{"product_id":"reliability-and-risk-models-9781118873328","title":"Reliability and Risk Models","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA 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. \u003cp\u003eIncludes:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eA unique set of 46 generic principles for reducing technical risk\u003c\/li\u003e \u003cli\u003eMonte Carlo simulation algorithms for improving reliability and reducing risk\u003c\/li\u003e \u003cli\u003eMethods for setting reliability requirements based on the cost of failure\u003c\/li\u003e \u003cli\u003eNew reliability measures based on a minimal separation of random events on a time interval\u003c\/li\u003e \u003cli\u003eOverstress reliability integral for determining the time to failure caused by overstress failure modes\u003c\/li\u003e \u003cli\u003eA powerful equation for determining the probability of failure controlled by defects in loaded componentswith complex shape\u003c\/li\u003e \u003cli\u003eComparative methods for improving reliability which do not requ\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eSeries Preface xvii\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePreface xix\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Failure Modes: Building Reliability Networks 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Failure Modes 1\u003c\/p\u003e \u003cp\u003e1.2 Series and Parallel Arrangement of the Components in a Reliability Network 5\u003c\/p\u003e \u003cp\u003e1.3 Building Reliability Networks: Difference between a Physical and Logical Arrangement 6\u003c\/p\u003e \u003cp\u003e1.4 Complex Reliability Networks Which Cannot Be Presented as a Combination of Series and Parallel Arrangements 10\u003c\/p\u003e \u003cp\u003e1.5 Drawbacks of the Traditional Representation of the Reliability Block Diagrams 11\u003c\/p\u003e \u003cp\u003e\u003ci\u003e1.5.1 Reliability Networks Which Require More Than a Single Terminal Node \u003c\/i\u003e11\u003c\/p\u003e \u003cp\u003e\u003ci\u003e1.5.2 Reliability Networks Which Require the Use of Undirected Edges Only,\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eDirected Edges Only or a Mixture of Undirected and Directed Edges \u003c\/i\u003e13\u003c\/p\u003e \u003cp\u003e\u003ci\u003e1.5.3 Reliability Networks Which Require Different Edges Referring to the Same Component \u003c\/i\u003e16\u003c\/p\u003e \u003cp\u003e\u003ci\u003e1.5.4 Reliability Networks Which Require Negative\u003c\/i\u003e\u003ci\u003e‐\u003c\/i\u003e\u003ci\u003eState Components \u003c\/i\u003e17\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Basic Concepts 21\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Reliability (Survival) Function, Cumulative Distribution and Probability Density Function of the Times to Failure 21\u003c\/p\u003e \u003cp\u003e2.2 Random Events in Reliability and Risk Modelling 23\u003c\/p\u003e \u003cp\u003e\u003ci\u003e2.2.1 Reliability and Risk Modelling Using Intersection of Statistically Independent Random Events \u003c\/i\u003e23\u003c\/p\u003e \u003cp\u003e\u003ci\u003e2.2.2 Reliability and Risk Modelling Using a Union of Mutually Exclusive Random Events \u003c\/i\u003e25\u003c\/p\u003e \u003cp\u003e\u003ci\u003e2.2.3 Reliability of a System with Components Logically Arranged in Series \u003c\/i\u003e27\u003c\/p\u003e \u003cp\u003e\u003ci\u003e2.2.4 Reliability of a System with Components Logically Arranged in Parallel \u003c\/i\u003e29\u003c\/p\u003e \u003cp\u003e\u003ci\u003e2.2.5 Reliability of a System with Components Logically Arranged in Series and Parallel \u003c\/i\u003e31\u003c\/p\u003e \u003cp\u003e\u003ci\u003e2.2.6 Using Finite Sets to Infer Component Reliability \u003c\/i\u003e32\u003c\/p\u003e \u003cp\u003e2.3 Statistically Dependent Events and Conditional Probability in Reliability and Risk Modelling 33\u003c\/p\u003e \u003cp\u003e2.4 Total Probability Theorem in Reliability and Risk Modelling. Reliability of Systems with Complex Reliability Networks 36\u003c\/p\u003e \u003cp\u003e2.5 Reliability and Risk Modelling Using Bayesian Transform and Bayesian Updating 43\u003c\/p\u003e \u003cp\u003e\u003ci\u003e2.5.1 Bayesian Transform \u003c\/i\u003e43\u003c\/p\u003e \u003cp\u003e\u003ci\u003e2.5.2 Bayesian Updating \u003c\/i\u003e44\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Common Reliability and Risk Models and Their Applications 47\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 General Framework for Reliability and Risk Analysis Based on Controlling Random Variables 47\u003c\/p\u003e \u003cp\u003e3.2 Binomial Model 48\u003c\/p\u003e \u003cp\u003e\u003ci\u003e3.2.1 Application: