Practical Engineering, Process, and Reliability Statistics

✍ Scribed by Mark Allen Durivage

• Publisher: Quality Press
• Year: 2022
• Tongue: English
• Leaves: 358
• Edition: 2
• Category: Library

✦ Table of Contents

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