Practical Engineering, Process, and Reliability Statistics

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Cover Title page CIP data Table of Contents List of Figures and Tables Preface Acknowledgments Chapter 1 Point Estimates and Measures of Dispersion ESTIMATES OF CENTRAL TENDENCY FOR VARIABLES DATA RANGE FOR VARIABLES DATA VARIANCE AND STANDARD DEVIATION FOR VARIABLES DATA SKEWNESS AND KURTOSIS FOR VARIABLES DATA ESTIMATES OF CENTRAL TENDENCY FOR ATTRIBUTES DATA ESTIMATES OF DISPERSION FOR ATTRIBUTES DATA STANDARD ERROR Chapter 2 Confidence Intervals CONFIDENCE INTERVAL FOR THE MEAN OF CONTINUOUS DATA CONFIDENCE INTERVAL FOR THE VARIANCE AND STANDARD DEVIATION CONFIDENCE INTERVAL FOR THE FRACTION NONCONFORMING —NORMAL DISTRIBUTION CONFIDENCE INTERVAL FOR PROPORTION (NORMAL APPROXIMATION OF THE BINOMIAL CONFIDENCE INTERVAL) SMALL SAMPLE SIZE CONFIDENCE INTERVALS CONFIDENCE INTERVAL FOR THE POISSON DISTRIBUTED DATA Chapter 3 Tolerance and Prediction Intervals TOLERANCE INTERVALS PREDICTION INTERVALS PREDICTION INTERVALS WHEN THE VARIANCE (σ2) IS KNOWN PREDICTION INTERVALS WHEN THE VARIANCE (σ2) IS UNKNOWN Chapter 4 Correlation and Regression Analysis CORRELATION ANALYSIS REGRESSION ANALYSIS NORMAL PROBABILITY PLOTS Chapter 5 Outliers OUTLIER DETECTION BASED ON THE STANDARD DEVIATION FOR A NORMAL DISTRIBUTION DISCORDANCE OUTLIER TEST OUTLIER DETECTION BASED ON THE STANDARD DEVIATION FOR AN UNKNOWN DISTRIBUTION OUTLIER DETECTION BASED ON THE INTERQUARTILE RANGE DIXON’S Q TEST DEAN AND DIXON OUTLIER TEST GRUBBS’ OUTLIER TEST WALSH’S OUTLIER TEST HAMPEL’S METHOD FOR OUTLIER DETECTION Chapter 6 Hypothesis Testing TYPE I AND TYPE II ERRORS ALPHA (α) AND BETA (β) RISKS THE EFFECT SIZE INDEX APPORTIONMENT OF RISK IN HYPOTHESIS TESTING THE HYPOTHESIS TEST FOR A ONE-TAIL (UPPER-TAILED) TEST THE HYPOTHESIS TEST FOR A ONE-TAIL (LOWER-TAILED) TEST THE HYPOTHESIS TEST FOR A TWO-TAIL TEST THE HYPOTHESIS TEST CONCLUSION STATEMENTS Chapter 7 Sample Size Determination for Tests of Hypotheses SAMPLE SIZE REQUIRED TO TEST AN OBSERVED MEAN VERSUS A HYPOTHESIZED MEAN WHENSTANDARD DEVIATION (σ) IS KNOWN SAMPLE SIZE REQUIRED TO TEST AN OBSERVED MEAN VERSUS A HYPOTHESIZED MEAN WHEN THE STANDARD DEVIATION (σ)IS ESTIMATED FROM OBSERVED VALUES SAMPLE SIZE REQUIRED TO TEST FOR DIFFERENCES IN TWO OBSERVED MEANS WHEN STANDARD DEVIATION (σ) FOR EACH POPULATION IS KNOWN SAMPLE SIZE REQUIRED TO TEST FOR DIFFERENCES IN TWO OBSERVED MEANS WHEN THE STANDARD DEVIATION (σ) IS ESTIMATED FROM THE OBSERVED DATA SAMPLE SIZE REQUIRED TO DETECT A DIFFERENCE IN THE MEAN WITH A GIVEN CONFIDENCE PAIRED SAMPLE t-TEST REQUIREMENTS SAMPLE SIZE REQUIRED FOR CHI-SQUARE TEST