Reliability Data Analysis with Excel and Minitab

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1 Reliability Data Analysis with Excel and Minitab Kenneth S. Stephens ASQ Quality Press Milwaukee, Wisconsin

2 Table of Contents CD-ROM Contents List of Figures and Tables xiii xvii Chapter 1 Introduction to Reliability and the Text Introduction Approach Taken by Text 3.0 Topic and Chapter Summary 5 2 Chapter 2 Basic Generic Reliability Relationships 9 I. 0 The Cumulative Distribution Function (CDF), F(x) The Reliability Function, R{t) The Failure Rate or Hazard Function, h(t) The Cumulative Hazard Function, H(t) The Average Failure Rate, AFR(rl5 f2) or AFR(t) The Mean Time to Failure, MTTF Hazard Function, h(t), Modeling DFR,IFR, and Constant Failure Rates and the "Bathtub Curve" Failure Rate or Rate of Occurrence of Failures (ROCOF) Aspects of Reliability Data 10.1 Complete and Censored Data Interval-Censored Data Multi-Censored Data Left-Censored Data Reliability Testing 29 II. 0 Probability Distribution Functions Generic Reliability Relationships 31 Chapter 3 Some Useful Discrete Distributions for Reliability Analysis Introduction 2.0 Discrete Probability Distribution Functions Hypergeometric Distribution Function Binomial Distribution Function The/Binomial Function Hypergeometric Approximation The Negative Binomial Distribution Function 52

3 viii Table ofcontents 2.5 The Geometric Distribution Function 2.6 The Poisson Distribution Function Chapter 4 Point and Interval Estimation for Discrete Distributions Introduction 2.0 Hypergeometric and Negative Hypergeometric Distributions Example 4-1 Hypergeometric Confidence Intervals Example 4-2 Hypergeometric Confidence Interval Computations 2.3 Negative Hypergeometric 3.0 Binomial Distribution 3.1 Example 4-4 Confidence Limits and Intervals for Binomial Proportion 3.2 Example 4-5 Confidence Intervals for Binomial Proportion viaminitab 4.0 Negative Binomial Distribution Example 4-6 Confidence Limits and Intervals for Negative Binomial 4.2 Example 4-7 Confidence Intervals for Negative Binomial Proportion via Minitab Poisson Distribution Example 4-8 Poisson Confidence Limits Example 4-9 Confidence Intervals for Poisson via Minitab 107 Chapter 5 Linear Rectification of Reliability Models For Least Squares Estimation of Parameters Introduction Least Squares Procedure Estimating F(t) Exponential Distribution Example 5-2 CDF Method Complete Data Example 5-2 CDF Method Censored Data Example 5-2 Cum Hazard Rate Method Complete 3.4 Example 5-2 Cum Hazard Rate Method Data 123 Censored Data Example 5-2 Readout or Interval Data Analysis via Least Squares Complete Example 5-2 Readout or Interval Data Analysis via Least Squares Censored Approximate Parameter Estimation from Graphs- -Exponential Normal and Lognormal Distributions Normal Distribution Lognormal Distribution Weibull Distribution Example 5-5 CDF Method Complete Data 134

4 Table of Contents ix 5.2 Example 5-5 CDF Method Censored Data Example 5-7 CDF Method Interval Data with Truncation Approximate Parameter Estimation from Graphs Weibull Extreme-Value Distributions Example 5-6 CDF Method Complete Data Logistic and Log-Logistic Distributions Example 5-7 CDF Method Complete Data Minitab's Simulation Capabilities Change of Variable and the Probability Integral Transformation Chapter 6 Exponential, Gamma, and Chi-Square (#2) Distributions Introduction The Exponential Distribution The Exponential Average Failure Rate, AFRO,, h) or AFR(r) Mean Time to Failure for the Exponential Model Percentile Function and Median, Mean, and Variance Lack of Memory for the Exponential Model Failure Rate Scaling Units The Exponential Distribution and System Reliability Closure Property The Gamma Distribution The Gamma, Poisson, and Negative Binomial Relationships The Chi-square Distribution Goodness-of-Fit Tests Point and Interval Estimation for the Exponential Distribution Confidence Limits and Intervals for Parameters X and Confidence Limits and Intervals for Reliability The Case of Zero Failures Test Characteristics Determination Planning Exponential Distribution Analysis via Minitab Exponential Distribution Simulation 190 Chapter 7 Weibull and Extreme-Value Distributions Introduction The Weibull Distribution The Weibull Average Failure Rate, AFR(? t2) or AFR(D Mean Time to Failure (MTTF) for the Weibull Distribution Percentile Function, Median, and Variance The Weibull Distribution and System Reliability Closure Property Point and Interval Estimation for the Weibull Distribution Weibull Distribution Reliability/Survival Examples The Smallest Extreme-Value Distribution The Principal Functions The SEV Average Failure Rate, AFRO,, h) or AFR(7") 209

5 x Teblt of Contents 3.3 Mean, Median, Mode, Variance, and Percentile Function SEV Distribution Estimation and Examples Weibull and SEV Distribution Simulation 213 Chapter 8 Normal and Lognormal Distributions Introduction The Normal Distribution Mean, Median, Mode, Variance, and Percentile Function The Central Limit Theorem and Its Practical Consequences Strength-Stress Analysis via Normal Distributions Point and Interval Estimation for the Normal Distribution Normal Distribution Reliability/Survival Example The Lognormal Distribution Mean, Median, Mode, Variance, and Percentile Function Point and Interval Estimation for the Lognormal Distribution Lognormal Distribution Reliability/Survival Example Normal and Lognormal Distribution Simulation 234 Chapter 9 Logistic and Log-Logistic Distributions Introduction The Logistic Distribution Mean, Median, Mode, Variance, and Percentile Function Point and Interval Estimation for the Logistic Distribution Logistic Distribution Reliability/Survival Example The Log-Logistic Distribution Mean, Median, Mode, Variance, and Percentile Function Point and Interval Estimation for the Logistic Distribution Logistic and Log-Logistic Distribution Simulation 251 Chapter 10 Systems Reliability Introduction 253 2,0 Series Systems Parallel or Active Redundancy Systems Parallel or Active Redundancy Systems, k out of n Parallel or Active Redundancy Shared Load Systems Standby Redundancy Systems Larger Systems Series and Parallel Subsystems Combined More-Complex Systems 265 Chapter 11 Reliability of Repairable Systems Introduction Example 11-1 System Age-Inter-arrival Time-Data Analysis Homogeneous Poisson Process 4.0 Non-Homogeneous Poisson Process, Power-Law Model, and Trend Tests 4.1 Power-Law Model '

6 Table of Contents xi 4.2 Trend Tests Summary 297 Chapter 12 Reliability Determination via Accelerated Life Testing Introduction Acceleration Factors and Relationships Example 12-1 Multiple Accelerated Levels Analysis Arrhenius Model Inverse Power Law Model The General Eyring Model and Useful Two-Stress Forms Summary 319 References 321 Index 331

KopyKitab. Quality, Reliability and Maintainability. Statistical Methods for. K. Muralidharan A. Syamsundar. Maintainability

KopyKitab. Quality, Reliability and Maintainability. Statistical Methods for. K. Muralidharan A. Syamsundar. Maintainability Statistical Methods for Quality, Reliability and Maintainability LSL Design width USL Bathtub failure rate curve Maintainability Time K. Muralidharan A. Syamsundar Statistical Methods for Quality, Reliability