statistical s for binomial data.doc

此文档收集于网络，如有侵权，请联系网站删除天马行空官方博客：/tmxk_docin ；QQ:1318241189；QQ群：175569632Statistical Methods for Binomial DataYou must go directly to the website at all times to get the CURRENT version of all BKMs and templates: /main.asp?Platform=ATMStatisticsCMS Revision 2, Revision date 8/21/00 (10045A&B)Stats Revision 2.0.5 February 2000Material Originators: Robert Cheney, Gayle Paraiso, Jenny Peraza, Woon Theng Saw此文档仅供学习与交流Files needed for Statistical Methods for Binomial DataJMP Templates:binomial.jmp - template for calculation of binomial probabilities1propan.jmp - analysis template for 1-sample cases2propan.jmp - analysis template for 2-sample caseszds.jmp - zero defect sampling sample size calculationspchart.jmp - template for creating control chartsprop_oc.jmp - template for creating OC curvesprop_calc.jmp - template for general binomial calculationsData Files for Exercises:ksample_ex01.jmpksample_ex02.jmpksample_ex03.jmpencap1.jmpencap2.jmpLaser_Mark.jmpbonder.jmplottab.jmpdefecttab.jmpHomework Data Files:Homework1_4.jmpHomework1_5.jmpHomework2_3.jmpHomework2_4.jmpSample Size Tables: ssprop.xlsWeb address for downloading course materials, JMP templates, data files, and sample size tables:/bkm/main.asp?Platform=ATMStatisticsStatistical Methods for Binomial DataTable of ContentsIntroduction to the Binomial DistributionPage 9Hypothesis Testing for ProportionsPage 12The Binomial DistributionPage 13Relating Yields to Defect RatesPage 17Sample Defect RatesPage 18Computing Binomial Probabilities using binomial.jmpPage 19Estimating a Defect Rate From a SamplePage 22One-Sided Confidence Intervals for ProportionsPage 25BKM for Using Binomial Methods versus ContinuousMethods for Defect Data or Yield DataPage 27Stability Assessment Using pchart.jmpPage 33Module 1 Key Points SummaryPage 35Module 1: Single ProportionAnalysisPage 37One-sided Hypothesis Tests for Proportional DataPage 41The “Statistically Equal or Better” HypothesisPage 42The “Statistically Better” HypothesisPage 43Rejection Regions for SEB and SBPage 45Sample Size Determination for 1-proportion DataPage 51Detectable Differences for SEB and SBPage 54Testing A 1-proportion HypothesisPage 57Using the JMP Template 1propan.jmpPage 58Zero Defect SamplingPage 65Key Points Summary for 1-proportion CasesPage 70Summary Procedure for 1-proportion CasesPage 71Module 2: Two Proportion AnalysisPage 73The SEB Hypothesis for Two ProportionsPage 77The SB Hypothesis for Two ProportionsPage 78Sample Size Determination for 2-proportion DataPage 81Testing a 2-proportion HypothesisPage 85Using the JMP Template 2propan.jmpPage 86Key Points Summary for 2-proportion CasesPage 92Summary Procedure for 2 Proportion CasesPage 93Module 3: More Than 2 Proportion AnalysisPage 95Comparison of k-proportion Hypotheses for Proportional Data With Hypotheses for Continuous DataPage 98Sample Size Determination for k-proportion CasesPage 100Testing a k-proportion HypothesisPage 101Data Formats for Analysis of k-proportion DataPage 102Analysis Procedure for k-proportion CasesPage 105Key Points Summary for k-proportion CasesPage 119Appendices:Appendix A - Equations for Binomial MethodsPage 121Sample Size DeterminationsPage 124Detectable Differences for ProportionsPage 125The “Ideal” OC CurvePage 126Testing the Hypothesis for 1-proportion CasesPage 132Confidence Intervals for 1-proportion CasesPage 133Testing the Hypothesis for 2-proportion CasesPage 134Confidence Intervals for 2-proportion CasesPage 136Testing the Hypothesis for k-proportion CasesPage 137Zero Defect SamplingPage 138Appendix B - Using the “Roll-up” Features of JMPPage 143Lot-Level versus Unit-Level InformationPage 145Procedure for Merging Lot-level and Unit-level Data using JMPPage 147Appendix C - Homework ProblemsPage 155Binomial Homework #1Page 157Binomial Homework #2Page 161Appendix E - Sample Size TablesPage 165Estimating the Detectable Difference for a DatasetPage 168When d is in the Tables, but p0 is not: Linear InterpolationPage 169When p0 is in the Tables, but d is not: Linear InterpolationPage 170Statistical Methods for Binomial DataObjectivesAfter completing this course, you will be able to:1. Recognize when it is appropriate to use statistical methods that are specific to binomial data.2. Analyze proportional data from a process to determine if the process meets or exceeds a quality goal.3. Compare proportional data from 2 or more processes to determine if one process has a different defect rate or yield.4. Use JMP statistical software to analyze binomial data.Course Overview and Prerequisites:Statistical Methods for Binomial Data is an introduction to the use of the binomial distribution in designing, analyzing, and interpreting experiments from Intel processes that generate pass/fail data. Many of the same topics from DOE 1 for continuous data are covered for binomial data: Single sample comparison of a proportion to a target. Comparison of two proportions. Comparison of more than two proportions. Sample sizes, hypothesis tests, & confidence intervals. Prerequisites Intro to JMP software DOE 1 Introduction to the Binomial Distribution Discrete DataMany times data is not continuous, but is discrete with only 2 possible levels, typically “pass” or “fail”: Electrical TestsSoftware TestsVisual TestsFAB SORTComponents PPVMaterials IVIComponents TESTCartridge SystestComponents PEVICartridge ICTComponents FVIOQACartridge PSVICartridge