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Transcript of 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