六西格玛培训教材GE课件

1、Minitab Primer Introduction to StatisticalData Analysis With MinitabIntroductionThis primer is designed to provide one with the skills necessary to effectively employ Minitab within the Six Sigma framework. It begins with an introduction to selected file, data manipulation, and help functions, follo

2、wed by a series of demonstrations related to transaction and service quality. The student is encouraged to work through each demonstration, following the lead of the instructor. Each demonstration begins with a page highlighting the Minitab functions applied in working-through the examples. These pa

3、ges reflect the commands that the user would see on the screen while using Minitab (the heirarchical structure of Minitab is preserved).It is assumed that the user is familiar with basic statistics, e.g., hypothesis testing and regression analysis. A companion primer, entitled Statistics Primer - In

4、troduction to Statistics Through Graphical Analysis is available on the World-Wide-Web (GE Corporate) for those requiring a review of fundamental statistics.Augie Stagliano Pittsfield, MAOctober 1996Takeaways After Completing This Training, You Will Be Able To Import Data Files Perform Basic Data Ma

5、nipulation Techniques Use Functions to Perform Calculations Construct and Interpret Various Graph Types Generate and Interpret Basic Statistical Information Apply One and Two Sample Hypothesis Tests Perform Simple Linear Regression Apply c2 Tests and One-Way ANOVA An Overview of Applied Statistical

6、Techniques Stressing Interpretation of Analytical ResultsFile Commands New Worksheet Open Worksheet Merge Worksheet Save Worksheet Print Window Get Worksheet Information Display Data Restart Minitab ExitHelp and Manip Commands Help Commands: Contents Getting Started. How Do I. Search for Help On. So

7、rt Stack UnstackManip Commands: Demonstration One STAT Basic Statistics Descriptive Statistics 1-Sample t 2-Sample t Correlation Tables Tally Chisquare Test CALC Probability Distributions Normal STAT ANOVA ONEWAYBasic Statistical Analysis GRAPH Plot Time Series Plot Histogram Boxplot Character Graph

8、s Dotplot STAT SPC Run ChartGraphical Analysis STAT Regression Regression Fitted Line PlotRegression AnalysisChoice of Tool Depends Upon the Requirements of the AnalysisExample: Receivables “Days-to-Collection” Data File: days.xlsVariable: DaysCollection terms for receivables is 60 days. Payments ar

9、e entered into a data collection system in the same time-order as they are received. Characterize this process and determine its long term z-value and sigma. Also, test that the average days-to-collection is equal to 50 days (Business Target).Demonstration One Receivables Process Characterization De

10、scriptive StatisticsVariable N N* Mean Median TrMean StDev SEMeanDays 50 0 63.80 64.00 63.75 8.45 1.19 Variable Min Max Q1 Q3Days 45.00 87.00 58.75 68.25Histogram.Time Series Plot.Measure - Analyze - Improve - Control Receivables Process - Yield & Sigma Values Days Count 45 1 48 2 49 1 53 1 54 3 55

11、1 58 3 59 3 60 1 61 2 62 1 63 4 64 4 65 1 66 2 67 6 68 2 69 1 70 2 71 2 72 1 74 2 77 1 78 1 79 1 87 1 N= 50 16 Items Within Spec (60 days)34 Items Outside of Spec Inverse Cumulative Distribution Function Normal with mean = 0 and standard deviation = 1.00000 P( X 50.00Variable N Mean StDev SE Mean T

12、P-ValueDays 50 63.80 8.45 1.19 11.55 0.0000Hypothesis Test of the Mean Business Target: 50 Days a = 0.05 Test for Mean 50 DaysConf. Level = 95.0%ResultsMeasure - Analyze - Improve - Control Choice of Tool Depends Upon the Requirements of the AnalysisDemonstration Two STAT Basic Statistics Descriptiv

13、e Statistics 1-Sample t 2-Sample t Correlation Tables Tally Chisquare Test CALC Probability Distributions Normal STAT ANOVA ONEWAYBasic Statistical Analysis GRAPH Plot Time Series Plot Histogram Boxplot Character Graphs Dotplot STAT SPC Run ChartGraphical Analysis STAT Regression Regression Fitted L

14、ine PlotRegression AnalysisExample: GE Stock DataData File: price.xlsVariable: Price Description: this data set contains actual daily price data for atime period of approximately two years. The data is ordered in its original time sequence. Characterize the data and checkfor stability over time.Meas

