Applied Reliability  book cover
3rd Edition

Applied Reliability

ISBN 9781584884668
Published August 26, 2011 by Chapman and Hall/CRC
600 Pages 310 B/W Illustrations

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Book Description

Since the publication of the second edition of Applied Reliability in 1995, the ready availability of inexpensive, powerful statistical software has changed the way statisticians and engineers look at and analyze all kinds of data. Problems in reliability that were once difficult and time consuming even for experts can now be solved with a few well-chosen clicks of a mouse. However, software documentation has had difficulty keeping up with the enhanced functionality added to new releases, especially in specialized areas such as reliability analysis.

Using analysis capabilities in spreadsheet software and two well-maintained, supported, and frequently updated, popular software packages—Minitab and SAS JMP—the third edition of Applied Reliability is an easy-to-use guide to basic descriptive statistics, reliability concepts, and the properties of lifetime distributions such as the exponential, Weibull, and lognormal. The material covers reliability data plotting, acceleration models, life test data analysis, systems models, and much more. The third edition includes a new chapter on Bayesian reliability analysis and expanded, updated coverage of repairable system modeling.

Taking a practical and example-oriented approach to reliability analysis, this book provides detailed illustrations of software implementation throughout and more than 150 worked-out examples done with JMP, Minitab, and several spreadsheet programs. In addition, there are nearly 300 figures, hundreds of exercises, and additional problems at the end of each chapter, and new material throughout.

Software and other files are available for download online

Table of Contents

Basic Descriptive Statistics
Populations and Samples
Histograms and Frequency Functions
Cumulative Frequency Function
The Cumulative Distribution Function and the Probability Density Function
Probability Concepts
Random Variables
Sample Estimates of Population Parameters
How to Use Descriptive Statistics
Data Simulation

Reliability Concepts
Reliability Function
Some Important Probabilities
Hazard Function or Failure Rate
Cumulative Hazard Function
Average Failure Rate
Bathtub Curve for Failure Rates
Recurrence and Renewal Rates
Mean Time to Failure and Residual Lifetime
Types of Data
Failure Mode Separation

Exponential Distribution
Exponential Distribution Basics
The Mean Time to Fail for the Exponential
The Exponential Lack of Memory Property
Areas of Application for the Exponential
Exponential Models with Duty Cycles and Failure on Demand
Estimation of the Exponential Failure Rate λ Exponential Distribution Closure Property
Testing Goodness of Fit—the Chi-Square Test
Testing Goodness of Fit—Empirical Distribution Function Tests
Confidence Bounds for λ and the MTTF
The Case of Zero Failures
Planning Experiments Using the Exponential Distribution
Simulating Exponential Random Variables
The Two-Parameter Exponential Distribution
Test Planning Via Spreadsheet Functions
Determining the Sample Size
EDF Goodness-of-Fits Tests Using Spreadsheets
KS Test

Weibull Distribution

Empirical Derivation of the Weibull Distribution
Properties of the Weibull Distribution
Extreme Value Distribution Relationship.
Areas of Application
Weibull Parameter Estimation: Maximum Likelihood Estimation Method
Weibull Parameter Estimation: Linear Rectification
Simulating Weibull Random Variables
The Three-Parameter Weibull Distribution
Goodness of Fit for the Weibull
Using a Spreadsheet to Obtain Weibull MLES
Using a Spreadsheet to Obtain Weibull MLES for Truncated Data
Spreadsheet Likelihood Profile Confidence Intervals for
Weibull Parameters

The Normal and Lognormal Distributions

Normal Distribution Basics
Applications of the Normal Distribution
The Central Limit Theorem
Normal Distribution Parameter Estimation
Simulating Normal Random Variables
The Lognormal Life Distribution
Properties of the Lognormal Distribution
Lognormal Distribution Areas of Application
Lognormal Parameter Estimation
Some Useful Lognormal Equations
Simulating Lognormal Random Variables
Using a Spreadsheet to Obtain Lognormal MLEs
Using a Spreadsheet to Obtain Lognormal MLEs for Interval Data

Reliability Data Plotting

Properties of Straight Lines
Least Squares Fit (Regression Analysis)
Probability Plotting for the Exponential Distribution
Probability Plotting for the Weibull Distribution
Probability Plotting for the Normal and Lognormal Distributions
Simultaneous Confidence Bands
Order Statistics and Median Ranks

Analysis of Multicensored Data

Multicensored Data
Analysis of Interval (Readout) Data
Life Table Data
Left-Truncated and Right-Censored Data
Left-Censored Data
Other Sampling Schemes (Arbitrary Censoring: Double and Overlapping Interval Censoring)—Peto–Turnbull Estimator
Simultaneous Confidence Bands for the Failure
Distribution (or Survival) Function
Cumulative Hazard Estimation for Exact Failure Times
Johnson Estimator
Obtaining Bootstrap Confidence Bands Using a Spreadsheet