FVINon-Intel Examples: Quality of Soap Products - pass or fail Print quality of Text books - good or bad Voting/Survey Sampling - yes or no response Medical Research - presence or absence of disease Analysis techniques for continuous data are typically inappropriate for discrete data. Instead, the binomial distribution is often used for the analysis of discrete data.Hypothesis Testing For ProportionsTests concerning proportions are required in many areas: Voting PollsWhat fraction of the voters will vote for a politician in the next election?ManufacturingWhat proportion of a shipment is defective? Health CareDoes the availability of pediatricians differ between regions? Medical ResearchDoes smoking affect the likelihood of getting lung cancer?Examples at Intel:- Does a process meet or exceed a target defect rate or a target yield? (Module 2)- Does a proposed change to a process lower a defect rate or increase a yield? (Module 3)The Binomial DistributionAll hypothesis testing BKMs and sample size determination BKMs rely on the assumption that the data follows a binomial distribution.The binomial distribution computes the probability of obtaining x defective units in a sample of size n when the true process defect rate is p. (Note: 0! = 1)where:p = true process defect rate n = sample sizex = number of defective units observed in the sampleBinomial Probability Calculation ExampleFor a process with a true defect rate of 1%:1. What is the probability of obtaining 1 defect in a random sample of 100 units?p = 1%n = 100x = 1Interpretation. There is a 37% chance of observing 1 defective unit in a random sample of size 100 if the true process defect rate is 1%.2. How many defective units would you “expect” in the random sample of 100 units?Binomial Calculation Example (Continued)3. What is the probability of having one or fewer defects in the sample? 4. What is the probability of two or more defects in the sample? Histograms for Binomial DataHistograms for binomial data show the probabilities for obtaining exactly x failing units.A histogram for the previous example: The likelihood of observing 4 or more defects in the sample is quite low. If you did observe 4 or more defects, would you conclude that 1% is a plausible true defect rate for the process?Relating Yields to Defect RatesProcess yields are also proportions and relate to defect rates as follows:Yield = 1 defect rate or,Defect Rate = 1 yield Questions concerning yields can easily be turned into questions concerning defect rates through the above relationship.Example:What is the probability of obtaining 100 good units in a sample of size 100 from a process with a true yield of 99%?This is equivalent to:What is the probability of obtaining 0 defective units in a sample of size 100 from a process with a true defect rate of 1%?Sample Defect Rates and Sample YieldsFor the previous example, x (the number of defective units) could take on values: 0, 1, 2, 3, 4, . . . 100Therefore, the sample defect rate could take on values:0/100, 1/100, 2/100, . . . 100/1000%, 1%, 2%, . . . 100% And the sample yields could take on values:100/100, 99/100, 98/100, . . . 97/100100%, 99%, 98%, . . . 97% Computing probabilities for sample defect rates simply requires computing a binomial probability for the appropriate x.Example: The probability of observing a sample defect rate of 1% for a sample size of 100 is computationally equivalent to the probability of observing 1 defective unit in a sample of 100.Exercise: For the previous example (n=100, p=1%), what is the probability of observing a sample defect rate less than or equal to 1%?Computing Binomial Probabilities Using binomial.jmpBinomial probabilities can be computed using the JMP template binomial.jmp. In the first three columns, enter the values for:p (the true proportion defective)x (the number of defects)n (sample size)The following are calculated by JMP:“Entry Error?” - a check for errors in your entries“Prob (Exactly X)” - probability for exactly X defects“Prob (X or fewer)” - cumulative probability for X defects“Prob (X or more)” - tail probability for X defectsNote: There are multiple rows in the spreadsheet to allow for calculations of probabilities for more than one set of p, x, and n.Example Screen for binomial.jmp JMP template: Binomial Calculations ExerciseUse the JMP template for the following questions where p=5%, n=100:Prob(x=5) = Prob(x 25%? Process stable on binomial p-chart?6. The JMP template pchart.jmp can be used to perform stability assessment for defect data or yield data.Module 1:Single Proportion AnalysisObjectives of Module 1The purpose of this module is to provide techniques to answer questions such as: Does a process meet or exceed a target defect rate? Does a process exceed a target yield goal?Intel Examples:- Does the SMTP line meet the 1% touch-up goal for primary side processing?- Does the factory line as a whole meet or exceed the target 99% yield goal?Comparisons of Hypotheses for Proportionswith Hypotheses for Continuous DataIn DOE I, most of the hypotheses tested were of the statistically equivalent type (SE):Continuous Data SE Hypotheses for Process Means: Null Hypothesis: m = m0Alternative Hypothesis:m m0 For proportional data, a target proportion (p0) plays the same role as a target mean:Proportional Data SE Hypotheses for Process Defect Rates:Null Hypothesis: p = p0Alternative Hypothesis: p p0 SE hypothesis tests are usual