15、ure - Analyze - Improve - Control Results of GE Stock Price Demonstration Measure - Analyze - Improve - Control Choice of Tool Depends Upon the Requirements of the Analysis STAT Basic Statistics Descriptive Statistics 1-Sample t 2-Sample t Correlation Tables Tally Chisquare Test CALC Probability Dis

16、tributions Normal STAT ANOVA ONEWAYBasic Statistical Analysis GRAPH Plot Time Series Plot Histogram Boxplot Character Graphs Dotplot STAT SPC Run ChartGraphical Analysis STAT Regression Regression Fitted Line PlotRegression AnalysisDemonstration ThreeExample: Comparing Two Different Business Regions

17、Data File: receive.xlsVariables: region1, region2 (t-test) region1, reg1$ (scatter diagram, correlation, and regression)Evaluate the relative performance of these two business regions using hypothesis testing. Also, prepare a scatter diagram and regression model (calculate correlation co-efficient)

18、using Reg1$ as the response variable and Region1 as the predictor.Measure - Analyze - Improve - Control Two Sample T-Test and Confidence IntervalTwosample T for region1 vs region2 N Mean StDev SE Meanregion1 100 46.10 10.1 1.01region2 100 44.48 9.84 0.9895% C.I. for mu region1 - mu region2: ( -1.2,

19、4.40)T-Test mu region1 = mu region2 (vs not =): T= 1.14 P=0.26 DF= 197Hypothesis Test Results.Is There a Difference in the Average Levelof Receivables Ages Between Regions 1 & 2?Measure - Analyze - Improve - Control Correlations (Pearson)Correlation of region1 and reg1$ = 0.930Correlation Coefficien

20、t (r).Scatter Plot.Establish a Relationship Between Responseand Predictor Before Building the ModelMeasure - Analyze - Improve - Control Fitted Line Plot.Measure - Analyze - Improve - Control Regression AnalysisThe regression equation isreg1$ = 29.1 + 9.66 region1Predictor Coef Stdev t-ratio pConsta

21、nt 29.08 18.22 1.60 0.114region1 9.6558 0.3861 25.01 0.000s = 38.95 R-sq = 86.5% R-sq(adj) = 86.3%Analysis of VarianceSOURCE DF SS MS F pRegression 1 948965 948965 625.40 0.000Error 98 148702 1517Total 99 1097667Unusual ObservationsObs. region1 reg1$ Fit Stdev.Fit Residual St.Resid 10 45.0 381.00 46

22、3.60 3.92 -82.60 -2.13R 31 41.0 525.00 424.97 4.36 100.03 2.58R 53 75.0 739.00 753.27 11.82 -14.27 -0.38 X 64 59.0 513.00 598.78 6.33 -85.78 -2.23R 70 47.0 404.00 482.91 3.91 -78.91 -2.04R 76 23.0 251.00 251.17 9.73 -0.17 -0.00 X 78 69.0 648.00 695.34 9.67 -47.34 -1.25 X 92 20.0 176.00 222.20 10.80

23、-46.20 -1.23 X 95 50.0 598.00 511.87 4.18 86.13 2.22R 98 45.0 558.00 463.60 3.92 94.40 2.44R R denotes an obs. with a large st. resid.X denotes an obs. whose X value gives it large influence.Regression Results.Measure - Analyze - Improve - Control Choice of Tool Depends Upon the Requirements of the

24、AnalysisDemonstration Four STAT Basic Statistics Descriptive Statistics 1-Sample t 2-Sample t Correlation Tables Tally Chisquare Test CALC Probability Distributions Normal STAT ANOVA ONEWAYBasic Statistical Analysis GRAPH Plot Time Series Plot Histogram Boxplot Character Graphs Dotplot STAT SPC Run

25、ChartGraphical Analysis STAT Regression Regression Fitted Line PlotRegression AnalysisDemonstration Four Example: Comparing Many Different Business RegionsData File: aging.xlsVariables: Country1 - Country5Evaluate the relative performance of five different business regions using boxplots and dotplot

26、s.Boxplot Results.Measure - Analyze - Improve - Control Character Dotplot . .: : : : : : .: : : .:. -+AGING (1) .: : :.: . .: . . . :. :.: -+AGING(2) . : : . : : : . . :.:.:.: : . .:.: :.:. -+AGING (3) . : . : . .: . . : .: . :.: -+AGING(4) . :.: . : . : : .: :. :.: :.:.:.: . -+AGING(5) -40 0 40 80

