Life Data Analysis Reference

Chapters and Topics...

Introduction

• Introduction
• How is this Online Reference Arranged?
• Contents

• Reliability Engineering
• Estimation
• A Brief Introduction to Reliability
  • Reliability Engineering and Business Plans
  • Key Reasons for Reliability Engineering
  • Disciplines Covered by Reliability Engineering
  • A Few Common Sense Applications
  • Advantages of a Reliability Engineering Program
  • Summary: Key Reasons for Implementing a Reliability Engineering Program
• Reliability and Quality Control

Statistical Background

• Statistical Background
• Basic Statistical Definitions
• The Probability Density and Cumulative Distribution Functions
• The Reliability Function
• The Failure Rate Function
• The Mean Life Function
• The Median Life Function
• The Mode Function
• Distributions
• Most Commonly Used Distributions
• Other Distributions
• Parameter Estimation
• Probability Plotting
• Least Squares Parameter Estimation (Regression Analysis)
• MLE (Maximum Likelihood) Parameter Estimation for Complete Data
• Bayesian Statistics

• Data & Data Types
• Data Classification
  • Complete Data
  • Censored Data
  • Data Types and Weibull++
• Analysis & Parameter Estimation Methods for Censored Data
  • Analysis of Right Censored (Suspended) Data
  • The Complete Likelihood Function

Confidence Bounds

• Confidence Bounds
• What are Confidence Bounds?
• Fisher Matrix Confidence Bounds
  • Approximate Estimates of the Mean and Variance of a Function
  • Approximate Confidence Intervals on the Parameters
  • Fisher Matrix Confidence Bounds on Time (Type 1)
  • Fisher Matrix Confidence Bounds on Reliability (Type 2)
• Beta Binomial Confidence Bounds
• Likelihood Ratio Confidence Bounds
  • Likelihood Ratio Confidence Bounds on the Parameters
  • Likelihood Ratio Confidence Bounds on Time (Type 1)
  • Likelihood Ratio Confidence Bounds on Reliability (Type 2)
• Bayesian Confidence Bounds
  • Bayesian Confidence Bounds on Time (Type 1)
  • Bayesian Confidence Bounds on Reliability (Type 2)
• Simulation Based Bounds

• The Weibull Distribution
• Weibull Probability Density Function
• Weibull Statistical Properties
• Characteristics of the Weibull Distribution
  • Characteristic Effects of the Shape Parameter, Beta, for the Weibull Distribution
  • Characteristic Effects of the Scale Parameter, Eta, for the Weibull Distribution
  • Characteristic Effects of the Location Parameter, Gamma, for the Weibull Distribution
• Estimation of the Weibull Parameters
  • Using Probability Plotting to Calculate the Parameters of the Weibull Distribution
  • Using Rank Regression on Y to Calculate the Parameters of the Weibull Distribution
  • Using Rank Regression on X to Calculate the Parameters of the Weibull Distribution
  • Using Three-Parameter Weibull Regression to Calculate the Parameters of the Weibull Distribution
  • Using Maximum Likelihood Estimation to Calculate the Parameters of the Weibull Distribution
• Confidence Bounds for the Weibull Distribution
  • Fisher Matrix Confidence Bounds for the Weibull Distribution
    • Fisher Matrix Confidence Bounds on the Parameters for the Weibull Distribution
    • Fisher Matrix Confidence Bounds on Reliability for the Weibull Distribution
    • Fisher Matrix Confidence Bounds on Time for the Weibull Distribution
  • Likelihood Ratio Confidence Bound for the Weibull Distribution
  • Bayesian Confidence Bounds for the Weibull Distribution
• Weibull-Bayesian Analysis
  • Posterior Distributions for Functions of Parameters in the Weibull-Bayesian Analysis
  • Confidence Bounds on R(T) for Weibull-Bayesian Analysis
  • Confidence Bounds on Time T for Weibull-Bayesian Analysis
• General Examples Using the Weibull Distribution
• Published Examples Using the Weibull Distribution

The Exponential Distribution

• The Exponential Distribution
• Exponential Probability Density Function
• Exponential Statistical Properties
• Characteristics of the Exponential Distribution
• Estimation of the Exponential Parameters
  • Using Probability Plotting to Calculate the Parameters of the Exponential Distribution
  • Using Rank Regression on Y to Calculate the Parameters of the Exponential Distribution
  • Using Rank Regression on X to Calculate the Parameters of the Exponential Distribution
  • Using Maximum Likelihood Estimation to Calculate the Parameters of the Exponential Distribution
• Confidence Bounds for the Exponential Distribution
  • Fisher Matrix Confidence Bounds for the Exponential Distribution
  • Likelihood Ratio Confidence Bounds for the Exponential Distribution
  • Bayesian Confidence Bounds for the Exponential Distribution
• General Examples Using the Exponential Distribution

• The Normal Distribution
• Normal Probability Density Function
• Normal Statistical Properties
• Characteristics of the Normal Distribution
• Estimation of the Normal Parameters
  • Using Probability Plotting to Calculate the Parameters of the Normal Distribution
  • Using Rank Regression on Y to Calculate the Parameters of the Normal Distribution
  • Using Rank Regression on X to Calculate the Parameters of the Normal Distribution
  • Using Maximum Likelihood Estimation to Calculate the Parameters of the Normal Distribution
• Confidence Bounds for the Normal Distribution
  • Fisher Matrix Confidence Bounds for the Normal Distribution
  • Likelihood Ratio Confidence Bounds for the Normal Distribution
  • Bayesian Confidence Bounds for the Normal Distribution
• General Examples Using the Normal Distribution