A Voting System \u003c\/i\u003e52\u003c\/p\u003e \u003cp\u003e3.3 Homogeneous Poisson Process and Poisson Distribution 53\u003c\/p\u003e \u003cp\u003e3.4 Negative Exponential Distribution 56\u003c\/p\u003e \u003cp\u003e\u003ci\u003e3.4.1 Memoryless Property of the Negative Exponential Distribution \u003c\/i\u003e57\u003c\/p\u003e \u003cp\u003e3.5 Hazard Rate 58\u003c\/p\u003e \u003cp\u003e\u003ci\u003e3.5.1 Difference between Failure Density and Hazard Rate \u003c\/i\u003e60\u003c\/p\u003e \u003cp\u003e\u003ci\u003e3.5.2 Reliability of a Series Arrangement Including Components with Constant Hazard Rates \u003c\/i\u003e61\u003c\/p\u003e \u003cp\u003e3.6 Mean Time to Failure 61\u003c\/p\u003e \u003cp\u003e3.7 Gamma Distribution 63\u003c\/p\u003e \u003cp\u003e3.8 Uncertainty Associated with the MTTF 65\u003c\/p\u003e \u003cp\u003e3.9 Mean Time between Failures 67\u003c\/p\u003e \u003cp\u003e3.10 Problems with the MTTF and MTBF Reliability Measures 67\u003c\/p\u003e \u003cp\u003e3.11 BX% Life 68\u003c\/p\u003e \u003cp\u003e3.12 Minimum Failure‐Free Operation Period 69\u003c\/p\u003e \u003cp\u003e3.13 Availability 70\u003c\/p\u003e \u003cp\u003e\u003ci\u003e3.13.1 Availability on Demand \u003c\/i\u003e70\u003c\/p\u003e \u003cp\u003e\u003ci\u003e3.13.2 Production Availability \u003c\/i\u003e71\u003c\/p\u003e \u003cp\u003e3.14 Uniform Distribution Model 72\u003c\/p\u003e \u003cp\u003e3.15 Normal (Gaussian) Distribution Model 73\u003c\/p\u003e \u003cp\u003e3.16 Log‐Normal Distribution Model 77\u003c\/p\u003e \u003cp\u003e3.17 Weibull Distribution Model of the Time to Failure 79\u003c\/p\u003e \u003cp\u003e3.18 Extreme Value Distribution Model 81\u003c\/p\u003e \u003cp\u003e3.19 Reliability Bathtub Curve 82\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Reliability and Risk Models Based on Distribution Mixtures 87\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Distribution of a Property from Multiple Sources 87\u003c\/p\u003e \u003cp\u003e4.2 Variance of a Property from Multiple Sources 89\u003c\/p\u003e \u003cp\u003e4.3 Variance Upper Bound Theorem 91\u003c\/p\u003e \u003cp\u003e\u003ci\u003e4.3.1 Determining the Source Whose Removal Results in the Largest Decrease of the Variance Upper Bound \u003c\/i\u003e92\u003c\/p\u003e \u003cp\u003e4.4 Applications of the Variance Upper Bound Theorem 93\u003c\/p\u003e \u003cp\u003e\u003ci\u003e4.4.1 Using the Variance Upper Bound Theorem for Increasing the Robustness of Products and Processes \u003c\/i\u003e93\u003c\/p\u003e \u003cp\u003e\u003ci\u003e4.4.2 Using the Variance Upper Bound Theorem for Developing Six\u003c\/i\u003e\u003ci\u003e‐\u003c\/i\u003e\u003ci\u003eSigma Products and Processes \u003c\/i\u003e97\u003c\/p\u003e \u003cp\u003eAppendix 4.1: Derivation of the Variance Upper Bound Theorem 99\u003c\/p\u003e \u003cp\u003eAppendix 4.2: An Algorithm for Determining the Upper Bound of the Variance of Properties from Sampling Multiple Sources 101\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Building Reliability and Risk Models 103\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 General Rules for Reliability Data Analysis 103\u003c\/p\u003e \u003cp\u003e5.2 Probability Plotting 107\u003c\/p\u003e \u003cp\u003e\u003ci\u003e5.2.1 Testing for Consistency with the Uniform Distribution Model \u003c\/i\u003e109\u003c\/p\u003e \u003cp\u003e\u003ci\u003e5.2.2 Testing for Consistency with the Exponential Model \u003c\/i\u003e109\u003c\/p\u003e \u003cp\u003e\u003ci\u003e5.2.3 Testing for Consistency with the Weibull Distribution \u003c\/i\u003e110\u003c\/p\u003e \u003cp\u003e\u003ci\u003e5.2.4 Testing for Consistency with the Type I Extreme Value Distribution \u003c\/i\u003e111\u003c\/p\u003e \u003cp\u003e\u003ci\u003e5.2.5 Testing for Consistency with the Normal Distribution \u003c\/i\u003e111\u003c\/p\u003e \u003cp\u003e5.3 Estimating Model Parameters Using the Method of Maximum Likelihood 113\u003c\/p\u003e \u003cp\u003e5.4 Estimating the Parameters of a Three‐Parameter Power Law 114\u003c\/p\u003e \u003cp\u003e\u003ci\u003e5.4.1 Some Applications of the Three\u003c\/i\u003e\u003ci\u003e‐\u003c\/i\u003e\u003ci\u003eParameter Power Law \u003c\/i\u003e116\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Load–Strength (Demand\u003c\/b\u003e\u003cb\u003e‐\u003c\/b\u003e\u003cb\u003eCapacity) Models 119\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 A General Reliability Model 119\u003c\/p\u003e \u003cp\u003e6.2 The Load–Strength Interference Model 120\u003c\/p\u003e \u003cp\u003e6.3 Load–Strength (Demand‐Capacity) Integrals 122\u003c\/p\u003e \u003cp\u003e6.4 Evaluating the Load–Strength Integral Using