Reliability and risk models : setting reliability requirements / Michael T. Todinov.

Format:

Book

Author/Creator:

Todinov, M. T., author.

Series:

Wiley series in quality and reliability engineering.

Wiley Series in Quality and Reliability Engineering

Language:

English

Subjects (All):

Reliability (Engineering)--Mathematical models.

Reliability (Engineering).

Risk assessment--Mathematics.

Risk assessment.

Physical Description:

1 online resource (0 p.)

Edition:

Second edition.

Place of Publication:

West Sussex, England : Wiley, 2016.

Language Note:

English

Summary:

A comprehensively updated and reorganized new edition. The updates include comparative methods for improving reliability; methods for optimal allocation of limited resources to achieve a maximum risk reduction; methods for improving reliability at no extra cost and building reliability networks for engineering systems. Includes: * A unique set of 46 generic principles for reducing technical risk * Monte Carlo simulation algorithms for improving reliability and reducing risk * Methods for setting reliability requirements based on the cost of failure * New reliability measures based on a minimal separation of random events on a time interval * Overstress reliability integral for determining the time to failure caused by overstress failure modes * A powerful equation for determining the probability of failure controlled by defects in loaded componentswith complex shape * Comparative methods for improving reliability which do not require reliability data * Optimal allocation of limited resources to achieve a maximum risk reduction * Improving system reliability based solely on a permutation of interchangeable components

Contents:

Intro

Title Page

Table of Contents

Series Preface

Preface

1 Failure Modes

1.1 Failure Modes

1.2 Series and Parallel Arrangement of the Components in a Reliability Network

1.3 Building Reliability Networks: Difference between a Physical and Logical Arrangement

1.4 Complex Reliability Networks Which Cannot Be Presented as a Combination of Series and Parallel Arrangements

1.5 Drawbacks of the Traditional Representation of the Reliability Block Diagrams

2 Basic Concepts

2.1 Reliability (Survival) Function, Cumulative Distribution and Probability Density Function of the Times to Failure

2.2 Random Events in Reliability and Risk Modelling

2.3 Statistically Dependent Events and Conditional Probability in Reliability and Risk Modelling

2.4 Total Probability Theorem in Reliability and Risk Modelling. Reliability of Systems with Complex Reliability Networks

