2 What is Six Sigma?It is a business process that allows companies todrastically improve their bottom line by designing and monitoring everyday business activities in ways that minimize waste and resources while increasing customer satisfaction.Mikel Harry, Richard Schroeder
3 What Six Sigma Can Do For Your Company? 4.8DFSSMAICAverage company
5 The Cost of Quality (COQ) Traditional Cost of Poor Quality (COQ)5-8%InspectionWarrantyRejectsReworkการติดตั้งยอดขายลดลงการขนส่งล่าช้างานเอกสารส่งผิดที่เวลาผลิตยาวนานค่าเร่งการผลิตรายการสั่งซื้อมากเกินไปใช้เวลา Set up นานค่าของเงินตามกาลเวลาการสั่งวัตถุดิบมากเกินความจำเป็นความไม่พอใจความปลอดภัยค่าบริการขนส่งค่าบัตรโทรศัพท์ข้อมูลที่ไม่ถูกต้องแนวทางที่แตกต่างในการทำธุรกิจLost OpportunityGroup activities: create the flow after rejected units have occurred in the process.Less Obvious Cost of Quality (COQ)15-20%Note: % of sales
6 DMAIC : The Yellow Brick Road DefineCOREPHASMeasureAnalyzeCharacterizationOptimizationBreakthroughStrategyImproveControl
8 Define What is my biggest problem? Customer complaints Low performance metricsToo much time consumedWhat needs to improve?Big budget itemsPoor performanceWhere are there opportunities to improve?How do I affect corporate and business group objectives?What’s in my budget?
9 Define : The ProjectProjects DIRECTLY tie to department and/or business unit objectivesProjects are suitable in scopeBBs are “fit” to the projectChampions own and support project selection
10 Define : The Defect Rework High Defect Rates Customer Complaints Excessive Test and InspectionConstrained Capacity with Highanticipated Capital ExpendituresBottlenecksHigh Defect RatesLow YieldsExcessive Cycle TimeExcessive Machine Down TimeHigh Maintenance CostsHigh Consumables Usage
11 ปัญหาฝังแน่น (Chronic) Define : The Chronic ProblemSpecial Cause ( ปัญหานาน ๆ ครั้ง )TimeReject Rateปัญหาฝังแน่น (Chronic)The BreakthroughStrategyOptimum Level
12 Define : The Persistent Problem Is process in control?
13 Define : Refine The Defect a2a3a4a5a6a7a1Refined Defect = a1
15 MeasureThe Measure phase serves to validate the problem, translate the practical to statistical problem and to begin the search for root causes
16 Measure : ToolsTo validate the problemMeasurement System AnalysisTo translate practical to statistical problemProcess Capability AnalysisTo search for the root causeProcess MapCause and Effect AnalysisFailure Mode and Effect Analysis
17 Work shop #1:Our products are the distance resulting from the Catapult.Product spec are +/- 4 Cm. for both X and Y axisShoot the ball for at least 30 trials , then collect yieldPrepare to report your result.
18 Measure : Measurement System Analysis Objectives:Validate the Measurement / Inspection SystemQuantify the effect of the Measurement System variability on the process variability
19 Measure : Measurement System Analysis Attribute GR&R : PurposeTo determine if inspectors across all shifts, machines, lines, etc… use the same criteria to discriminate “good” from “bad”To quantify the ability of inspectors or gages to accurately repeat their inspection decisionsTo identify how well inspectors/gages conform to a known master (possibly defined by the customer) which includes:How often operators decide to over rejectHow often operators decide to over accept
21 Measure : Measurement System Analysis % Appraiser Score% REPEATIBILITY OF OPERATOR # 1 = 16/20 = 80%% REPEATIBILITY OF OPERATOR # 2 = 13/20 = 65%% REPEATIBILITY OF OPERATOR # 3 = 20/20 = 100%
22 Measure : Measurement System Analysis % Attribute Score% UNBIAS OF OPERATOR # 1 = 12/20 = 60%% UNBIAS OF OPERATOR # 2 = 12/20 = 60%% UNBIAS OF OPERATOR # 3 = 17/20 = 85%% Screen Effective Score% REPEATABILITY OF INSPECTION = 11/20 = 55 %% Attribute Screen Effective Score% UNBIAS OF INSPECTION 50 % = 10/20 = 50%
23 Measure : Measurement System Analysis Variable GR&R : PurposeStudy of your measurement system will reveal the relative amount of variation in your data that results from measurement system error.It is also a great tool for comparing two or more measurement devices or two or more operators.MSA should be used as part of the criteria for accepting a new piece of measurement equipment to manufacturing.It should be the basis for evaluating a measurement system which is suspect of being deficient.