Numerical Methods 124\u003c\/p\u003e \u003cp\u003e6.5 Normally Distributed and Statistically Independent Load and Strength 125\u003c\/p\u003e \u003cp\u003e6.6 Reliability and Risk Analysis Based on the Load–Strength Interference Approach 130\u003c\/p\u003e \u003cp\u003e\u003ci\u003e6.6.1 Influence of Strength Variability on Reliability \u003c\/i\u003e130\u003c\/p\u003e \u003cp\u003e\u003ci\u003e6.6.2 Critical Weaknesses of the Traditional Reliability Measures ‘Safety Margin’ and ‘Loading Roughness’ \u003c\/i\u003e134\u003c\/p\u003e \u003cp\u003e\u003ci\u003e6.6.3 Interaction between the Upper Tail of the Load Distribution and the Lower Tail of the Strength Distribution \u003c\/i\u003e136\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Overstress Reliability Integral and Damage Factorisation Law 139\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Reliability Associated with Overstress Failure Mechanisms 139\u003c\/p\u003e \u003cp\u003e\u003ci\u003e7.1.1 The Link between the Negative Exponential Distribution and the Overstress Reliability Integral \u003c\/i\u003e141\u003c\/p\u003e \u003cp\u003e7.2 Damage Factorisation Law 143\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Solving Reliability and Risk Models Using a Monte Carlo Simulation 147\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Monte Carlo Simulation Algorithms 147\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.1.1 Monte Carlo Simulation and the Weak Law of Large Numbers \u003c\/i\u003e147\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.1.2 Monte Carlo Simulation and the Central Limit Theorem \u003c\/i\u003e149\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.1.3 Adopted Conventions in Describing the Monte Carlo Simulation Algorithms \u003c\/i\u003e149\u003c\/p\u003e \u003cp\u003e8.2 Simulation of Random Variables 151\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.2.1 Simulation of a Uniformly Distributed Random Variable \u003c\/i\u003e151\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.2.2 Generation of a Random Subset \u003c\/i\u003e152\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.2.3 Inverse Transformation Method for Simulation of Continuous Random Variables \u003c\/i\u003e153\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.2.4 Simulation of a Random Variable following the Negative Exponential Distribution \u003c\/i\u003e154\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.2.5 Simulation of a Random Variable following the Gamma Distribution \u003c\/i\u003e154\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.2.6 Simulation of a Random Variable following a Homogeneous Poisson Process in a Finite Interval \u003c\/i\u003e155\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.2.7 Simulation of a Discrete Random Variable with a Specified Distribution \u003c\/i\u003e156\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.2.8 Selection of a Point at Random in the N\u003c\/i\u003e\u003ci\u003e‐\u003c\/i\u003e\u003ci\u003eDimensional Space Region \u003c\/i\u003e157\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.2.9 Simulation of Random Locations following a Homogeneous Poisson Process in a Finite Domain \u003c\/i\u003e158\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.2.10 Simulation of a Random Direction in Space \u003c\/i\u003e158\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.2.11 Generating Random Points on a Disc and in a Sphere \u003c\/i\u003e160\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.2.12 Simulation of a Random Variable following the Three\u003c\/i\u003e\u003ci\u003e‐\u003c\/i\u003e\u003ci\u003eParameter Weibull Distribution \u003c\/i\u003e162\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.2.13 Simulation of a Random Variable following the Maximum Extreme Value Distribution \u003c\/i\u003e162\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.2.14 Simulation of a Gaussian Random Variable \u003c\/i\u003e162\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.2.15 Simulation of a Log\u003c\/i\u003e\u003ci\u003e‐\u003c\/i\u003e\u003ci\u003eNormal Random Variable \u003c\/i\u003e163\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.2.16 Conditional Probability Technique for Bivariate Sampling \u003c\/i\u003e164\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.2.17 Von Neumann’s Method for Sampling Continuous Random Variables \u003c\/i\u003e165\u003c\/p\u003e \u003cp\u003e\u003ci\u003e8.2.18 Sampling from a Mixture Distribution \u003c\/i\u003e166\u003c\/p\u003e \u003cp\u003eAppendix 8.1 166\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Evaluating Reliability and Probability