1、Additional Department InfoCopyright 2002 Motorola. All rights reserved.Six Sigma Black Belt Program 2.3 Evaluate Variation2.3 - 1Six SigmaBlack Belt Program2.3 - Evaluate VariationThese materials, including all attachments, are protected under the copyright laws of the United States and other countr

2、ies asan unpublished work. These materials contain information that is proprietary and confidential to Motorola University and are thesubject of a License and Nondisclosure Agreement. Under the terms of the License and Nondisclosure Agreement, thesematerials shall not be disclosed outsider the recip

3、ients company or duplicated, used or disclosed in whole or in part by therecipient for any purpose other than for the uses described in the License and Nondisclosure Agreement. Any other use ordisclosure of this information, in whole or in part, without the express written permission of Motorola Uni

4、versity is prohibited.Copyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 22.3 Evaluate VariationObjectiveTo develop an understanding of the importance of variation in managingprocesses and how to measure variation.Key TopicsUnderstanding VariationMeasuring Variation Summary Sta

5、tisticsCharting VariationControl ChartsHandling Discrete Data2.1DetermineWhat toMeasure2.2ManageMeasurement2.4EvaluateMeasurementSystems2.3EvaluateVariation2.5DetermineProcessPerformanceAdditional Department InfoCopyright 2002 Motorola. All rights reserved.Six Sigma Black Belt Program 2.3 Evaluate V

6、ariation2.3 - 3Understanding VariationCopyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 4Data VariationUnderstanding Variation Variation means that a process does not produce exactly thesame result every time the product or service is delivered. Variation exists in all process

7、es. Variation costs money. Measuring and understanding variation in our business processeshelps identify specifically what the current level of performanceis and what needs to change in order to reduce the variabilityand therefore reduce the defects delivered to customers.Additional Department InfoC

8、opyright 2002 Motorola. All rights reserved.Six Sigma Black Belt Program 2.3 Evaluate Variation2.3 - 5Example Variation Costs MoneyCopyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 6What Causes Variation?SuppliersProcess InputsBusiness ProcessProcess OutputsCriticalCustomerReq

9、uirementsDefectsVariation in theoutput ofprocesses causesdefectsRoot causeanalysis ofvariation leads topermanent defectreductionY vs. XFrequencyofDeliveryTimesCopyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 7Delivery TimeEffects of Variation?Critical CustomerRequirement = 10

10、 dayss = Variation or data spreadDefects: Serviceunacceptable to customerx = 7.7 days123456789101112FrequencyofDeliveryTimesCopyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 8Delivery TimeRequirement = 10 daysx = 7.7 days123456789101112s = Variation or data spreadDefects: Serv

11、iceunacceptable tocustomerDefect ReductionVariation ReductionIf we reduce variation, then fewer observations will fall abovethe customer requirement of 10 days.Critical CustomerFrequencyofDeliveryTimesCopyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 9Delivery TimeCritical Cus

12、tomer Requirement= 10 daysDefects: Serviceunacceptable to customerx = 6 days123456789101112Variation and Mean ReductionIf we reduce both the average delivery time and the variationin delivery time, we can further reduce those times that do notmeet customer requirements.Copyright 2002 Motorola. All r

13、ights reserved.2.3 Evaluate Variation2.3 - 10How Does Variation Affect ProcessPerformance? Measuring variation means that we can clearly define how well we aremeeting customer requirements. By observing or measuring the process over time you can determinethe mean and standard deviation, and therefor

14、e, the performance ofthe process against customer requirements. Measuring process performance requires that we measure twoelements: process performance. customer requirements. The goals of Sigma Business Improvement are to center the processwell within customer requirements through reducing variatio

15、n, first byeliminating special causes of variation, and then the common causesthat are necessary in order to center the process outputs fully withincustomer requirements.Additional Department InfoCopyright 2002 Motorola. All rights reserved.Six Sigma Black Belt Program 2.3 Evaluate Variation2.3 - 11

16、Summary StatisticsCopyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 12Summary Statistics Data can be summarized both numerically andgraphically using Summary Statistics and graphs orplots. Attribute data can usually be summarized by counts,proportions or time graphs of these t