27、120 160Dotplot Results.One-Way Analysis of VarianceAnalysis of Variance on AGING Source DF SS MS F pCOUNTRY 4 424064 106016 246.30 0.000Error 295 126978 430Total 299 551042 Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev + 1 60 25.93 4.87 (*-) 2 60 13.97 16.54 (-*) 3 60 46.00 16

28、.20 (*-) 4 60 118.25 27.76 (-*) 5 60 25.53 28.66 (*-) +Pooled StDev = 20.75 35 70 105ANOVA Results.Measure - Analyze - Improve - Control Choice of Tool Depends Upon the Requirements of the Analysis STAT Basic Statistics Descriptive Statistics 1-Sample t 2-Sample t Correlation Tables Tally Chisquare

29、Test CALC Probability Distributions Normal STAT ANOVA ONEWAYBasic Statistical Analysis GRAPH Plot Time Series Plot Histogram Boxplot Character Graphs Dotplot STAT Control Charts Xbar-S SPC Run ChartGraphical Analysis STAT Regression Regression Fitted Line PlotRegression AnalysisDemonstration Five Ex

30、ample: Invoice DisputesData File: chisq.xlsVariables: Process, Invoices, and DisputesDescription: this data set contains the number of invoices issued to customers using six different processes. Invoices is thenumber issued and Disputes is the number of customer issuespending problem resolution. Det

31、ermine whether the results of this test indicate a difference in the six processes.Measure - Analyze - Improve - Control processinvoicesdisputes1541624713352154538549156522Results of the Six Trials.Results of the Chi-Square Test.Hypothesis TestHo: (O-E)2 = 0Ha: (O-E)2 0a: 0.05n: (n-1) = 5Decision Ru

32、le: If p a, Reject HoExpected counts are printed below observed counts invoices disputesTotal 1 54 1670 57.15 12.85 2 47 13 60 48.99 11.01 3 5215 67 54.70 12.30 4 53 8 61 49.81 11.19 5 49 15 64 52.26 11.74 6 52 2 54 44.09 9.91Total 307 69 376ChiSq = 0.174 + 0.775 + 0.081 + 0.359 + 0.134 + 0.595 + 0.

33、205 + 0.911 + 0.203 + 0.902 + 1.419 + 6.313 = 12.071df = 5, p = 0.035Is the Result Significant at the 0.05 Alpha Level? Measure - Analyze - Improve - Control Example: Receivables Process ControlData File: days.xlsVariables: DaysDescription: Collection terms are 60 days. Payments are entered into a d

34、ata collection system in the same time-order as they are received. Determine whether or not the process isin control and capable of satisfying the terms.Measure - Analyze - Improve - Control Results of Analysis.Is the Process in Control and Capable? Measure - Analyze - Improve - Control State the Go

35、al of Your Work Identify the Desired Output Collect the “Right” DataDont Use Data “Just Because Its Available” Select the Tool(s) that Will Deliver the Desired Results Conclusion Avoid “Over Analysis” . Identify Your Needs Up-front and Focus on ResultsAppendices1) Solutions to Problems Using Excel a

36、) Demonstration Oneb) Demonstration Two2) Formulae for Calculating Sample Sizea) Attributes Testsb) Variables Tests 3) Minitab Tools and the Breakthrough StrategyAppendix 1a - ExcelResults of Receivables Demonstration Using Excel Normally Distributed Data Data Stable Over Time Average 64 Days-to-Col

37、lection About 68% of the Payments Occur Between 56 and 72 Days About 50% of the Payments Exceed 64 Days ObservationsDescriptive StatisticsDaysMean63.8Standard Error1.19Median64Mode67Standard Deviation8.4Sample Variance71.3Kurtosis0.44Skewness0.07Range42Minimum45Maximum87Sum3,190Count50ConfidLevel(95

38、.000%)2.34Data Set.PaymentDays15527236946657767077986596410631167HistogramRun ChartRun Chart: Days-to-Collection4045505560657075808590135791113151719212325272931333537394143454749PaymentDaysavgGraphical Analysis Reveals Unusual EventsRun ChartData Setdayprice1104.002103.633103.004103.885104.386105.0

39、07105.638106.009105.2510106.8811107.1312108.3813108.7514108.3815108.25.HistogramDescriptive Statistics Bimodal Data - Two Different Groups Data Unstable Over Time Descriptive Statistics Unreliable Due to Data Distribution & Instability Significant Event Occurred at Time “100” Data is Upward Trending After Time “100” The Data Set is GE Stock Price and the Significant Event is a Stock