The Lognormal Distribution

• The Lognormal Distribution
• Lognormal Probability Density Function
• Lognormal Statistical Properties
• Characteristics of the Lognormal Distribution
• Estimation of the Lognormal Parameters
  • Using Probability Plotting to Calculate the Parameters of the Lognormal Distribution
  • Using Rank Regression on Y to Calculate the Parameters of the Lognormal Distribution
  • Using Rank Regression on X to Calculate the Parameters of the Lognormal Distribution
  • Using Maximum Likelihood Estimation to Calculate the Parameters of the Lognormal Distribution
• Confidence Bounds for the Lognormal Distribution
  • Fisher Matrix Confidence Bounds for the Lognormal Distribution
  • Likelihood Ratio Confidence Bounds for the Lognormal Distribution
  • Bayesian Confidence Bounds for the Lognormal Distribution
• General Examples Using the Lognormal Distribution

• Other Distributions
• Mixed Weibull Distribution
  • Background on the Mixed Weibull Distribution
  • The Mixed Weibull Equations
  • Mixed Weibull Parameter Estimation
  • Mixed Weibull Confidence Bounds
  • Using the Mixed Weibull Distribution in Weibull++
  • About the Mixed Weibull Calculated Parameters
  • Other Uses for the Mixed Weibull Distribution
• The Generalized Gamma Distribution
  • Generalized Gamma Probability Density Function
  • Generalized Gamma Statistical Properties
  • Characteristics of the Generalized Gamma Distribution
  • Confidence Bounds for the Generalized Gamma Distribution
• The Gamma Distribution
  • Gamma Probability Density Function
  • Gamma Statistical Properties
  • Characteristics of the Gamma Distribution
  • Confidence Bounds for the Gamma Distribution
• The Logistic Distribution
  • Logistic Probability Density Function
  • Logistic Statistical Properties
  • Characteristics of the Logistic Distribution
  • Logistic Probability Paper
  • Confidence Bounds for the Logistic Distribution
• The Loglogistic Distribution
  • Loglogistic Probability Density Function
  • Loglogistic Statistical Properties
  • Characteristics of the Loglogistic Distribution
  • Confidence Bounds for the Loglogistic Distribution
  • A Loglogistic Distribution Example
• The Gumbel/SEV Distribution
  • Gumbel Probability Density Function
  • Gumbel Statistical Properties
  • Characteristics of the Gumbel Distribution
  • Gumbel Probability Paper
  • Confidence Bounds for the Gumbel Distribution
  • A Gumbel Distribution Example

Recurrent Event Data Analysis

• Recurrent Event Data Analysis
• Non-Parametric Recurrence Data Analysis
  • The Mean Cumulative Function (MCF) for Recurrence Data
  • Confidence Limits for the MCF
• Parametric Recurrence Data Analysis
  • The GRP Model for Parametric Recurrence Data Analysis
  • Confidence Bounds for Parametric Recurrence Data Analysis

Additional Reliability Analysis Tools

• Additional Reliability Analysis Tools
• Degradation Analysis
• Warranty Analysis
• Warranty Analysis Data Entry Types
• Warranty Analysis (Nevada) Format
• Warranty Prediction
• Analysis of Non-Homogeneous Warranty Data
• Monitoring Warranty Returns Using Statistical Process Control (SPC)
• Test Design
  • Demonstration Test Design
  • Constant Failure Rate/Chi-Squared Test Design
• SimuMatic
  • Parameter Estimation and Confidence Bounds Techniques
  • Using Simulation to Design Reliability Tests
• Nonparametric Life Data Analysis
  • Kaplan-Meier Estimator
  • Simple Actuarial Method
  • Standard Actuarial Method
  • Nonparametric Confidence Bounds
• Competing Failure Modes
  • Plotting Competing Failure Modes
  • Confidence Bounds for Competing Failure Modes
  • Confidence Bounds on Reliability
  • Confidence Bounds on Time
  • Complex Competing Failure Modes
• Tests of Comparison
  • Simple Plotting
  • Using Contour Plots
  • Estimating P[t₂ >= t₁] Using the Comparison Wizard
• Stress-Strength Analysis
• Risk Analysis and Probabilistic Design with Monte Carlo Simulation

• Appendix A: Parameter Estimation
• Least Squares/Rank Regression Equations
• Maximum Likelihood Estimation
  • Illustrating the MLE Method Using the Exponential Distribution
  • Illustrating the MLE Method Using the Normal Distribution

Appendix B: Special Analysis Methods

• Appendix B: Special Analysis Methods
  • Grouped Data Analysis
  • ReliaSoft's Alternate Ranking Method (RRM) Step-by-Step Example

• Appendix C: Distribution Log-Likelihood Equations
• Weibull Log-Likelihood Functions and their Partials
• Exponential Log-Likelihood Functions and their Partials
• Normal Log-Likelihood Functions and their Partials
• Lognormal Log-Likelihood Functions and their Partials
• Mixed-Weibull Log-Likelihood Functions and their Partials
• Logistic Log-Likelihood Functions and their Partials
• The Loglogistic Log-Likelihood Functions and their Partials
• The Gumbel Log-Likelihood Functions and their Partials
• The Gamma Log-Likelihood Functions and their Partials

Appendix D: References

• References