25 Measure : Measurement System Analysis Resolution?“Precision” (R&R)Calibration?Stability?Linearity?Bias?
26 Measurement System Metrics Measurement System Variance:s2meas = s2repeat + s2reprodTo determine whether the measurement system is “good” or “bad” for a certain application, you need to compare the measurement variation to the product spec or the process variationComparing s2meas with Tolerance:Precision-to-Tolerance Ratio (P/T)Comparing s2meas with Total Observed Process Variation (P/TV):% Repeatability and Reproducibility (%R&R)Discrimination Index
27 Uses of P/T and P/TV (%R&R) The P/T ratio is the most common estimate of measurement system precisionEvaluates how well the measurement system can perform with respect to the specificationsThe appropriate P/T ratio is strongly dependent on the process capability. If Cpk is not adequate, the P/T ratio may give a false sense of security.The P/TV (%R&R) is the best measure for AnalysisEstimates how well the measurement system performs with respect to the overall process variation%R&R is the best estimate when performing process improvement studies. Care must be taken to use samples representing full process range.
28 Number of Distinct Categories Automobile Industry Action Group (AIAG) recommendations:Categories Remarks< 2 System cannot discern one part from another= 2 System can only divide data in two groupse.g. high and low= 3 System can only divide data in three groupse.g. low, middle and high 4 System is acceptable
29 Measure : Measurement System Analysis Variable GR&R : Decision CriterionNote : Stability is analyzed by control chart
30 Enter the data and tolerance information into Minitab. Example: MinitabEnter the data and tolerance information into Minitab.Stat > Quality Tools > Gage R&R Study (Crossed )Enter Gage Infoand Options.(see next page)FN: Gageaiag.mtwANOVA method is preferred.
31 Enter the data and tolerance information into Minitab. Stat > Quality Tools > Gage R&R StudyGage Info (see below) & Options
34 Gage R&R, Variation Components Variance due to the measurement system (broken down into repeatability and reproducibility)%ContributionSource VarComp (of VarComp)Total Gage R&RRepeatabilityReproducibilityOperatorOperator*PartIDPart-To-PartTotal VariationStdDev Study Var %Study Var %ToleranceSource (SD) (5.15*SD) (%SV) (SV/Toler)Total Gage R&RRepeatabilityReproducibilityOperatorOperator*PartIDPart-To-PartTotal VariationTotal varianceStandard deviation for each variance componentVariance due to the parts
35 Gage R&R, Results%ContributionSource VarComp (of VarComp)Total Gage R&RRepeatabilityReproducibilityOperatorOperator*PartIDPart-To-PartTotal VariationStdDev Study Var %Study Var %ToleranceSource (SD) (5.15*SD) (%SV) (SV/Toler)Total Gage R&RRepeatabilityReproducibilityOperatorOperator*PartIDPart-To-PartTotal VariationQuestion: What is our conclusion about the measurement system?
36 Measure : Process Capability Analysis Process capability is a measure of how well the process is currently behaving with respect to the output specification.Process capability is determined by the total variation that comes from common causes -the minimum variation that can be achieved after all special causes have been eliminated.Thus, capability represents the performance of the process itself,as demonstrated when the process is being operated in a state of statistical control
37 Measure : Process Capability Analysis Translate practical problem to statistical problemCharacterizationVariationLargeLSLUSLOff-TargetLSLUSLOutliersLSLUSL
38 Measure : Process Capability Analysis Two measures of process capabilityProcess PotentialCpProcess PerformanceCpuCplCpkCpm
39 Measure : Process Capability Analysis Process Potential
40 Measure : Process Capability Analysis The Cp index compares the allowable spread (USL-LSL) against the process spread (6).It fails to take into account if the process is centered between the specification limits.Process is centeredProcess is not centered
41 Measure : Process Capability Analysis Process PerformanceThe Cpk index relates the scaled distance between the process mean and the nearest specification limit.
