 11: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 12: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 13: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 14: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 15: Six Sigma Statistical Methods Using Minitab 13 Manual

GENESIS OF 6 SIGMAGENESIS OF 6 SIGMA

DefineRequirements and

Set Targets

Measure ResultsAgainst Targets

AnalyzeDifferences

Between Targetsand Results

Recommend andImplement

Improvements

Page 16: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 17: Six Sigma Statistical Methods Using Minitab 13 Manual

ELEMENT 1ELEMENT 1

Page 18: Six Sigma Statistical Methods Using Minitab 13 Manual

PORTER’S 5 FORCES MODELPORTER’S 5 FORCES MODEL

Page 19: Six Sigma Statistical Methods Using Minitab 13 Manual

PEST MODELPEST MODEL

Page 20: Six Sigma Statistical Methods Using Minitab 13 Manual

‘‘BONUS’ MODELBONUS’ MODEL

A key elementA key element

Page 21: Six Sigma Statistical Methods Using Minitab 13 Manual

VOICE OF THE CUSTOMERVOICE OF THE CUSTOMER

2 Brands of customers2 Brands of customersinternalinternalexternalexternal

Page 22: Six Sigma Statistical Methods Using Minitab 13 Manual

ALL ON THE SAME PAGEALL ON THE SAME PAGE

Voice of the Voice of the customercustomer

Page 23: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 24: Six Sigma Statistical Methods Using Minitab 13 Manual

IMPROVING THE PROCESSIMPROVING THE PROCESS

EliminationElimination SimplificationSimplification CombinationCombination ReuseReuse Parallel processingParallel processing SubcontractingSubcontracting

Page 25: Six Sigma Statistical Methods Using Minitab 13 Manual

CRITICAL EXAMINATIONCRITICAL EXAMINATION

Page 26: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 27: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 28: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 29: Six Sigma Statistical Methods Using Minitab 13 Manual

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)

Page 30: Six Sigma Statistical Methods Using Minitab 13 Manual

THE NORMAL DISTRIBUTIONTHE NORMAL DISTRIBUTION

Page 31: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 32: Six Sigma Statistical Methods Using Minitab 13 Manual

A KEY FORMULAA KEY FORMULA

Page 33: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 34: Six Sigma Statistical Methods Using Minitab 13 Manual

VISUALIZING VARIATIONVISUALIZING VARIATION

Page 35: Six Sigma Statistical Methods Using Minitab 13 Manual

THE HUNT FOR XTHE HUNT FOR X

Page 36: Six Sigma Statistical Methods Using Minitab 13 Manual

FIXING BELIEFFIXING BELIEF

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

Page 37: Six Sigma Statistical Methods Using Minitab 13 Manual

THE SCIENTIFIC METHODTHE SCIENTIFIC METHOD

Page 38: Six Sigma Statistical Methods Using Minitab 13 Manual

VISUALIZING VARIATIONVISUALIZING VARIATION

Page 39: Six Sigma Statistical Methods Using Minitab 13 Manual
Page 40: Six Sigma Statistical Methods Using Minitab 13 Manual

PROCESS CAPABILITYPROCESS CAPABILITY

Page 41: Six Sigma Statistical Methods Using Minitab 13 Manual

PROCESS CAPABILITY IIPROCESS CAPABILITY II

Page 42: Six Sigma Statistical Methods Using Minitab 13 Manual

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 = ?)

Page 43: Six Sigma Statistical Methods Using Minitab 13 Manual

CpkCpk

Page 44: Six Sigma Statistical Methods Using Minitab 13 Manual

HYDRAULIC LIFT COMPANYHYDRAULIC LIFT COMPANY

See case on Page 37See case on Page 37

Page 45: Six Sigma Statistical Methods Using Minitab 13 Manual

CAPABILITY ST & LTCAPABILITY ST & LT

Page 46: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 47: Six Sigma Statistical Methods Using Minitab 13 Manual

ST to LTST to LT

Page 48: Six Sigma Statistical Methods Using Minitab 13 Manual

NEW METRICSNEW METRICS

dpudpu dmpodmpo

THE CAVEATTHE CAVEAT

Page 49: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 50: Six Sigma Statistical Methods Using Minitab 13 Manual

2 ROADS TO PROFITABILITY2 ROADS TO PROFITABILITY

Page 51: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 52: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 53: Six Sigma Statistical Methods Using Minitab 13 Manual