OF OBSERVED VARIANCE TO A HYPOTHESIZED VARIANCE SAMPLE SIZE REQUIRED FOR F-TEST OF TWO OBSERVED VARIANCES Chapter 8 Hypothesis Testing for a Difference in Means TESTING A SAMPLE MEAN VERSUS A HYPOTHESIZED MEAN WHEN THE STANDARD DEVIATION (σ) IS KNOWN TESTING A SAMPLE MEAN VERSUS A HYPOTHESIZED MEAN WHEN THE STANDARD DEVIATION (σ) IS ESTIMATED FROM THE SAMPLE DATA TESTING FOR A DIFFERENCE IN TWO POPULATION MEANS—STANDARD DEVIATIONS (σ) KNOWN TESTING A SAMPLE MEAN VERSUS A HYPOTHESIZED MEAN WHEN THE STANDARD DEVIATION (σ) IS ESTIMATED FROM THE SAMPLE DATA TESTING FOR A DIFFERENCE IN TWO POPULATION MEANS—STANDARD DEVIATIONS (σ) NOT KNOWN AND NOT ASSUMED EQUAL TESTING FOR DIFFERENCES IN MEANS OF PAIRED SAMPLES HYPOTHESIS TEST ONE PROPORTION TESTING FOR DIFFERENCES IN TWO PROPORTIONS TESTING FOR DIFFERENCES IN COUNT DATA—EQUAL SAMPLE SIZES TESTING FOR DIFFERENCES IN COUNT DATA—UNEQUAL SAMPLE SIZES HYPOTHESIS TESTING FOR DIFFERENCES IN MEANS—CONFIDENCE INTERVAL APPROACH (STANDARD DEVIATIONS KNOWN) HYPOTHESIS TESTING FOR DIFFERENCES IN MEANS—CONFIDENCE INTERVAL APPROACH (STANDARD DEVIATIONS NOT KNOWN BUT ASSUMED EQUAL) KRUSKAL–WALLIS MEANS TEST Chapter 9 Hypothesis Testing for a Difference in Variances TESTING A VARIANCE CALCULATED FROM A SAMPLE AGAINST A HYPOTHESIZED VARIANCE TESTING AN OBSERVED VARIANCE AGAINST A HYPOTHESIZED VARIANCE—LARGE SAMPLES TESTING FOR A DIFFERENCE BETWEEN TWO OBSERVED VARIANCES USING SAMPLE DATA TESTING FOR A DIFFERENCE BETWEEN TWO OBSERVED VARIANCES USING LARGE SAMPLES LEVENE’S TEST FOR EQUALITY OF VARIANCES Chapter 10 Discrete Probability Distributions BINOMIAL DISTRIBUTION POISSON DISTRIBUTION HYPERGEOMETRIC DISTRIBUTION GEOMETRIC DISTRIBUTION NEGATIVE BINOMIAL DISTRIBUTION Chapter 11 Control Charts CONTROL CHART TYPES AND SELECTION CONTROL CHART INTERPRETATION X-BAR AND R CONTROL CHARTS X-BAR AND s CONTROL CHARTS c-CHARTS u-CHARTS np-CHARTS p-CHARTS g-CHARTS X AND mR (MOVING RANGE) CONTROL CHARTS PRE-CONTROL CHARTS Chapter 12 Process Capability PROCESS CAPABILITY FOR VARIABLES DATA PROCESS CAPABILITY CONFIDENCE INTERVALS PROCESS CAPABILITY FOR ATTRIBUTES DATA INCREASING PROCESS CAPABILITY FALL-OUT RATES DEFECTS PER MILLION OPPORTUNITIES (DPMO) Chapter 13 Acceptance Sampling C = 0 SAMPLING PLAN AVERAGE OUTGOING QUALITY UPPER RISK LEVEL (CONFIDENCE STATEMENT) SAMPLE SIZE REQUIRED TO FIND PERCENTAGE DEFECTIVE WITH A GIVEN CONFIDENCE LEVEL AQL CALCULATIONS LTPD CALCULATIONS Chapter 14 ANOVA ONE-WAY ANOVA TWO-WAY ANOVA Chapter 15 The Reliability Bathtub Curve Chapter 16 Availability INHERENT AVAILABILITY ACHIEVED AVAILABILITY OPERATIONAL AVAILABILITY Chapter 17 Exponential Distribution Chapter 18 Censoring