42 Measure : Process Capability Analysis There are 2 kind of variation : Short term Variation and Long term Variation
43 Measure : Process Capability Analysis Short Term VS LongTerm ( Cp Vs Pp or Cpk vs Ppk )
44 Measure : Process Capability Analysis Process Potential VS. Process Performance ( Cp Vs Cpk )1.If Cp > 1.5 , it means the standard deviation is suitable2.Cp is not equal to Cpk, it means that the process mean is off-centered
45 Workshop#3Design the appropriate check sheetDefine the subgroupShoot the ball for at least 30 trials per subgroupPerform process capability analysis, translate Cp, Cpk , Pp and Ppk into statistical problemReport your results.
46 Measure : Process MapProcess Map is a graphical representation of the flow of a “as-is” process. It contains all the major steps and decision points in a process.It helps us understand the process better, identifythe critical or problems area, and identify where improvement can be made.
47 Measure : Process Map OPERATION All steps in the process where the object undergoes a change in form or condition.TRANSPORTATIONAll steps in a process where the object moves from one location to another, outside of the OperationSTORAGEAll steps in the process where the object remains at rest, in a semi-permanent or storage conditionDELAYAll incidences where the object stops or waits on a an operation, transportation, or inspectionINSPECTIONAll steps in the process where the objects are checked for completeness, quality, outside of the Operation.DECISION
48 Measure : Process Map • How many Operational Steps are there? GoodBadScrapWarehouse•How many Operational Steps are there?How many Decision Points?How many Measurement/Inspection Points?How many Re-work Loops?How many Control Points?
49 Measure : Process Map High Level Process Map Major StepKPIVsKPOVsThese KPIVs and KPOVs can then be used as inputs toCause and Effect Matrix
50 Workshop #2 : Do the process map and report the process steps and KPIVs that may be the cause
51 Measure : Cause and Effect Analysis A visual tool used to identify, explore and graphically display, in increasing detail, all the possible causes related to a problemor condition to discover root causesTo discover the most probable causes for further analysisTo visualize possible relationships between causes for any problem current or futureTo pinpoint conditions causing customer complaints, process errors or non-conforming productsTo provide focus for discussionTo aid in development of technical or other standards or process improvements
52 Measure : Cause and Effect Matrix There are two types of Cause and Effect Matrix1. Fishbone Diagram - traditional approach to brainstorming and diagramming cause-effect relationships. Good tool when there is one primary effect being analyzed.2. Cause-Effect Matrix - a diagram in table form showing the direct relationships between outputs (Y’s) and inputs (X’s).
53 Measure : Cause and Effect Matrix MethodsMaterialsMachineryManpowerProblem/DesiredImprovementC/N/XCNFishbone DiagramC = Control FactorN = Noise FactorX = Factor for DOE (chosen later)
55 Workshop #4:Team brainstorming to create the fishbone diagram
56 Measure : Failure Mode and Effect Analysis FMEA is a systematic approach used to examine potential failures and prevent their occurrence. It enhances an engineer’s ability to predict problems and provides a system of ranking, or prioritization, so the most likely failure modes can be addressed.
60 Workshop # 5 :Team Brainstorming to create FMEA
61 Measure : Measure Phase’s Output Check and fix the measurement systemDetermine “where” you areRolled throughput yield, DPPMProcess CapabilityEntitlementIdentify potential KPIV’sProcess Mapping / Cause & Effect / FMEADetermine their likely impact
62 AnalyzeThe Analyze phase serves to validate the KPIVs, and to study the statistical relationship between KPIVs and KPOVs
63 Analyze : ToolsTo validate the KPIVsHypothesis Test2 samples t testAnalysis Of Variancesetc.To reveal the relationship between KPIVs and KPOVsRegression analysisCorrelation
64 Analyze : Hypothesis Testing The Null HypothesisStatement generally assumed to be true unless sufficient evidence is found to the contraryOften assumed to be the status quo, or the preferred outcome. However, it sometimes represents a state you strongly want to disprove.Designated as H0
65 The Alternative Hypothesis Analyze : Hypothesis TestingThe Alternative HypothesisStatement generally held to be true if the null hypothesis is rejectedCan be based on a specific engineering difference in a characteristic value that one desires to detectDesignated as HA
66 Analyze : Hypothesis Testing NULL HYPOTHESIS: Nothing has changed:For Tests Of Process Mean: H0: m = m0For Tests Of Process Variance: H0: s2 = s20ALTERNATE HYPOTHESIS: Change has occurred:MEAN VARIANCEINEQUALITY Ha: 0 Ha: 2 20NEW OLD Ha: 0 Ha: 2 20NEW OLD Ha: 0 Ha: 2 20
68 Analyze : Hypothesis Testing See Hypothesis Testing Roadmap
69 Example: Single Mean Compared to Target The example will include 10 measurements of a random sample:The question is: Is the mean of the sample representative of a target value of 54?The Hypotheses:Ho: m = 54Ha: m 54Ho can be rejected if p < .05
70 Single Mean to a Target - Using Minitab Stat > Basic Statistics > 1-Sample tP-value is greater than 5%,so we say the sample meanis representative of 54One-Sample T: C1Test of mu = 54 vs mu not = 54Variable N Mean StDev SE MeanCVariable % CI T PC ( , )
71 Our Conclusion Statement Because the p value was greater than our critical confidence level (.05 in this case), or similarly, because the confidence interval on the mean contained our target value, we can make the following statement:“We have insufficient evidence to reject the null hypothesis.”Does this say that the null hypothesis is true (that the true population mean = 54)? No!However, we usually then choose to operate under the assumption that Ho is true.