17、wo statistics. Variables data can be summarized by: A measure of the center or location of the data. A measure of the spread of the data. Various plots or graphs of the data. Summary statistics are numbers based on samples froma population. They are point estimates (singlenumbers) of characteristics

18、 of the distribution ofpopulation values.xi nCopyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 13Measures of Location Two measures of the location, or center, of thedata are the mean and the median. The mean measures the average of the data. The median, or 50th percentile, is

19、a measure ofthe middle of the data.x =sumcount=ni = 1902.3 - 14Measures of Location Median = the point where half the data is above andhalf the data is below:Median =Mean = 5.62244667799Median =2244669990Median =Mean = 21.822446677The Mean is more sensitive to outliers, or unusual data points, thant

20、he Median.2.3 Evaluate Variation Copyright 2002 Motorola. All rights reserved. (x x )Copyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 15Measures of SpreadTwo different data sets can have the same mean (i.e.,location) but a different spread. Range:Measures the distance between

21、 the extreme values.R = Maxdata Mindata Variance: The average squared distance of each datapoint from the mean.s2 =2ni =1in 1Copyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 16Measures of Spread Standard deviation: The square root of the variance.s = s2The standard deviation

22、is measured in the same units asthe mean. The range is more sensitive to outliers than the varianceor standard deviation. Note: For moderate values of n, say n 10, thestandard deviation is a better measure of spread.However, for the small sub-group sample sizes oftenused in control charts (n = 4, 5,

23、 6), the range issatisfactory.Copyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 17Measures of Spread Interquartile range (IQR): The measure of the middle 50% of thedata, or, the difference between the 75th percentile point and the25th percentile point. The pth percentile point

24、 (or quantile) of a set of data is defined as: A value below which at least p% of the data falls andsimultaneously at least(1-p)% of the data exceeds the value. The 75th percentile of a data set is a value that exceeds at least75% of the data points and is less than or equal to at least 25% ofthe da

25、ta. The 25th percentile of a data set is a value that exceeds at least25% of the data points and is less than or equal to at least 75% ofthe data. Quartiles are the 75th and 25th percentiles of the data set.Additional Department InfoCopyright 2002 Motorola. All rights reserved.Six Sigma Black Belt P

26、rogram 2.3 Evaluate Variation2.3 - 18Charting VariationCopyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 19Charting Variation - HistogramsA histogram is a bar graph that displays the results for a sampleof performance data (daily commuting time, for example) inpicture form. Th

27、is picture is sometimes called a frequencydistribution because it shows clearly how frequently eachseparate value appears in the data.Copyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 20Charting Variation NormalDistributionsingle peak equal to averagecontinuouslydeclining on b

28、othsidessymmetrical sidesxCopyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 21A normal distribution is completely described whenwe know the x and s of the data.Charting Variation Standard DeviationThe standard deviation noted as - for the population.s - for the sample.Normal D

29、istributionSXiXCopyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 22Standard Variation: Yield and the NormalCurveThe normal curve can also be partitioned as shown below,and because of its perfect symmetry, the following rulesapply:Number of standard deviationson either side of

30、the mean123456% of data betweenthese limits68.2695.4699.7399.993799.99994399.9999998Standard Normal DistributionXNumber of Standard Deviations from the Mean-6-5-4-3-2-10123456Copyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 23What type of distribution is this?What could cause

31、 this?Discussion: Histogram Interpretation1201008060402010233649627588 101 114 127What type of distribution is this?What could cause this?3025201510534.567.5910.5 12 13.5 15 16.5Copyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 24Box Plots Box Plot: An alternative to the histo

32、gram for graphicallyrepresenting the distribution of data. Combines both distribution information and summary statistics onthe same graph. Especially valuable when the objective is to compare two or moregroups, such as two different measuring tools or three shifts. A box plot consists of a “box,” tw

33、o “tails,” “outliers” andinformation on various summary statistics. The length of the box describes the middle 50% of the data (theinterquartile range). The two tails extend out to the expected range of themeasurements. Outliers, if they exist in the data, are indicated aspoints outside this expecte