of a Faulty Assembly Using Monte Carlo Simulation 169\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 A General Algorithm for Determining Reliability Controlled by Statistically Independent Random Variables 169\u003c\/p\u003e \u003cp\u003e9.2 Evaluation of the Reliability Controlled by a Load–Strength Interference 170\u003c\/p\u003e \u003cp\u003e\u003ci\u003e9.2.1 Evaluation of the Reliability on Demand, with No Time Included \u003c\/i\u003e170\u003c\/p\u003e \u003cp\u003e\u003ci\u003e9.2.2 Evaluation of the Reliability Controlled by Random Shocks on a Time Interval \u003c\/i\u003e171\u003c\/p\u003e \u003cp\u003e9.3 A Virtual Testing Method for Determining the Probability of Faulty Assembly 173\u003c\/p\u003e \u003cp\u003e9.4 Optimal Replacement to Minimise the Probability of a System Failure 177\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Evaluating the Reliability of Complex Systems and Virtual Accelerated Life Testing Using Monte Carlo Simulation 181\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Evaluating the Reliability of Complex Systems 181\u003c\/p\u003e \u003cp\u003e10.2 Virtual Accelerated Life Testing of Complex Systems 183\u003c\/p\u003e \u003cp\u003e\u003ci\u003e10.2.1 Acceleration Stresses and Their Impact on the Time to Failure of Components \u003c\/i\u003e183\u003c\/p\u003e \u003cp\u003e\u003ci\u003e10.2.2 Arrhenius Stress–Life Relationship and Arrhenius\u003c\/i\u003e\u003ci\u003e‐\u003c\/i\u003e\u003ci\u003eType Acceleration Life Models \u003c\/i\u003e185\u003c\/p\u003e \u003cp\u003e\u003ci\u003e10.2.3 Inverse Power Law Relationship and Inverse Power Law\u003c\/i\u003e\u003ci\u003e‐\u003c\/i\u003e\u003ci\u003eType Acceleration Life Models \u003c\/i\u003e185\u003c\/p\u003e \u003cp\u003e\u003ci\u003e10.2.4 Eyring Stress–Life Relationship and Eyring\u003c\/i\u003e\u003ci\u003e‐\u003c\/i\u003e\u003ci\u003eType Acceleration Life Models \u003c\/i\u003e185\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Generic Principles for Reducing Technical Risk 189\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Preventive Principles: Reducing Mainly the Likelihood of Failure 191\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.1 Building in High Reliability in Processes, Components and Systems with Large Failure Consequences \u003c\/i\u003e191\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.2 Simplifying at a System and Component Level \u003c\/i\u003e192\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.2.1 Reducing the Number of Moving Parts \u003c\/i\u003e193\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.3 Root Cause Failure Analysis \u003c\/i\u003e193\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.4 Identifying and Removing Potential Failure Modes \u003c\/i\u003e194\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.5 Mitigating the Harmful Effect of the Environment \u003c\/i\u003e194\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.6 Building in Redundancy \u003c\/i\u003e195\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.7 Reliability and Risk Modelling and Optimisation \u003c\/i\u003e197\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.7.1 Building and Analysing Comparative Reliability Models \u003c\/i\u003e197\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.7.2 Building and Analysing Physics of Failure Models \u003c\/i\u003e198\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.7.3 Minimising Technical Risk through Optimisation and Optimal Replacement \u003c\/i\u003e199\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.7.4 Maximising System Reliability and Availability by Appropriate Permutations of Interchangeable Components \u003c\/i\u003e199\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.7.5 Maximising the Availability and Throughput Flow Reliability by Altering the Network Topology \u003c\/i\u003e199\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.8 Reducing Variability of Risk-Critical Parameters and Preventing them from Reaching Dangerous Values \u003c\/i\u003e199\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.9 Altering the Component Geometry \u003c\/i\u003e200\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.10 Strengthening or Eliminating Weak Links \u003c\/i\u003e201\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.11 Eliminating Factors Promoting Human Errors \u003c\/i\u003e202\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.12 Reducing Risk by Introducing Inverse States \u003c\/i\u003e203\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.12.1 Inverse States Cancelling the Anticipated State with a Negative Impact \u003c\/i\u003e203\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.12.2 Inverse States Buffering the Anticipated State with a Negative Impact \u003c\/i\u003e203\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.12.3 Inverting the Relative Position of Objects and the Direction of Flows \u003c\/i\u003e204\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.12.4 Inverse State as a Counterbalancing Force \u003c\/i\u003e205\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.13 Failure Prevention Interlocks \u003c\/i\u003e206\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.14 Reducing the Number of Latent Faults \u003c\/i\u003e206\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.15 Increasing the Level of Balancing \u003c\/i\u003e208\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.16 Reducing the Negative Impact of Temperature by Thermal Design \u003c\/i\u003e209\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.17 Self\u003c\/i\u003e\u003ci\u003e‐\u003c\/i\u003e\u003ci\u003eStability \u003c\/i\u003e211\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.18 Maintaining the Continuity of a Working State \u003c\/i\u003e212\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.19 Substituting Mechanical Assemblies with Electrical, Optical or Acoustic Assemblies and Software \u003c\/i\u003e212\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.20 Improving the Load Distribution \u003c\/i\u003e212\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.21 Reducing the Sensitivity of Designs to the Variation of Design Parameters \u003c\/i\u003e212\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.22 Vibration Control \u003c\/i\u003e216\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.1.23 Built\u003c\/i\u003e\u003ci\u003e‐\u003c\/i\u003e\u003ci\u003eIn Prevention \u003c\/i\u003e216\u003c\/p\u003e \u003cp\u003e11.2 Dual Principles: Reduce Both the Likelihood of Failure and the Magnitude of Consequences 217\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.1 Separating Critical Properties, Functions and Factors \u003c\/i\u003e217\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.2 Reducing the Likelihood of Unfavourable Combinations of Risk\u003c\/i\u003e\u003ci\u003e‐\u003c\/i\u003e\u003ci\u003eCritical Random Variables \u003c\/i\u003e218\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.3 Condition Monitoring \u003c\/i\u003e219\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.4 Reducing the Time of Exposure or the Space of Exposure \u003c\/i\u003e219\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.4.1 Time of Exposure \u003c\/i\u003e219\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.4.2 Length of Exposure and Space of Exposure \u003c\/i\u003e220\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.5 Discovering and Eliminating a Common Cause: Diversity in Design \u003c\/i\u003e220\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.6 Eliminating Vulnerabilities \u003c\/i\u003e222\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.7 Self\u003c\/i\u003e\u003ci\u003e‐\u003c\/i\u003e\u003ci\u003eReinforcement \u003c\/i\u003e223\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.8 Using Available Local Resources \u003c\/i\u003e223\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.9 Derating \u003c\/i\u003e224\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.10 Selecting Appropriate Materials and Microstructures \u003c\/i\u003e225\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.11 Segmentation \u003c\/i\u003e225\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.11.1 Segmentation Improves the Load Distribution \u003c\/i\u003e225\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.11.2 Segmentation Reduces the Vulnerability to a Single Failure \u003c\/i\u003e225\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.11.3 Segmentation Reduces the Damage Escalation \u003c\/i\u003e226\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.11.4 Segmentation Limits the Hazard Potential \u003c\/i\u003e226\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.12 Reducing the Vulnerability of Targets \u003c\/i\u003e226\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.13 Making Zones Experiencing High Damage\/Failure Rates Replaceable \u003c\/i\u003e227\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.14 Reducing the Hazard Potential \u003c\/i\u003e227\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.2.15 Integrated Risk Management \u003c\/i\u003e227\u003c\/p\u003e \u003cp\u003e11.3 Protective Principles: Minimise the Consequences of Failure 229\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.3.1 