72 Single Std Dev Compared to Standard A study was performed in order to evaluate the effectiveness of two devices for improving the efficiency of gas home-heating systems. Energy consumption in houses was measured after 2 device (damper=1& damper =2) were installed. The energy consumption data (BTU.In) are stacked in one column with a grouping column (Damper) containing identifiers or subscripts to denote the population. You are interested in comparing the variances of the two populations to the current (s=2.4).ฉ All Rights Reserved Minitab, Inc.
73 Example: Single Std Dev Compared to Standard (Data: Furnace.mtw, Use “BTU_in”)Note: Minitab does not provide an individual c2 test for standard deviations. Instead, it is necessary to look at the confidence interval on the standard deviation and determine if the CI contains the claimed value.
74 Example: Single Standard Deviation Stat > Basic Statistics > Display Descriptive Statistics
77 Two Parameter Testing Step 1: State the Practical Problem Means: 2 Sample t-testSigmas: Homog. Of VarianceMedians: NonparametricsFailure Rates: 2 ProportionsStep 1: State the Practical ProblemStep 2: Are the data normally distributed?Step 3: State the Null Hypothesis:For s: For m:Ho: spop1= spop2 Ho: m pop1 = m pop2 (normal data)Ho: M1 = M2 (non-normal data)State the Alternative Hypothesis:Ha: spop1 ¹ spop2 Ha: m pop1 ¹ m pop2Ha: M1 ¹ M2 (non-normal data)
78 Two Parameter Testing (Cont.) Step 4: Determine the appropriate test statisticF (calc) to test Ho: spop1 = spop2T (calc) to test Ho: m pop1 = m pop2 (normal data)Step 5: Find the critical value from the appropriate distribution and alphaStep 6: If calculated statistic > critical statistic, then REJECT Ho.OrIf P-Value < (P-Value < Alpha), then REJECT Ho.Step 7: Translate the statistical conclusion into process terms.
79 Comparing Two Independent Sample Means The example will make a comparison between two group meansData in Furnace.mtw ( BTU_in)Are the mean the two groups the same?The Hypothesis is:Ho: m1 = m2Ha : m1 m2Reject Ho if t > t a/2 or t < -t a/2 for n1 + n2 - 2 degrees of freedom
80 t-test Using Stacked Data Stat >Basic Statistics > 2-Sample t
81 t-test Using Stacked Data Descriptive Statistics Graph: BTU.In by DamperTwo-Sample T-Test and CI: BTU.In, DamperTwo-sample T for BTU.InDamper N Mean StDev SE MeanDifference = mu (1) - mu (2)Estimate for difference:95% CI for difference: (-1.464, 0.993)T-Test of difference = 0 (vs not =): T-Value = P-Value = DF = 80
84 Characteristics About Multiple Parameter Testing One type of analysis is called Analysis of Variance (ANOVA).Allows comparison of two or more process means.We can test statistically whether these samples represent a single population, or if the means are different.The OUTPUT variable (KPOV) is generally measured on a continuous scale (Yield, Temperature, Volts, % Impurities, etc...)The INPUT variables (KPIV’s) are known as FACTORS. In ANOVA, the levels of the FACTORS are treated as categorical in nature even though they may not be.When there is only one factor, the type of analysis used is called “One-Way ANOVA.” For 2 factors, the analysis is called “Two-Way ANOVA. And “n” factors entail “n-Way ANOVA.”