and MTBF and MCBF Calculations TYPE I CENSORING TYPE II CENSORING Chapter 19 Confidence Intervals for MTBF/MCBF TESTING TO A PREDETERMINED TIME/CYCLES TESTING TO A PREDETERMINED NUMBER OF FAILURES FAILURE-FREE TESTING Chapter 20 Nonparametric and Related Test Designs CALCULATING RELIABILITY IN ZERO-FAILURE SITUATIONS Chapter 21 Sample Size, Reliability, and Confidence Determination SAMPLE SIZE DETERMINATION BASED ON CONFIDENCE AND RELIABILITY WITH ZERO FAILURES ALLOWED RELIABILITY ESTIMATE WHEN SAMPLE SIZE IS PROVIDED SAMPLE SIZE CALCULATION WITH FAILURES ALLOWED RELIABILITY ESTIMATE WHEN SAMPLE SIZES ARE SPECIFIED Chapter 22 Wear-Out Distribution WEAR-OUT DISTRIBUTION—STANDARD DEVIATION KNOWN WEAR-OUT DISTRIBUTION—STANDARD DEVIATION UNKNOWN WEAR-OUT AND CHANCE FAILURE COMBINED Chapter 23 Conditional Probability of Failure Chapter 24 System Reliability SERIES RELIABILITY SYSTEMS PARALLEL RELIABILITY SYSTEMS COMBINATION RELIABILITY SYSTEMS STANDBY PARALLEL SYSTEMS EQUAL FAILURE RATES—PERFECT SWITCHING UNEQUAL FAILURE RATES—PERFECT SWITCHING EQUAL FAILURE RATES—IMPERFECT SWITCHING UNEQUAL FAILURE RATES—IMPERFECT SWITCHING SHARED LOAD PARALLEL SYSTEMS K-OUT-OF-N SYSTEM BAYES’ THEOREM Chapter 25 Stress-Strength Interference Chapter 26 Weibull Distribution WEIBULL DISTRIBUTION PARAMETERS WEIBULL FIT DETERMINATION Chapter 27 Log-Normal Distribution Chapter 28 Beta Distribution Chapter 29 Taguchi Methods NOMINAL IS BEST S/N RATIO LARGER IS BETTER S/N RATIO SMALLER IS BETTER S/N RATIO ZERO IS BEST (SIGNED VALUE) S/N RATIO FRACTION DEFECTIVE S/N RATIO ORDERED CATEGORICAL S/N RATIO CONVERT dB TO PERCENTAGE Appendix A Normal Distribution Probability Points—Area below Z Appendix B Normal Distribution Probability Points—Area above Z Appendix C Selected Single-Sided Normal Distribution Probability Points Appendix D Selected Double-Sided Normal Distribution Probability Points Appendix E Percentage Points of the Student’s t-Distribution Appendix F Distribution of the Chi-Square Appendix G Percentages of the F-Distribution Appendix H Tolerance Interval Factors Appendix I Critical Values of the Correlation Coeffecient Appendix J Critical Values of the Dean and Dixon Outlier Test Appendix K Critical Values for the Grubbs’ Outlier Test Appendix L Critical Values for the Discordance Outlier Test Appendix M The Binomial Distribution Appendix N The Poisson Distribution Appendix O Control Chart Constants Appendix P C = 0 Sampling Plan Appendix Q Fall-Out Rates Appendix R Beta Table Appendix S Gamma Function of Γ(x) Appendix T Selected Median Rank Percentages Appendix U Weibull Graph Paper Acronyms Definitions References Bibliography Index About the Author