Contents

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Introduction

What is Reliability Growth?

• Why Reliability Growth?

• Elements of a Reliability Growth Program

• Why Are Reliability Growth Models Needed?

• Reliability Growth Analysis

• A Simple Reliability Growth Model

• Fielded Systems

• Failure Rate and Failure Intensity

Data Types

• Time-to-Failure Data

• Success/Failure Data

• Reliability Data

• Fielded Systems

Duane Model History and Development

• Parameter Estimation for the Duane Model

• Graphical Method

• Least Squares (Linear Regression)

• Maximum Likelihood Estimators

• Confidence Bounds for the Duane Model

• Parameter Bounds

• Other Bounds

• General Examples Using the Duane Model

Crow-AMSAA (N.H.P.P.)

• Parameter Estimation for the Crow-AMSAA Model

• Confidence Bounds for the Crow-AMSAA Model

• Confidence Bounds on Beta

• Confidence Bounds on Lambda

• Confidence Bounds on Growth Rate

• Confidence Bounds on MTBF

• Confidence Bounds on Failure Intensity

• Confidence Bounds on Time Given Cumulative Failure Intensity

• Confidence Bounds on Time Given MTBF

• Confidence Bounds on Time Given Instantaneous Failure Intensity

• Confidence Bounds on Cumulative Number of Failures

• Confidence Bounds Examples for the Crow-AMSAA Model

• Grouped Data for the Crow-AMSAA Model

• Grouped Data Confidence Bounds for the Crow-AMSAA Model

• Grouped Data Confidence Bounds on Beta

• Grouped Data Confidence Bounds on Lambda

• Grouped Data Confidence Bounds on Growth Rate

• Grouped Data Confidence Bounds on MTBF

• Grouped Data Confidence Bounds on Failure Intensity

• Grouped Data Confidence Bounds on Time Given MTBF

• Grouped Data Confidence Bounds on Time Given Failure Intensity

• Grouped Data Confidence Bounds on Cumulative Number of Failures

• Grouped Data Confidence Bounds Examples for the Crow-AMSAA Model

• Goodness-of-Fit Tests for the Crow-AMSAA Model

• Estimation and Analysis Missing Data

• Crow Discrete Reliability Growth Model

• Applicability of the Crow-AMSAA Model

• General Examples Using the Crow-AMSAA Model

Lloyd-Lipow

• Parameter Estimation for the Lloyd Lipow Model

• Confidence Bounds for the Lloyd Lipow Model

• General Examples Using the Lloyd Lipow Model

Gompertz Models (Standard and Modified)

• Parameter Estimation for the Gompertz Models Using Least Squares

• Linear Regression (Least Squares) for the Gompertz Models

• Nonlinear Regression for the Gompertz Models

• Choice of Initial Values for the Gompertz Models

• Confidence Bounds for the Gompertz Model

• Cumulative Reliability for the Gompertz Models

• Modified Gompertz Model

• Parameter Estimation for the Modified Gompertz Model

• Confidence Bounds for the Modified Gompertz Model

• General Example Using the Gompertz Models

Logistic

• Parameter Estimation for the Logistic Model

• Confidence Bounds for the Logistic Model

• General Examples Using the Logistic Model

Crow Extended

• Crow Extended Model Background

• Test-Find-Test

• Test-Fix-Find-Test

• Failure Mode Management Strategy

• Confidence Bounds for the Crow Extended Model

• Confidence Bounds on Demonstrated Failure Intensity

• Confidence Bounds on Demonstrated MTBF

• Confidence Bounds on Projected Failure Intensity

• Confidence Bounds on Projected MTBF

• Confidence Bounds on Growth Potential Failure Intensity

• Confidence Bounds on Growth Potential MTBF

• Confidence Bounds Examples for the Crow Extended Model

• Grouped Data for the Crow Extended Model

• General Examples Using the Crow Extended Model

Fielded Systems

• Repairable Systems

• Distribution Example for Repairable Systems

• Process Example for Repairable Systems

• Using the Power Law Model to Analyze Complex Repaiable Systems

• Parameter Estimation for Repairable Systems

• Goodness-of-Fit Tests for Repairable Systems

• Cramér von Mises Test

• Chi-Squared Test

• Confidence Bounds for Repairable Systems

• Confidence Bounds on Beta

• Confidence Bounds on Lambda

• Confidence Bounds on Growth Rate

• Confidence Bounds on MTBF

• Confidence Bounds on Failure Intensity

• Confidence Bounds on Time Given MTBF

• Confidence Bounds on Time Given Failure Intensity

• Confidence Bounds on Reliability

• Confidence Bounds on Time Given Reliability and Mission Time

• Confidence Bounds on Mission Time Given Reliability and Time

• Confidence Bounds on Cumulative Failure Number

• Confidence Bounds Examples for Repairable Systems

• Economical Life Model for Repairable Systems

• Fleet Analysis

• Methodology for Fleet Analysis

• Data Analysis for Fleet Analysis

• Applying the Crow Extended Model to Fleet Data

• Confidence Bounds for Fleet Systems

• General Examples Using Fielded Systems

Appendix A: Failure Discounting

• Appendix A Example

Appendix B: Hypothesis Tests

• Common Beta Hypothesis Test

• Laplace Trend Test

• Critical Values for Cramér von Mises Test

References

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