85 General Method Step 1: State the Practical Problem Step 2: Do the assumptions for the model hold?Response means are independent and normally distributedPopulation variances are equal across all levels of the factorRun a homogeneity of variance analysis--by factor level—firstStep 3: State the hypothesisStep 4: Construct the ANOVA TableStep 5: Do the assumptions for the errors hold (residual analysis)?Errors of the model are independent and normally distributedStep 6: Interpret the P-Value (or the F-statistic) for the factor effectP-Value < 0.05, then REJECT HoOtherwise, operate as if the null hypothesis is trueStep 7: Translate the statistical conclusion into process terms
86 Step 2: Do the Assumptions for the Model Hold? Are the means independent and normally distributedRandomize runs during the experimentEnsure adequate sample sizesRun a normality test on the data by levelMinitab: Stat > Basic Stats > Normality TestPopulation variances are equal for each factor level (run a homogeneity of variance analysis first)For s Ho: pop1 = pop2 = pop3 = pop4 = ..Ha: at least two are different
87 Step 3: State the Hypotheses Mathematical Hypotheses:Ho: ’s = 0Ha: k 0Conventional Hypotheses:Ho: 1 = 2 = 3 = 4Ha: At least one k is different
88 Step 4: Construct the ANOVA Table One-Way Analysis of VarianceAnalysis of Variance for TimeSource DF SS MS F POperatorErrorTotalSOURCE SS df MS Test StatisticBetween SStreatment g - 1 MStreatment = SStreatment / (g-1) F = MStreatment / MSerrorWithin SSerror N - g MSerror = SSerror / (N-g)Total SStotal N - 1Where:g = number of subgroupsn = number of readings per subgroupWhat’s important the probabilitythat the Operator variation in meanscould have happened by chance.
89 Steps 5 - 7 Residual Analysis Step 5:Do the assumptions for the errors hold (residual analysis) ?Errors of the model are independent and normally distributedRandomize runs during the experimentEnsure adequate sample sizePlot histogram of error termsRun a normality check on error termsPlot error against run order (I-Chart)Plot error against model fitStep 6:Interpret the P-Value (or the F-statistic) for the factor effectP-Value < 0.05, then REJECT Ho.Otherwise, operate as if the null hypothesis is true.Step 7:Translate the statistical conclusion into process termsResidualAnalysis
90 Example, Experimental Setup Twenty-four animals receive one of four diets.The type of diet is the KPIV (factor of interest).Blood coagulation time is the KPOVDuring the experiment, diets were assigned randomly to animals. Blood samples taken and tested in random order. Why ?DIET A DIET B DIET C DIET D6359
91 Example, Step 2 Do the assumptions for the model hold? Population by level are normally distributedWon’t show significance for small # of samplesVariances are equal across all levels of the factorStat > ANOVA > Test for Equal VariancesHo: _____________Ha :_____________
92 Example, Step 3 State the Null and Alternate Hypotheses Ho: µ diet1= µ diet2= µ diet3= µ diet4 (or) Ho: t’s = 0Ha: at least two diets differ from each other(or) Ha:’s0Interpretation of the null hypothesis: the average bloodcoagulation time of each diet is the same (or) what youeat will NOT affect your blood coagulation time.Interpretation of the alternate hypothesis: at least onediet will affect the average blood coagulation timedifferently than another (or) what type of diet you keepdoes affect blood coagulation time.
93 Example, Step 4 Construct the ANOVA Table (using Minitab): Stat > ANOVA > One-way ...Hint: Store Residuals & Fits for later use
94 Example, Step 4 One-way Analysis of Variance Analysis of Variance for Coag_TimSource DF SS MS F PDiet_NumErrorTotalIndividual 95% CIs For MeanBased on Pooled StDevLevel N Mean StDev(------*------)(-----*----)(----*-----)(----*----)Pooled StDev =
95 Example, Step 5 Do the assumptions for the errors hold? Best way to check is through a “residual analysis”Stat > Regression > Residual Plots ...Determine if residuals are normally distributedAscertain that the histogram of the residuals looks normalMake sure there are no trends in the residuals (it’s often best to graph these as a function of the time order in which the data was taken)The residuals should be evenly distributed about their expected (fitted) values
96 Example, Step 5 Individual residuals - trends? Or outliers? How normal arethe residuals ?This graph investigateshow the Residualsbehave across theexperiment. This isprobably the mostimportant graph, since itwill signal that somethingoutside the experimentmay be operating.Nonrandom patternsare warnings.This graph investigateswhether the mathematicalmodel fits equally for lowto high values of the FitsHistogram - bell curve ?Ignore for small datasets (<30)Random about zerowithout trends?
