著名跨國公司的6_Sigma_BB黑帶培訓(xùn)資料-__Booster_Wk2_02_REVIEW_0704_V3

1、Booster Week 1 ReviewUse this entire section to give a good review of week 1. Spend time on each slide and get the class to interact and address what they learned/remember from week 1.Let the class lead discussions.It is Monday morning and you may have to “drag” them into the discussions.The purpose

2、 is to stimulate their memories and to reinforce the week 1 concepts.They will need to recall some of this material in order to make the second week more meaningful.KEEP THEM ENGAGED!2Step 1: DEFINEGoal Define the projects purpose and scope and get background on the process and customerOutput A clea

3、r statement of the intended improvement and how it is to be measured A high level map of the process A list of what isimportant to thecustomerIMPROVEProjectCharterINSTRUCTORS NOTES:Discuss each output. 3Step 2: MEASUREGoalFocus the improvement effort by gathering information on the current situation

4、Output Baseline data on current process performance Data that pinpoints problem location or occurrence A more focused problem statementIMPROVEData Collection PlanCapabilitySamplingPatternsMSAINSTRUCTORS NOTES:Really planning to measure. Set up base line data. Need plan to collect data in a way that

5、it can be properly analyzed. Most of the data available today is output data, not necessarily input data.Discuss each item of Measure.MSA; Measurement System Analysis4Step 3: ANALYZEGoalIdentify deep causes and confirm them with dataOutputA theory that has been tested and confirmedDOEData AnalysisIM

6、PROVE5Step 4: IMPROVEGoalDevelop, try out, and implement solutions that address root causesOutputPlanned, tested actions that should eliminate or reduce the impact of the identified root causesSolutionsFMEAPilotImplemen-tationIMPROVEINSTRUCTORS NOTES:Develop potential solutions. Obtain potential sol

7、utions from FMEA. Always pilot your potential solution to determine if it is effective. Implementation is last phase of Improve.6Step 5: CONTROLGoal Use data to evaluate both the solutions and the plans Validate that all changes adhere to all operating company change control, and compliance requirem

8、ents Maintain the gains by standardizing processes Outline next steps for on-going improvement including opportunities for replicationOutput Before and After analysis Monitoring system Completed documentation of results, learning learned, and recommendationsControlStandardizeDocumentMonitorEvaluateC

9、losureIMPROVEINSTRUCTORS NOTES:Money belts will enter and and track your savings to see if the savings are real. Will track improvements to see if they are in effect over time. Monitor by process owner.7Desired Measurement Characteristic for Continuous VariablesData from repeated measurement of same

10、 itemGood repeatability if variation is small *1. AccuracyThe measured value has little deviation from the actual value. Accuracy is usually tested by comparing an average of repeated measurements to a known standard value for that unit.2. RepeatabilityThe same person taking a measurement on the sam

11、e unit gets the same result.INSTRUCTOR NOTES:Ensure students understand difference between accuracy, repeatability, reproducibility, and stability, and adequacy of resolution.Continued on subsequent slides8Desired Measurement Characteristic for Continuous Variables, cont.3. ReproducibilityOther peop

12、le (or other instruments or labs) get the same result you get when measuring the same item or characteristic.* Small relative to a) product variationandb) product tolerance (the width of the product specifications)Data from Part XData Collector 1Data Collector 2Good reproducibility if difference is

13、small *Data from Part X9Desired Measurement Characteristic for Continuous Variables, cont.4. StabilityMeasurements taken by a single person in the same way vary little over time.* Small relative to a) product variationandb) product tolerance (the width of the product specifications)INSTRUCTOR NOTES:

14、This is different from “repeatability” in that we are talking about the object of measure or the measurement tool being somehow affected by the passage of time. Repeatability addressed the “measurers” consistency.10Desired Measurement Characteristic for Continuous Variables, cont.5. Adequate Resolut

15、ionThere is enough resolution in the measurement device so that the product can have many different values. 5.1 5.2 5.3 5.4 5.5XXXXXXXXXXXXXXXXGood if 5 or more distinct values are observedINSTRUCTOR NOTES:At a simple and somewhat obvious level, the resolution must be in sync with project goals11Mea

16、surement System Indices %R&RDescribes the variation of the measurement system in comparison to the part variation of the process %P/TDescribes the variation of the measurement system in comparison to the part tolerances totalsystemtmeasuremenSSRR_&%TolerancesSTPsystemtmeasuremen _*15. 5/%Unacceptabl

