Introduction to Reliability Engineering

Chapter 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

Chapter 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)

Chapter 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

Chapter 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

Chapter 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™

Chapter 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

Chapter 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

Chapter 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

Chapter 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

Chapter 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

Chapter 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

Chapter A: USEFUL MATHEMATICAL RELATIONSHIPS

Chapter B: BINOMIAL CONFIDENCE CHARTS

Chapter C: STANDARD NORMAL CDF

Chapter 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

Chapter ANSWERS TO ODD-NUMBERED EXERCISES: ANSWERS TO ODD-NUMBERED EXERCISES