2.5 Reliability and Risk Modelling Using Bayesian Transform and Bayesian Updating

3 Common Reliability and Risk Models and Their Applications

3.1 General Framework for Reliability and Risk Analysis Based on Controlling Random Variables

3.2 Binomial Model

3.3 Homogeneous Poisson Process and Poisson Distribution

3.4 Negative Exponential Distribution

3.5 Hazard Rate

3.6 Mean Time to Failure

3.7 Gamma Distribution

3.8 Uncertainty Associated with the MTTF

3.9 Mean Time between Failures

3.10 Problems with the MTTF and MTBF Reliability Measures

3.11 BX% Life

3.12 Minimum Failure-Free Operation Period

3.13 Availability

3.14 Uniform Distribution Model

3.15 Normal (Gaussian) Distribution Model

3.16 Log-Normal Distribution Model

3.17 Weibull Distribution Model of the Time to Failure

3.18 Extreme Value Distribution Model

3.19 Reliability Bathtub Curve.

4 Reliability and Risk Models Based on Distribution Mixtures

4.1 Distribution of a Property from Multiple Sources

4.2 Variance of a Property from Multiple Sources

4.3 Variance Upper Bound Theorem

4.4 Applications of the Variance Upper Bound Theorem

5 Building Reliability and Risk Models

5.1 General Rules for Reliability Data Analysis

5.2 Probability Plotting

5.3 Estimating Model Parameters Using the Method of Maximum Likelihood

5.4 Estimating the Parameters of a Three-Parameter Power Law

6 Load-Strength (Demand-Capacity) Models

6.1 A General Reliability Model

6.2 The Load-Strength Interference Model

6.3 Load-Strength (Demand-Capacity) Integrals

6.4 Evaluating the Load-Strength Integral Using Numerical Methods

6.5 Normally Distributed and Statistically Independent Load and Strength

6.6 Reliability and Risk Analysis Based on the Load-Strength Interference Approach

7 Overstress Reliability Integral and Damage Factorisation Law

7.1 Reliability Associated with Overstress Failure Mechanisms

7.2 Damage Factorisation Law

8 Solving Reliability and Risk Models Using a Monte Carlo Simulation

8.1 Monte Carlo Simulation Algorithms

8.2 Simulation of Random Variables

Appendix 8.1

9 Evaluating Reliability and Probability of a Faulty Assembly Using Monte Carlo Simulation

9.1 A General Algorithm for Determining Reliability Controlled by Statistically Independent Random Variables

9.2 Evaluation of the Reliability Controlled by a Load-Strength Interference

9.3 A Virtual Testing Method for Determining the Probability of Faulty Assembly

9.4 Optimal Replacement to Minimise the Probability of a System Failure

10 Evaluating the Reliability of Complex Systems and Virtual Accelerated Life Testing Using Monte Carlo Simulation

10.1 Evaluating the Reliability of Complex Systems.

10.2 Virtual Accelerated Life Testing of Complex Systems

11 Generic Principles for Reducing Technical Risk

11.1 Preventive Principles: Reducing Mainly the Likelihood of Failure

11.2 Dual Principles: Reduce Both the Likelihood of Failure and the Magnitude of Consequences

11.3 Protective Principles: Minimise the Consequences of Failure

12 Physics of Failure Models

12.1 Fast Fracture

12.2 Fatigue Fracture

12.3 Early-Life Failures

13 Probability of Failure Initiated by Flaws

13.1 Distribution of the Minimum Fracture Stress and a Mathematical Formulation of the Weakest-Link Concept

13.2 The Stress Hazard Density as an Alternative of the Weibull Distribution

13.3 General Equation Related to the Probability of Failure of a Stressed Component with Complex Shape

13.4 Link between the Stress Hazard Density and the Conditional Individual Probability of Initiating Failure

13.5 Probability of Failure Initiated by Defects in Components with Complex Shape

13.6 Limiting the Vulnerability of Designs to Failure Caused by Flaws

14 A Comparative Method for Improving the Reliability and Availability of Components and Systems

14.1 Advantages of the Comparative Method to Traditional Methods

14.2 A Comparative Method for Improving the Reliability of Components Whose Failure is Initiated by Flaws

14.3 A Comparative Method for Improving System Reliability

14.4 A Comparative Method for Improving the Availability of Flow Networks

15 Reliability Governed by the Relative Locations of Random Variables in a Finite Domain

15.1 Reliability Dependent on the Relative Configurations of Random Variables

15.2 A Generic Equation Related to Reliability Dependent on the Relative Locations of a Fixed Number of Random Variables.

15.3 A Given Number of Uniformly Distributed Random Variables in a Finite Interval (Conditional Case)

15.4 Probability of Clustering of a Fixed Number Uniformly Distributed Random Events

15.5 Probability of Unsatisfied Demand in the Case of One Available Source and Many Consumers

15.6 Reliability Governed by the Relative Locations of Random Variables following a Homogeneous Poisson Process in a Finite Domain

Appendix 15.1

16 Reliability and Risk Dependent on the Existence of Minimum Separation Intervals between the Locations of Random Variables on a Finite Interval

16.1 Applications Requiring Minimum Separation Intervals and Minimum Failure-Free Operating Periods

16.2 Minimum Separation Intervals and Rolling MFFOP Reliability Measures

16.3 General Equations Related to Random Variables following a Homogeneous Poisson Process in a Finite Interval

16.4 Application Examples

16.5 Setting Reliability Requirements to Guarantee a Rolling MFFOP Followed by a Downtime

16.6 Setting Reliability Requirements to Guarantee an Availability Target

16.7 Closed-Form Expression for the Expected Fraction of the Time of Unsatisfied Demand

17 Reliability Analysis and Setting Reliability Requirements Based on the Cost of Failure

17.1 The Need for a Cost-of-Failure-Based Approach

17.2 Risk of Failure

17.3 Setting Reliability Requirements Based on a Constant Cost of Failure

17.4 Drawbacks of the Expected Loss as a Measure of the Potential Loss from Failure

17.5 Potential Loss, Conditional Loss and Risk of Failure

17.6 Risk Associated with Multiple Failure Modes

17.7 Expected Potential Loss Associated with Repairable Systems Whose Component Failures Follow a Homogeneous Poisson Process

17.8 A Counterexample Related to Repairable Systems.

17.9 Guaranteeing Multiple Reliability Requirements for Systems with Components Logically Arranged in Series

18 Potential Loss, Potential Profit and Risk

18.1 Deficiencies of the Maximum Expected Profit Criterion in Selecting a Risky Prospect

18.2 Risk of a Net Loss and Expected Potential Reward Associated with a Limited Number of Statistically Independent Risk-Reward Bets in a Risky Prospect

18.3 Probability and Risk of a Net Loss Associated with a Small Number of Opportunity Bets

18.4 Samuelson's Sequence of Good Bets Revisited

18.5 Variation of the Risk of a Net Loss Associated with a Small Number of Opportunity Bets

18.6 Distribution of the Potential Profit from a Limited Number of Risk-Reward Activities

19 Optimal Allocation of Limited Resources among Discrete Risk Reduction Options

19.1 Statement of the Problem

19.2 Weaknesses of the Standard (0-1) Knapsack Dynamic Programming Approach

19.3 Validation of the Model by a Recursive Backtracking

Appendix A

A.1 Random Events

A.2 Union of Events

A.3 Intersection of Events

A.4 Probability

A.5 Probability of a Union and Intersection of Mutually Exclusive Events

A.6 Conditional Probability

A.7 Probability of a Union of Non-disjoint Events

A.8 Statistically Dependent Events

A.9 Statistically Independent Events

A.10 Probability of a Union of Independent Events

A.11 Boolean Variables and Boolean Algebra

Appendix B

B.1 Random Variables: Basic Properties

B.2 Boolean Random Variables

B.3 Continuous Random Variables

B.4 Probability Density Function

B.5 Cumulative Distribution Function

B.6 Joint Distribution of Continuous Random Variables

B.7 Correlated Random Variables

B.8 Statistically Independent Random Variables

B.9 Properties of the Expectations and Variances of Random Variables.

B.10 Important Theoretical Results Regarding the Sample Mean.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781118873250

1118873254

9781118873311

1118873319

9781118873199

111887319X

OCLC:

929527581