17、eDesired Acceptable Borderline 0%10%20%30%100% General guidelines for interpreting Gage R&R results.INSTRUCTOR NOTES:Discuss each of the indices:%R&R quantifies the variation attributable to the measurement system as a percent of total variation. The “R&R” is repeatability and reproducibility as you

18、 might guess.%P/T describes how of the tolerance is taken up by the measurement system. The “5.15” comes from +- 2.575 std devs which captures 99% of the data and has become the standard figure for % P/T . . The graphic at the bottom will be clarified upon running through the Minitab example.12Outpu

19、t From Gage Run ChartINSTRUCTOR NOTES:*Explain the meaning of the chart, and interpret the results.Ie. Is there a difference between or within measurements and people ?13Interpreting the Gage R&R Output From MinitabINSTRUCTOR NOTES:* Work slowly through the minitab exercise, and ask for progress and

20、 understanding, for none native speakers and computer skill level.* Explain that minitab produces large amounts of statistical data, and that, the only important figures are :-%R&R 30%P/T 414Interpreting Gage R&R:Minitabs Graphical OutputINSTRUCTOR NOTES:*Explain the meaning of the charts, and inter

21、pret the results.*Hone in on specific / important charts i.e. Components of variation.Ask trainees to give feedback on conclusions they have drawn, from the charts.15Minitabs Attribute OutputINSTRUCTOR NOTES:* Explain minitab output, and interpret results16INSTRUCTOR NOTES:* Explain output graphsMin

22、itabs Attribute Output17The Focus of Analyze Y = f (X1, X2, X3, ., Xn)X1, X3, X5IdentificationVerificationQuantificationWhat vital few process and input variables (Xs) affect critical to quality process performance or output measures (Ys)?18Process or Data Door?Process DoorData DoorTo understand the

23、 drivers of variation in the processTo tackle quality problems and wasteTo understand the root cause of differences between outputsTo improve the under-standing of process flowTo tackle cycle time problemsTo identify opportunities to reduce process costsStratificationScatter DiagramsMulti-Vari Analy

24、sisDetailed Process MapValue Added AnalysisCycle Time AnalysisIt is recommended to go through both doors to make sure that potential causes are not overlooked.19Multi-Vari DisplayBack Front0.050.040.030.020.01 Finish Thickness Day 1Day 2AMPMAMPMExample of Multi-vari display231Panel 1 2 3 1 2 3 1 2 3

25、 1 2 3Sample, 3 consecutive panels taken at one time. This multi-vari chart shows four families of variation. We plot measures of film thickness on front and back sides of panels produced on a paint line.1. Within-panel variation 2. Unit-to-unit variation 3. Morning-to-afternoon variation 4. Day-to-

26、day variation 204/19/994/18/99PMPMAMAMPMPMAMAM0.0450.0350.0550.0450.03512Date123Multi-Vari Chart for FilmThicknessFactor 1: Sample; Factor 2: AM/PM; Factor 3: Date; Factor 4: LineLineSampleShowing Changes in Average on the Multi-Vari ChartThe vertical change in the lines connecting mean symbols show

27、s the average contribution of the factor to the observed variation.The largest vertical change matches the dashed lines connecting the squares (the AM to PM variation). The smallest vertical change matches the dotted line connecting the diamonds (the day to day variation).21 1 2 3 4 5 6 7 8 91011121

28、2341234123412341234123412341234123412341234123410.1510.2510.3510.45CoilThicknessLMRMulti-Vari Chart for Thickness By Width - CoilLengthWidthShowing Changes in Average on the Multi-Vari Chart22Z-Value: Same As a “Standard” Normal ValueSXinterest)-of-(valueZ-3-2-10123-3-2-10123mean=0st. dev. =1Z-value

29、 anywhere on this scaleA “Standard” Normal DistributionZ-value How many standard deviations the value-of-interest is away from the mean23Normal Tables: Looking Up ProbabilitiesTwo types of tables1. Reports area (to the left of) the value-of-interestZTabled AreaWe used this table in the basic courseA

30、rea under the curve = probabilityZ Whole Number 0.000032 0.000021 0.000013 0.000009 0.000005 0.000003 0.000002 0.000001 0.000001 0.000000 0.001350 0.000968 0.000687 0.000483 0.000337 0.000233. 0.000159 0.000108 0.000072 0.000048 0.022750 0.017864 0.013903 0.010724 0.008198 0.006210 0.004661 0.003467

31、 0.002555 0.001866 0.158655 0.135666 0.115070 0.096801 0.080757 0.066807 0.054799 0.044565 0.035930 0.028716 0.500000 0.460172 0.420740 0.382019 0.344578 0.308538 0.274253 0.241964 0.211855 0.184060 0.500000 0.539828 0.579260 0.617911 0.655422 0.691462 0.725747 0.758036 0.788145 0.815940 0.841345 0.