97 When group sizes are equal Example, Step 6Interpret the P-Value (or the F-statistic) for the factor effectAssuming the residual assumptions are satisfied:If P-Value < 0.05, then REJECT HoOtherwise, operate as if null hypothesisis trueIf P is less than 5% thenat least one group meanis different. In this case,we reject the hypothesisthat all the group meansare equal. At least oneDiet mean is different.An F-test this large couldhappen by chance, but inless than one time out of2000 chances. Thiswould be like getting 11heads in a row from afair coin.Analysis of Variance for Coag_TimSource DF SS MS F PDiet_NumErrorTotalF-test is close to 1.00when group meansare similar. In thiscase, The F-test ismuch greater.When group sizes are equal
98 Work shop#6:Run Hypothesis to validate your KPIVs from Measure phase
99 Analyze : Analyze Phase’s output Refine: KPOV = F(KPIV’s)Which KPIV’s cause mean shifts?Which KPIV’s affect the standard deviation?Which KPIV’s affect yield or proportion?How did KPIV’s relate to KPOV’s?
100 ImproveThe Improve phase serves to optimize the KPIV’s and study the possible actions or ideas to achieve the goal
101 Improve : ToolsTo optimize KPIV’s in order to achieve the goalDesign of ExperimentEvolutionary OperationResponse Surface Methodology
102 Improve : Design Of Experiment Factorial ExperimentsThe GOAL is to obtain a mathematical relationship which characterizes:Y = F (X1, X2, X3, ...).Mathematical relationships allow us to identify the most important or critical factors in any experiment by calculating the effect of each.Factorial Experiments allow investigation of multiple factors at multiple levels.Factorial Experiments provide insight into potential “interactions” between factors. This is referred to as factorial efficiency.
103 Improve : Design Of Experiment Factors: A factor (or input) is one of the controlled or uncontrolledvariables whose influence on a response (output) is being studied inthe experiment. A factor may be quantitative, e.g., temperature indegrees, time in seconds. A factor may also be qualitative, e.g.,different machines, different operator, clean or not clean.
104 Improve : Design Of Experiment Level: The “levels” of a factor are the values of the factor being studied in the experiment. For quantitative factors, each chosen value becomes a level, e.g., if the experiment is to be conducted at two different temperatures, then the factor of temperature has two “levels”. Qualitative factors can have levels as well, e.g for cleanliness , clean vs not clean; for a group of machines, machine identity.“Coded” levels are often used,e.g. +1 to indicate the “high level” and -1 to indicate the “low level” . Coding can be useful in both preparation & analysis of the experiment
105 Improve : Design Of Experiment k1 x k2 x k3 …. Factorial : Description of the basic design.The number of “ k’s ” is the number of factors. The value of each“ k ” is the number of levels of interest for that factor.Example : A2 x 3 x 3 design indicates three input variables.One input has two levels and the other two, each have three levels.Test Run (Experimental Run ) : A single combination of factorlevels that yields one or more observations of the output variable.
106 Center Point Method to check linearity of model called Center Point. Center Point is treatment that set all factor as center for quantitative.Result will be interpreted through “curvature” in ANOVA table.If center point’s P-value show greater than a level, we can do analysis by exclude center point from model. ( linear model )If center point’s P-value show less than a level, that’s mean we can not use equation from software result to be model. ( non - linear )There are no rule to specify how many Center point per replicate will be take, decision based on how difficult to setting and control.
107 Sample Size by MinitabRefer to Minitab, sample size will be in menu of Stat->Power and Sample Size.
108 Sample Size By Minitab Specify number of factor in experiment design. Specify number of run per replicated.Enter power value, 1-b, which can enter more than one. And effect is critical difference that would like to detect (d).Process sigma
109 Center Point case Exercise : DOECPT.mtw “0” indicated that these treatments are center point treatment.
110 Center Point Case H0 : Model is linear Ha : Model is non linear Estimated Effects and Coefficients for Weight (coded units)Term Effect Coef StDev Coef T PConstantABCDA*BA*CA*DB*CB*DC*DA*B*CA*B*DA*C*DB*C*DA*B*C*DCt PtH0 : Model is linearHa : Model is non linearP-Value of Ct Pt (center point) show greater than a level, we can exclude Center Point from model.