Physical Acceleration Models

Accelerated Testing Theory
Exponential Distribution Acceleration
Acceleration Factors for the Weibull Distribution
Likelihood Ratio Tests of Models
Confidence Intervals Using the LR Method
Lognormal Distribution Acceleration
Acceleration Models
The Arrhenius Model
Estimating ΔH with More Than Two Temperatures
Eyring Model
Other Acceleration Models
Acceleration and Burn-In
Life Test Experimental Design
An Alternative JMP Input for Weibull Analysis of High-Stress Failure Data
Using a Spreadsheet for Weibull Analysis of High-Stress Failure Data
Using A Spreadsheet for MLE Confidence Bounds for Weibull Shape Parameter
Using a Spreadsheet for Lognormal Analysis of the High-Stress Failure Data Shown in Table 8.5
Using a Spreadsheet for MLE Confidence Bounds for the Lognormal Shape Parameter
Using a Spreadsheet for Arrhenius–Weibull Model
Using a Spreadsheet for MLEs for Arrhenius–Power Relationship Lognormal Model
Spreadsheet Templates for Weibull or Lognormal MLE Analysis

Alternative Reliability Models

Step Stress Experiments
Degradation Models
Lifetime Regression Models
The Proportional Hazards Model
Defect Subpopulation Models
JMP Solution for Step Stress Data in Example 9.1
Lifetime Regression Solution Using Excel
JMP Likelihood Formula for the Defect Model
JMP Likelihood Formulas for Multistress Defect Model Example

System Failure Modeling: Bottom-Up Approach

Series System Models
The Competing Risk Model (Independent Case)
Parallel or Redundant System Models
Standby Models and the Gamma Distribution
Complex Systems
System Modeling: Minimal Paths and Minimal Cuts
General Reliability Algorithms
Burn-In Models
The "Black Box" Approach—An Alternative to Bottom-Up Methods

Quality Control in Reliability: Applications of Discrete Distributions
Sampling Plan Distributions
Nonparametric Estimates Used with the Binomial Distribution
Confidence Limits for the Binomial Distribution
Normal Approximation for Binomial Distribution
Confidence Intervals Based on Binomial Hypothesis Tests
Simulating Binomial Random Variables
Geometric Distribution
Negative Binomial Distribution
Hypergeometric Distribution and Fisher’s Exact Test
Poisson Distribution
Types of Sampling
Generating a Sampling Plan
Minimum Sample Size Plans
Nearly Minimum Sampling Plans
Relating an OC Curve to Lot Failure Rates
Statistical Process Control Charting for Reliability

Repairable Systems Part I: Nonparametric Analysis and Renewal Processes

Repairable versus Nonrepairable Systems
Graphical Analysis of a Renewal Process
Analysis of a Sample of Repairable Systems
Confidence Limits for the Mean Cumulative Function (Exact Age Data)
Nonparametric Comparison of Two MCF Curves
Renewal Processes.
Homogeneous Poisson Process
MTBF and MTTF for a Renewal Process
MTTF and MTBF Two-Sample Comparisons
Renewal Rates
Simulation of Renewal Processes
Superposition of Renewal Processes
CDF Estimation from Renewal Data (Unidentified Replacement)
True Confidence Limits for the MCF
Cox F-Test for Comparing Two Exponential Means
Alternative Approach for Estimating CDF Using the
Fundamental Renewal Equation

Repairable Systems Part II: Nonrenewal Processes

Graphical Analysis of Nonrenewal Processes
Two Models for a Nonrenewal Process
Testing for Trends and Randomness
Laplace Test for Trend
Reverse Arrangement Test
Combining Data from Several Tests
Nonhomogeneous Poisson Processes
Models for the Intensity Function of an NHPP
Rate of Occurrence of Failures
Reliability Growth Models
Simulation of Stochastic Processes

Bayesian Reliability Evaluation

Classical versus Bayesian Analysis
Classical versus Bayes System Reliability
Bayesian System MTBF Evaluations
Bayesian Estimation of the Binomial p
The Normal/Normal Conjugate Prior
Informative and Noninformative Priors
A Survey of More Advanced Bayesian Methods
Gamma and Chi-Square Distribution Relationships
Answers to Selected Exercises

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Dr. David C. Trindade is the chief officer of best practices and fellow at Bloom Energy. He was previously a distinguished principal engineer at Sun Microsystems, senior director of software quality at Phoenix Technologies, senior fellow and director of reliability and applied statistics at Advanced Micro Devices, worldwide director of quality and reliability at General Instruments, and advisory engineer at IBM. He has also been an adjunct lecturer at the University of Vermont and Santa Clara University, teaching courses in statistical analysis, reliability, probability, and applied statistics. In 2008, he was the recipient of the IEEE Reliability Society’s Lifetime Achievement Award.


"I have used the second edition of this book for an Introduction to Reliability course for over 15 years. … The third edition … retains the features I liked about the second edition. In addition, it includes improved graphics … [and] examples of popular software used in industry … There is a new chapter on Bayesian reliability and additional material on reliability data plotting, and repairable systems’ analysis. … The book does a good and comprehensive job of explaining the basic reliability concepts; types of data encountered in practice and how to treat this data; reliability data plotting; and the common probability distributions used in reliability work, including motivations for their use and practical areas of application. … an excellent choice for a first course in reliability. The book also does a good job of explaining more advanced topics … the book will continue to be a popular desk reference in industry and a textbook for advanced undergraduate or first-year graduate students."
Journal of the American Statistical Association, June 2014