32、864334 0.884930 0.903199 0.919243 0.933193 0.945201 0.955435 0.964070 0.971284 0.977250 0.982136 0.986097 0.989276 0.991802 0.993790 0.995339 0.996533 0.997445 0.998134 0.998650 0.999032 0.999313 0.999517 0.999663 0.999767 0.999841 0.999892 0.999928 0.999952 0.999968 0.999979 0.999987 0.999991 0.999

33、995 0.999997 0.999998 0.999999 0.999999 1.000000-4-3-2-1-0012340.0Z Decimal24Looking up p-values in MinitabCumulative Distribution FunctionNormal with mean = 500.000 and standard deviation = 50.0000 x P( X Probability Plot If the data are Normal, the points will fall on a

34、“straight” line “Straight” means within the 95% confidence bandsYou can say the data are Normal if approximately 95% of the data points fall within the confidence bands25354555 1 51020304050607080909599DataPercentML EstimatesMean:StDev:40.12714.8672195% confidence bands29What Is a Normal Probability

35、 Plot? Data values are on X-axis Percentiles of the Normal distribution are on the Y-axis (unequal spacing of lines is deliberate)Normal Probability PlotTen equally spaced percentilesfrom the Normal distribution Equally spaced percentiles divide the Normal curve into equal areas The percentiles matc

36、h the percents on the vertical axis of the Normal probability plot25354555 1 51020304050607080909599DataPercentML EstimatesMean:StDev:40.12714.867212030107080905010%10%10%10%10%10%30Conclusions FromTwo Normal Probability PlotsConclusion Not a serious departure from NormalityConclusion There is a ser

37、ious departure from Normality25354555 1 51020304050607080909599DataPercentML EstimatesMean:StDev:40.12714.86721-2-101234 1 51020304050607080909599DataPercentML EstimatesMean:StDev:1.136271.0736331Log: A Commonly Used Shape-Changing Transformation The log transformation is usually appropriate for cyc

38、le time data. One unit on the log scale is equal to a factor of 10 on the measurement scale:MeasurementScaleLog Scale100031002101100.1-10.01-20.001-332Frequently Used TransformationsLog(Y)YYYSquare Root-NormalLog-NormalYYTLog(Y)YTData DistributionTransformationTransformed Distribution33Frequently Us

39、ed Transformations, cont.Y1YYInverse-NormalInverse Square Root-NormalY1YTY1YTY1Data DistributionTransformationTransformed Distribution34Power Transformations A power transformation raises Y to the power of Power transformations include those weve already seen:(Power)Common Names Y-2 -1 -0.5 0 0.5 1

40、2 Reciprocal (inverse) squared Reciprocal (inverse) Reciprocal square root (inverse) Log Square root - Squared 1 Y21 Y 1 YLog(Y)YNo transformationY235Using the Box-Cox Method to Select a Transformation-5-4-3-2-101234512395% Confidence IntervalStDevLambdaLast Iteration InfoLambdaStDev0.3930.4500.5070

41、.5530.5530.553LowEstUpBox-Cox Plot for Y Choose a lambda (power) from within the recommended 95% confidence interval that corresponds to a simple transformation, if possible (like those shown in the power transformation table)36Two Types of Errors in Hypothesis TestingActual (Truth)Groups areSameGro

42、ups areDifferentAccept H0:Groups are SameNo ErrorType II ErrorConclusionorDecisionReject H0:Groups are DifferentType I ErrorNo ErrorThere are four possible outcomes to any decision we make based on a hypothesis test: We can decide the groups are the same or different, and we can be right or wrong. B

43、oth types of error are important. Guarding too heavily against one error increases the risk of the other error. Increasing the sample size: Reduces the risk of Type II errors.Allows you to detect smaller differences.Actual (Truth)InnocentGuiltyInnocentInnocentGuilty & you walkConclusionorDecisionGui

44、ltyInnocent & in jailGuiltyExample:Court Cases.INSTRUCTOR NOTESRefer to the example: Criminal case is based on reasonable doubt (Innocent until proven guilty ). The preference is to have a low Type I (alpha) error and high Type II (beta) error. They would like to have a higher percentage that are gu

45、ilty and walk then are innocent and go to jail.Civil case is based on a low Type II (beta) error and high Type I error. They prefer that you pay some type of fine whether or not you are innocent, instead of getting away with the crime and fine.37The F-Distribution Test for Equal Variances2221SSF 222

