Introduction to Reliability Engineering

James E. Breneman established and headed the Engineering Technical University at Pratt and Whitney, which provided more than 450,000 hours of instruction to employees during his tenure. Now retired, Breneman has taught many public course offerings for the ASQ Reliability & Risk Division. In 2018 he was awarded the Eugene L. Grant Medal for outstanding leadership in educational programs in quality. Chittaranjan Sahay holds the Vernon D. Roosa Distinguished Professor Chair in Manufacturing and Professorship in Mechanical Engineering at the University of Hartford, where he has held various offices including Associate Dean and Director of the Graduate Programs of the College of Engineering, Technology, and Architecture, and Chairman of the Mechanical Engineering Department. Elmer E. Lewis is Professor of Mechanical Engineering at Northwestern University’s McCormick School of Engineering and Applied Science. He has held appointments as Visiting Professor at the University of Stuttgart and as Guest Scientist at the Nuclear Research Center at Karlsruhe, Germany. He has been a frequent consultant to Argonne and Los Alamos National Laboratories as well as a number of industrial firms.

1 INTRODUCTION  

1.1 Reliability Defined

1.2 Performance, Cost and Reliability

1.3 Quality, Reliability and Safety Linkage

1.4 Quality, Reliability and Safety Engineering Tasks

1.5 Preview

2 PROBABILITY AND DISCRETE DISTRIBUTIONS

2.1 Introduction

2.2 Probability Concepts

Sample Space

Outcome

Event

Probability Axioms

More than two events

Combinations and Permutations

2.3 Discrete Random Variables

Properties of Discrete Variables

The Binomial Distribution

The Poisson Distribution

Confidence Intervals

Motivation for Confidence Intervals

Introduction to Confidence Intervals

Binomial Confidence Intervals

Cumulative sums of the Poisson Distribution (Thorndike Chart)

3 Exponential Distribution and Reliability Basics

3.1 Introduction

3.2 Reliability Characterization

Basic definitions

The Bathtub curve

3.3 Constant Failure Rate model

The Exponential Distribution

Demand failures

Time determinations

3.4 Time Dependent Failure rates

3.5 Component Failures and Failure Modes

Failure mode rates

Component counts

3.6 Replacements

3.7 Redundancy

Active and Standby Redundancy

Active Parallel

Standby Parallel

Constant Failure Rate Models

3.8 Redundancy limitations

Common-mode failures

Load sharing

Switching & Standby failures

Cool, Warm and Hot Standby

3.9 Multiply Redundant Systems

1/N Active Redundancy

1/N Standby Redundancy

m/N Active Redundancy

3.10 Redundancy Allocation

High and Low level redundancy

Fail-safe and Fail-to-Danger

Voting Systems

3.11 Redundancy in Complex Configurations

Serial-Parallel configurations

Linked configurations

4 Continuous Distributions- Part 1 Normal & Related Distributions

4.1 Introduction

4.2 Properties of Continuous Random variables

Probability Distribution Functions

Characteristics of a Probability Distribution

Sample Statistics

Transformation of Variables

4.3 Empirical Cumulative Distribution Function

4.4 Uniform Distribution

4.5 Normal and Related Distributions

The Normal Distribution

Central Limit Theorem

The Central Limit Theorem in Practice

The Log Normal Distribution

Log Normal Distribution from a Physics of Failure Perspective

4.6 Confidence Intervals

Point & Interval Estimates

Estimate of the Mean

Normal & Lognormal parameters

5 Continuous Distributions- Part 2 Weibull & Extreme Value Distributions

5.1 Introduction

The “weakest link” theory from a Physics of Failure point of view

Uses of Weibull and Extreme Value Distributions

Other Considerations

Age parameters and sample sizes

Engineering Changes, Maintenance Plan Evaluation and Risk Prediction

Weibulls with cusps or curves

System Weibulls

No failure Weibulls

Small sample Weibulls                  

5.2 Statistics of the Weibull Distribution

Weibull “Mathematics”

The Weibull Probability Plot

Probability Plotting Points—Median Ranks

How to do a “Weibull Analysis”

Weibull plots and their estimates of b, h

The 3-Parameter Weibull didn’t work, what are my choices?

The data has a “dogleg” bend or cusp when plotted on Weibull paper.

Steep Weibull slopes (β’s)  may hide problems.

Low Time Failures and close Serial numbers---Batch problems

Maximum Likelihood Estimates of β and η

Weibayes Analysis

Weibayes background

Weibull Analysis with failure times only and unknown times on remaining population

Shifting Weibull Procedure

Confidence bounds and the Weibull Distribution

Arbitrary Censored Data

The Weibull Distribution in a System of Independent failure modes

5.3 Extreme Value Distributions

Smallest & Largest Extreme Value distributions

Extreme Value and Weibull Distribution Point Estimates & Confidence Intervals

5.4 Introduction to Risk analysis

Risk Analysis “Mathematics”

Supplement 1- Weibull derived from weakest link theory

Supplement 2: Comparing two distributions using Supersmith™

6 RELIABILITY TESTING

6.1 Introduction

6.2 Attribute Testing (Binomial Testing)

The Classical Success Run

Zero Failure Attribute Tests

Non-ZERO Failure Attribute Tests

6.3 Constant Failure Rate Estimates

Censoring on the Right

MTTF Estimates

Confidence Intervals

6.4 Weibull Substantiation and Reliability Testing

Zero-Failure Test Plans for Substantiation Testing

Weibull Zero-Failure test Plans for Reliability Testing

Designing the Test Plan

Total Test Time

Why not Simply Test to Failure?