111 Reduced ModelRefer to effect table, we can excluded factor that show no statistic significance by remove term from analysis.For last page, we can exclude 3-Way interaction and 4-Way interaction due to no any term that have P-Value greater than a level.We can exclude 2 way interaction except term A*B due to P-value of this term less than a level.For main effect, we can not remove B whether P-Value of B is greater than a level, due to we need to keep term A*B in analysis.
112 Center Point Case Final equation that we get for model is Fractional Factorial Fit: Weight versus A, B, CEstimated Effects and Coefficients for Weight (coded units)Term Effect Coef SE Coef T PConstantABCA*BFinal equation that we get for model isWeight = A – 5.62B C + 60AB
113 DOE for Standard Deviations The basic approach involves taking “n” replicates at each trial settingThe response of interest is the standard deviation (or the variance) of those n values, rather than the mean of those valuesThere are then three analysis approaches:Normal Probability Plot of log(s2) or log(s)*Balanced ANOVA of log(s2) or log(s)*F tests of the s2 (not shown in this package)* log transformation permits normal distribution analysis approach
114 Standard Deviation Experiment The following represents the results from 2 different 23 experiments, where 24 replicates were run at each trial combinationThe implication of this data set is that the standard deviations have already been calculated and that these columns represent the “crunched” data. Some students may feel that you would have been better off starting from the original data, but it’s worthwhile to emphasize that the class is oriented to learning new techniques and not performing mundane analyses.File: Sigma DOE.mtw*
115 Std Dev Experiment Analysis Set Up After putting this into the proper format as a designed experiment:Stat > DOE > Factorial > Analyze Factorial DesignUnder the Graph option / Effects Plots Normalln(s2)
116 Normal Probability Plots Plot all the effects of a 23 on a normal probability plotThree main effects: A, B and CThree 2-factor interactions: AB, AC and BCOne 3-factor interaction: ABCIf no effects are important, all the points should lie approximately on a straight lineSignificant effects will lie off the lineSingle significant effects should be easily detectableMultiple significant effects may make it hard to discern the line.
117 Probability Plot: Experiment 1 Results from Experiment 1 Using ln(s2)BMinitab does not identify these points unless they are very significant. You need to look at Minitab’s Session Window to identify.The plot shows one of the points--corresponding to the B main effect--outside of the rest of the effects
118 ANOVA Table: Experiment 1 Results from Experiment 1 Using ln(s2)Analysis of Variance for Expt 1Source DF SS MS F PABCErrorTotal
119 Sample Size Considerations The sample size computed for experiments involving standard deviations should be based on a and b, as well as the critical ratio that you want to detect--just as it is for hypothesis testingThe Excel program “Sample Sizes.xls” can be used for this purposeIf “m” is the sample size for each level (computed by the program), and the experiment has k treatment combinations, then the number of replicates, n, per treatment combination= 1 + 2(m-1)This sample size methodology is valid for situations where the factor effects are multiplicative; that is, one level of a variable may increase the standard deviation by 1.3, while one level of another variable may increase the standard deviation by 1.5, so that when those two levels are combined in a treatment, the net effect is (1.3(1.5) = 1.95.Of course, the sample size is valid only for the F testing approach.The additive model is much more complex, and the theory is not defined, particularly with regard to appropriate sample size.In case someone asks about the sample size per treatment combination, it’s based on the following.The sample size program gives the size m. Need df = m-1. Df is what is needed across k/2 treatments. So each treatment is to contribute 2df/k degrees of freedom each. Since the standard deviation takes 1 degree of freedom, the sample size per treatment combination n = 1 + 2df/k = 1+2(m-1)/k.k*
120 Workshop # 7 : Run DOE to optimize the validate KPIV to get the desired KPOV
121 Improve : Improve Phase’s output Which KPIV’s cause mean shifts?Which KPIV’s affect the standard deviation?Levels of the KPIV’s that optimize process performance
122 ControlThe Control phase serves to establish the action to ensurethat the process is monitored continuously for consistencyin quality of the product or service.