34、d range.Copyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 25Outliers (w/case #s)Upper TailUpper QuartileMedianLower QuartileLower TailOutlier (w/case #s)325233Box Plots andHistogramsCopyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 26Box Plots contain th

35、e following:The Median (M):The “middle” value of the data,the 50% percentile or quantile.The Upper Quartile (UQ):The 75% quantile of the data.The Lower Quartile (LQ):The 25% quantile of the data.The Interquartile Range (IQR):The upper quartile minus thelower quartile.Upper Tail:The largest data valu

36、e that issmaller than UQ + 1.5(IQR).Lower Tail:The smallest data value that islarger than LQ 1.5 (IQR).Outliers:Points that are too extremerelative to the othermeasurements:If a value is UQ + 1.5 IQR, orIf a value is LQ 1.5 IQR.Box PlotsCopyright 2002 Motorola. All rights reserved.2.3 Evaluate Varia

37、tion2.3 - 271915 74Box Plots - Skewed DistributionCopyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 28262524232221201918171615142625242322212019181716151426252423222120191817161514XXXXCharting Variation Run ChartsThree Different Run Charts with the Same DistributionXXXXXXXXX16

38、X17X18X19X20X21X22X23X24Additional Department InfoCopyright 2002 Motorola. All rights reserved.Six Sigma Black Belt Program 2.3 Evaluate Variation2.3 - 29Control ChartsCommutingTime(mins)Copyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation252423222120191817161514Charting Variation Con

39、trol Charts26MT W Th F MT W Th F M T W Th F M T W Th F MDays2.3 - 30UCLCLLCLCopyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 31Control Charts - BasicsControl charts Help manage variation. Help monitor the process. Provide an easy to understand visual indicator of processperfo

40、rmance. Help sigma improvement teams understand the rootcause of the variation in a process. Provides a method to determine process stability.Copyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 32Control Charts - BasicsSteps to building an appropriate control chart.1. Determine

41、the type of data.2. Collect data consistently with control chartingin mind.3. Select the appropriate control chart.4. Build the control chart.5. Analyze process performance.6. Take corrective action.Copyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 33Control Chart TheoryThe co

42、ntrol chart, invented by Dr. Shewhart, is a common sense way todetermine if a process is exhibiting common cause or special causevariation.This is another way of asking, is the process “in control” or “out ofcontrol?”Common Cause Variation:Variation that is random and inherent inthe system.Special C

43、ause Variation:Variation that is unpredictable,intermittent, and usually related to onlyone element of the process. May causethe process to be unstable.CommutingTime(mins)CommutingTime(mins)Copyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 34Eliminate Special CausesUCLCLLCLIn

44、Control Variation15141716182019212322262524M T W Th F M T W Th F M T W Th F M T W Th F MDays23456TimeUCLCLLCL1143Out of Control Variation2 53Additional Department InfoCopyright 2002 Motorola. All rights reserved.Six Sigma Black Belt Program 2.3 Evaluate Variation2.3 - 35Handling Discrete DataNumbero

45、fDefectsIncorrectSettingsComponentMissingOtherMountedWrong2.3 - 36Defects FoundArranging data on a Pareto charthighlights “the vital few,”providing focus for constructingthe problem statement andconducting further analysis todetermine root cause.2.3 Evaluate VariationIncorrect setting8 = 50%16Compon

46、ent Missing8 + 3 = 69%16Mounted Wrong8 + 3 + 2 = 81%16Other8 + 3 + 2 + 3 = 100%16Copyright 2002 Motorola. All rights reserved.323n = 1650%869%81%100%75%50%25%0%161412108642Type of DefectPareto AnalysisPareto Charts A Way to Stratify DataPareto analysis is used to organize data to show what major fac

47、tors make up the subject beinganalyzed. Frequently it is referred to as “the search for significance.”The Pareto chart is arranged with its bars descending in order, beginning from the left.The basis for building a Pareto is the 80/20 rule. Typically, approximately 80% of the problem(s) resultfrom approximately 20% of the causes.Copyright 2002 Motorola. All rights reserved.2.3 Evaluate Variation2.3 - 37Pareto ConstructionHow to C