46、1 The F-distribution is the ratio of two variances: Its skewed with a tail to the right The lower bound is 0 The mode (most common value) is almost 1 It depends on two separate degrees of freedom:df for variance in numeratordf for variance in denominator It assumes each group of data Is from a Norma

47、l distribution The Null hypothesis is: The F-test can be used when comparing the variances of two groups The statistical test is called “Test for Equal Variances” or “F-test”.01FTail area = P-valueThe degrees of freedom is important, but beyond the scope of this class. In Minitab we will use the p-v

48、alue.38Practice: AnswersTest for Equal VariancesBoth P-values are .05, so do not reject the H0. Conclude the variances (of scrap) for each of the seven materials (vendors AG) are not significantly different. The assumption of “same variances” for each group is satisfied.0.51.01.52.095% Confidence In

49、tervals for SigmasBartletts TestTest Statistic: 5.639P-Value : 0.465Levenes TestTest Statistic: 0.940P-Value : 0.470Factor LevelsABCDEFGTest for Equal Variances for Scrap39t-test: A Statistical Test for Comparing Two Group AveragesWe judge the difference between two group averages by using a statist

50、ical test called a t-test (we will use Minitab to do it). The t-distribution:Has more variation than a Z distribution (and thus different areas in the tails, meaning different P-values).Its spread of variation depends on the “degrees of freedom” (df). We wont go into details here about df, but think

51、 of it as the amount of information left in the sample after estimating the means and standard deviations of the two groups.Is appropriate to use since we estimated the means and variances (proven through statistical theory)(S0 - )XX( BABA )B-A(tINSTRUCTOR NOTESEmphasize that Minitab will do the com

52、putations.40Minitab Follow Along: t-testMinitab output (session window)Two Sample T-Test and Confidence IntervalTwo sample T for New$Scrap vs Std$Scrap N Mean StDev SE MeanNew$Scra 10 143.3 32.4 10Std$Scra 10 149.4 31.7 1095% CI for mu New$Scra - mu Std$Scra: ( -36, 24)T-Test mu New$Scra = mu Std$Sc

53、ra (vs not =): T = -0.42 P = 0.68 DF = 18Both use Pooled StDev = 32.1H0:Ha:Confidence interval goes from negative to positive (includes 0); P-value is not .05ConclusionBased on this regular t-test, do not reject the H0. Cannot conclude there is a significant difference between $Scrap for the new and

54、 standard methods. If there is a true difference, either the variation is too large or the sample is too small to detect it.41Matched or Paired Data StructureData formatSampling Unit1 2 3 n Measure AMeasure B DurabilityPersonJohn Sally Kai Fred NewShoe SoleOriginal Shoe Sole 7 5 9 811 915 12Example4

55、2Minitab Follow Along: Paired t-testQuestion 2 Answers12.510.07.55.02.50.0-2.53210DifferencesFrequencyHistogram of Differences(with Ho and 95% t-confidence interval for the mean)X_Ho1050DifferencesBoxplot of Differences(with Ho and 95% t-confidence interval for the mean)X_Ho1050DifferencesDotplot of

56、 Differences(with Ho and 95% t-confidence interval for the mean)X_Ho43Minitab Follow Along: Paired t-testPaired T-Test and Confidence IntervalPaired T for New$Scrap - Std$Scrap N Mean StDev SE MeanNew$Scrap 10 149.4 31.7 10.0Std$Scrap 10 143.3 32.4 10.2Difference 10 6.08 4.82 1.5295% CI for mean dif

57、ference: (2.63, 9.53)T-Test of mean difference = 0 (vs not = 0): T-Value = 3.99 P-Value = 0.003HoHaConfidence interval does not include 0;P-value Power and Sample Size To use this menu, youll need to know four things, shown in the following table.Sample size (n) depends on Where to get itEffect on s

58、ample size (n)1. Standard deviation of dataYou estimate itAs standard deviation increases, n increases2. Significance level (P-value = probability of Type I error = 1 confidence level)You decide (usually set at .05)As the P-value decreases, (or confidence increases), n increases3. Size of difference

59、 (effect) you want to detectAs size of the difference you need to detect decreases, n increasesYou decide what size is important4. Power the probability of detecting the difference when it truly exists (1probability of Type II error)*As power increases, n increasesYou decide how important it is to d

60、etect (usually set at 80% 51Power and Sample Size2-Sample t TestTesting mean 1 = mean 2 (versus not =)Calculating power for mean 1 = mean 2 + differenceAlpha = 0.05 Sigma = 10 Sample Target ActualDifference Size Power Power 12 16 0.9000 0.9072Minitab Follow Along: Determine n for Comparing Two Group