123 Control: ToolsTo monitor and control the KPIV’sError Proofing (Poka-Yoke)SPCControl Plan
124 Control: Poka-YokeWhy Poka-Yoke?Strives for zero defectsLeads to Quality Inspection EliminationRespects the intelligence of workersTakes over repetitive tasks/actions that depend on one’s memoryFrees an operator’s time and mind to pursue more creative and value added activities
125 Control: Poka-Yoke Benefit of Poka-Yoke? Enforces operational procedures or sequencesSignals or stops a process if an error occurs or a defect is createdEliminates choices leading to incorrect actionsPrevents product damagePrevents machine damagePrevents personal injuryEliminates inadvertent mistakes
126 Control: SPCSPC is the basic tool for observing variation and using statistical signals to monitor and/or improve performance. This tool can be applied to nearly any area.Performance characteristics of equipmentError rates of bookkeeping tasksDollar figures of gross salesScrap rates from waste analysisTransit times in material management systemsSPC stands for Statistical Process Control. Unfortunately, most companies apply it to finished goods (Y’s) rather than process characteristics (X’s).Until the process inputs become the focus of our effort, the full power of SPC methods to improve quality, increase productivity, and reduce cost cannot be realized.
127 Types of Control Charts The quality of a product or process may be assessed bymeans ofVariables :actual values measured on a continuous scalee.g. length, weight, strength, resistance, etcAttributes :discrete data that come from classifying units(accept/reject) or from counting the numberof defects on a unitIf the quality characteristic is measurablemonitor its mean value and variability(range or standard deviation)If the quality characteristic is not measurablemonitor the fraction (or number) of defectivesmonitor the number of defects
128 Defectives vs Defects Defective or Nonconforming Unit a unit of product that does not satisfy one or more of the specifications for the producte.g. a scratched media, a cracked casing, a failed PCBADefect or Nonconformitya specific point at which a specification is not satisfiede.g. a scratch, a crack, a defective IC
129 Shewhart Control Charts - Overview Walter A Shewhart
131 Control: SPC Choosing The Correct Control Chart Type u c p, np p X, mR Type ofdataIndividualmeasurements orsub-groups?NormallyDistributeddata?Interestedprimarily insudden shifts inmean?Constantsub-group size?Area of opportunityconstant from sample tosample?Counting defectsor defectives?ucp, nppX, mRMA, EWMA,or CUSUMX-bar, RX-bar, sUse of modified controlchart rules okay onx-bar chartData tends to be normallydistributed because of centrallimit theoremMore effective indetecting graduallong-term changesAttributesVariablesDefectivesYesNoDefectsMeasurementSub-groupsIndividuals
132 Control: Control Phase’s output Y is monitored with suitable toolsX is controlled by suitable toolsManage the INPUTS and good OUTPUTS will follow
134 Hard SavingsSavings which flow to Net Profit Before Income Tax (NPBIT)Can be tracked and reported by the Finance organizationIs usually a reduction in labor, material usage, material cost, or overheadCan also be cost of money for reduction in inventory or assets
135 Finance Guidelines - Savings Definitions Hard SavingsDirect Improvement to Company EarningsBaseline is Current Spending ExperienceDirectly Traceable to ProjectCan be AuditedHard Savings ExampleProcess is Improved, resulting in lower scrapScrap reduction can be linked directly to thesuccessful completion of the project
136 Potential SavingsSavings opportunities which have been documented and validated, but require action before actual savings could be realizedan example is capital equipment which has been exceeded due to increased efficiencies in the process. Savings can not be realized because we are still paying for the equipment. It has the potential for generating savings if we could sell or put back into use because of increases in schedules.Some form of a management decision or action is generally required to realize the savings
137 Finance Guidelines - Savings Definitions Potential SavingsImprove Capability of company ResourcePotential Savings ExampleProcess is Improved, resulting in reducedmanpower requirementHeadcount is not reduced or reduction cannotbe traced to the projectPotential Savings might turn into hard savings if the resource is productively utilized in the future
138 Identifying Soft Savings Dollars or other benefits exist but they are not directly traceableProjected benefits have a reasonable probability (TBD) that they will occurSome or all of the benefits may occur outside of the normal 12 month tracking windowAssessment of the benefit could/should be viewed in terms of strategic value to the company and the amount of baseline shift accomplished
139 Finance Guidelines - Savings Definitions Soft SavingsBenefit Expected from Process ImprovementBenefit cannot be directly traced to SuccessfulCompletion of ProjectBenefit cannot be quantifiedSoft Savings ExampleProcess is Improved; decreasing cycle time
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