Reliability and Risk Models : Setting Reliability Requirements.

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.

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