6.5 How to Reduce Test Time

Run (simultaneously) more test samples than you intend to fail

Sudden Death Testing

Sequential Testing

6.6 Normal & Lognormal Reliability Testing

6.7 Accelerated Life Testing

Compressed Time Testing

Advanced Stress Testing-Linear & Acceleration Models

Linear Model Stress testing

Advanced Stress Testing – Acceleration Models

The Arrhenius Model

The Inverse Power Law Model

Other Acceleration Models

6.8 Reliability Enhancement Procedures

Reliability Growth Modeling & Testing

Calculation of Reliability Growth parameters

Goodness of Fit tests for Reliability Growth Models

Environmental Stress Screening

What “Screens” are used for ESS?

Thermal cycling

Random Vibration

Other Screens

Highly Accelerated Life Tests

Highly Accelerated Stress Screening

Supplement 1 Substantiation Testing: Characteristic Life multipliers for Zero failure Test  at 80%, 90%, 95%, 99% Confidence

Supplement 2 Substantiation Testing Tables for Zero failure Test  at 80%, 90%, 95%, 99% Confidence

Supplement 3 CRITICAL VALUES FOR CRAMER-VON MISES GOODNESS-OF-FIT TEST

Supplement 4 Other Reliability Growth Models

Supplement 5 Chi-Square Table

7 Failure Modes & Effects Analysis (FMEA) – Design & Process

7.1 Introduction

7.2 Functional FMEA

7.3 Design FMEA

Design FMEA Procedure

7.4 Process FMEA(PFMEA)

7.5 FMEA Summary

FMEA Outputs

FMEA Pitfalls that can be prevented

Supplement 1 Shortcut tables for stalled FMEA Teams

Supplement 2 Future changes in FMEA Approaches

Supplement 3 DFMEA and PFMEA Forms

8 LOADS, CAPACITY, AND RELIABILITY

8.1 Introduction

8.2 Reliability with a Single Loading

Load Application

Definitions

8.3 Reliability and Safety Factors

Normal Distributions

Lognormal Distributions

Combined Distributions

8.4 Repetitive Loading

Loading Variability

Variable Capacity

8.5 The Bathtub Curve—Reconsidered

Single Failure Modes

Combined Failure Modes

Supplement 1: The Dirac Delta Distribution

9 MAINTAINED SYSTEMS

9.1 Introduction

9.2 Preventive Maintenance

Idealized Maintenance

Imperfect Maintenance

Redundant Components

9.3 Corrective Maintenance

Availability

Maintainability

9.4 Repair: Revealed Failures

Constant Repair Rates

Constant Repair Times

9.5 Testing and Repair: Unrevealed Failures

Idealized Periodic Tests

Real Periodic Tests

9.6 System Availability

Revealed Failures

Unrevealed Failures

10 FAILURE INTERACTIONS

10.1 Introduction

10.2 Markov Analysis

 Two Independent Components

 Load-Sharing Systems

10.3 Reliability with Standby Systems

Idealized System

Failures in the Standby State

Switching Failures

Primary System Repair

10.4 Multicomponent Systems

Multicomponent Markov Formulations

Combinations of Subsystems

10.5 Availability

Standby Redundancy

Shared Repair Crews

Markov Availability-Advantages & Disadvantages

11 SYSTEM SAFETY ANALYSIS

11.1 Introduction

11.2 Product and Equipment Hazards

11.3 Human Error

Routine Operations

Emergency Operations

11.4 Methods of Analysis

Failure Modes Effects and Criticality Analysis (FMECA)

Event Trees

11.5 Fault Trees

Fault-Tree Construction

Nomenclature

Fault Classification

Fault Tree Examples

Direct Evaluation of Fault Trees

Qualitative Evaluation

Quantitative Evaluation

Fault-Tree Evaluation by Cut Sets

Qualitative Analysis

Quantitative Analysis

11.6 Reliability/Safety Risk Analysis

APPENDICES

A USEFUL MATHEMATICAL RELATIONSHIPS

B BINOMIAL CONFIDENCE CHARTS

C STANDARD NORMAL CDF

D NONPARAMETRIC METHODS AND PROBABILITY PLOTTING

D1 Introduction

D2 Nonparametric Methods for Probability Plotting

D3 Parametric Methods

D4 Goodness-of-Fit        

Supplement 1 Further Details of Weibull Probability plotting

Supplement 2 Median Rank adjustment for SUSPENDED TEST ITEMS

Supplement 3 Generating a Probability Plot in MINITAB

ANSWERS TO ODD-NUMBERED EXERCISES

INDEX