Applied Reliability: 3rd Edition (Hardback) book cover

Applied Reliability

3rd Edition

By Paul A. Tobias, David Trindade

Chapman and Hall/CRC

600 pages | 310 B/W Illus.

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pub: 2011-08-26
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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 Reliabilityis 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


"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

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



About the Authors

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.

Subject Categories

BISAC Subject Codes/Headings:
BUSINESS & ECONOMICS / Quality Control
MATHEMATICS / Probability & Statistics / General