SDWT’sSDWT’s

See Appendix GSee Appendix G

Page 54: Six Sigma Statistical Methods Using Minitab 13 Manual

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%

Page 55: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 56: Six Sigma Statistical Methods Using Minitab 13 Manual

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%

Page 57: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 58: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 59: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 60: Six Sigma Statistical Methods Using Minitab 13 Manual

THE ALCOA SEQUENCETHE ALCOA SEQUENCE

Page 61: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 62: Six Sigma Statistical Methods Using Minitab 13 Manual

STATISTICSSTATISTICS

CollectingCollecting OrganizingOrganizing SummarizingSummarizing AnalyzingAnalyzing PresentingPresenting

Page 63: Six Sigma Statistical Methods Using Minitab 13 Manual

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)

Page 64: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 65: Six Sigma Statistical Methods Using Minitab 13 Manual
Page 66: Six Sigma Statistical Methods Using Minitab 13 Manual

3 KINDS OF STATISTICS3 KINDS OF STATISTICS

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

Page 67: Six Sigma Statistical Methods Using Minitab 13 Manual

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)

Page 68: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 69: Six Sigma Statistical Methods Using Minitab 13 Manual

DATA TYPESDATA TYPES

DiscreteDiscrete ContinuousContinuous

Page 70: Six Sigma Statistical Methods Using Minitab 13 Manual

CHART TYPESCHART TYPES

Page 71: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 72: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 73: Six Sigma Statistical Methods Using Minitab 13 Manual

OROR

Page 74: Six Sigma Statistical Methods Using Minitab 13 Manual

FOR RFOR R

Page 75: Six Sigma Statistical Methods Using Minitab 13 Manual

X & MOVING RANGE CHARTSX & MOVING RANGE CHARTS

Page 76: Six Sigma Statistical Methods Using Minitab 13 Manual

PLOTTING RPLOTTING R

Page 77: Six Sigma Statistical Methods Using Minitab 13 Manual

PLOTTING XPLOTTING X

Page 78: Six Sigma Statistical Methods Using Minitab 13 Manual

P CHARTSP CHARTS

Page 79: Six Sigma Statistical Methods Using Minitab 13 Manual

AN EXAMPLE P. 102AN EXAMPLE P. 102

Page 80: Six Sigma Statistical Methods Using Minitab 13 Manual

A SUMMARY TABLE OF FORMULASA SUMMARY TABLE OF FORMULAS

Page 81: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 82: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 83: Six Sigma Statistical Methods Using Minitab 13 Manual

PATTERN ANALYSIS FIG. 41PATTERN ANALYSIS FIG. 41

Page 84: Six Sigma Statistical Methods Using Minitab 13 Manual

CHANGE OR JUMP IN LEVELCHANGE OR JUMP IN LEVEL

Page 85: Six Sigma Statistical Methods Using Minitab 13 Manual

RECURRING CYCLES F. 43RECURRING CYCLES F. 43

Page 86: Six Sigma Statistical Methods Using Minitab 13 Manual

TREND OR STEADY CHANGE IN LEVELTREND OR STEADY CHANGE IN LEVEL

Page 87: Six Sigma Statistical Methods Using Minitab 13 Manual

NO BRAINERSNO BRAINERS

Page 88: Six Sigma Statistical Methods Using Minitab 13 Manual

50% ABOVE/BELOW MEAN50% ABOVE/BELOW MEAN

Page 89: Six Sigma Statistical Methods Using Minitab 13 Manual

6 POINT RUN6 POINT RUN

Page 90: Six Sigma Statistical Methods Using Minitab 13 Manual

CYCLICAL PATTERNCYCLICAL PATTERN

Page 91: Six Sigma Statistical Methods Using Minitab 13 Manual

CYCLICAL PATTERNCYCLICAL PATTERN

Page 92: Six Sigma Statistical Methods Using Minitab 13 Manual

SHORT TERM TREND WITH ADJUSTMENTSHORT TERM TREND WITH ADJUSTMENT

Page 93: Six Sigma Statistical Methods Using Minitab 13 Manual

68% WITHIN 1 SIGMA68% WITHIN 1 SIGMA

Page 94: Six Sigma Statistical Methods Using Minitab 13 Manual

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

Page 95: Six Sigma Statistical Methods Using Minitab 13 Manual