Fault\u003c\/i\u003e\u003ci\u003e‐\u003c\/i\u003e\u003ci\u003eTolerant System Design \u003c\/i\u003e229\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.3.2 Preventing Damage Escalation and Reducing the Rate of Deterioration \u003c\/i\u003e229\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.3.3 Using Fail\u003c\/i\u003e\u003ci\u003e‐\u003c\/i\u003e\u003ci\u003eSafe Designs \u003c\/i\u003e230\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.3.4 Deliberately Designed Weak Links \u003c\/i\u003e231\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.3.5 Built\u003c\/i\u003e\u003ci\u003e‐\u003c\/i\u003e\u003ci\u003eIn Protection \u003c\/i\u003e231\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.3.6 Troubleshooting Procedures and Systems \u003c\/i\u003e232\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.3.7 Simulation of the Consequences from Failure \u003c\/i\u003e232\u003c\/p\u003e \u003cp\u003e\u003ci\u003e11.3.8 Risk Planning and Training \u003c\/i\u003e233\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Physics of Failure Models 235\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Fast Fracture 235\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.1.1 Fast Fracture: Driving Forces behind Fast Fracture \u003c\/i\u003e235\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.1.2 Reducing the Likelihood of Fast Fracture \u003c\/i\u003e241\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.1.2.1 Basic Ways of Reducing the Likelihood of Fast Fracture \u003c\/i\u003e242\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.1.2.2 Avoidance of Stress Raisers or Mitigating Their Harmful Effect \u003c\/i\u003e244\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.1.2.3 Selecting Materials Which Fail in a Ductile Fashion \u003c\/i\u003e245\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.1.3 Reducing the Consequences of Fast Fracture \u003c\/i\u003e247\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.1.3.1 By Using Fail-Safe Designs \u003c\/i\u003e247\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.1.3.2 By Using Crack Arrestors \u003c\/i\u003e250\u003c\/p\u003e \u003cp\u003e12.2 Fatigue Fracture 251\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.2.1 Reducing the Risk of Fatigue Fracture \u003c\/i\u003e257\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.2.1.1 Reducing the Size of the Flaws \u003c\/i\u003e257\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.2.1.2 Increasing the Final Fatigue Crack Length by Selecting Material with a Higher Fracture Toughness \u003c\/i\u003e257\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.2.1.3 Reducing the Stress Range by an Appropriate Design \u003c\/i\u003e257\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.2.1.4 Reducing the Stress Range by Restricting the Springback of Elastic Components \u003c\/i\u003e258\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.2.1.5 Reducing the Stress Range by Reducing the Magnitude of Thermal Stresses \u003c\/i\u003e259\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.2.1.6 Reducing the Stress Range by Introducing Compressive Residual Stresses at the Surface \u003c\/i\u003e261\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.2.1.7 Reducing the Stress Range by Avoiding Excessive Bending \u003c\/i\u003e262\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.2.1.8 Reducing the Stress Range by Avoiding Stress Concentrators \u003c\/i\u003e263\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.2.1.9 Improving the Condition of the Surface and Eliminating Low-Strength Surfaces \u003c\/i\u003e263\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.2.1.10 Increasing the Fatigue Life of Automotive Suspension Springs \u003c\/i\u003e264\u003c\/p\u003e \u003cp\u003e12.3 Early‐Life Failures 265\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.3.1 Influence of the Design on Early\u003c\/i\u003e\u003ci\u003e‐\u003c\/i\u003e\u003ci\u003eLife Failures \u003c\/i\u003e265\u003c\/p\u003e \u003cp\u003e\u003ci\u003e12.3.2 Influence of the Variability of Critical Design Parameters on Early\u003c\/i\u003e\u003ci\u003e‐\u003c\/i\u003e\u003ci\u003eLife Failures \u003c\/i\u003e266\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Probability of Failure Initiated by Flaws 269\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Distribution of the Minimum Fracture Stress and a Mathematical Formulation of the Weakest‐Link Concept 269\u003c\/p\u003e \u003cp\u003e13.2 The Stress Hazard Density as an Alternative of the Weibull Distribution 274\u003c\/p\u003e \u003cp\u003e13.3 General Equation Related to the Probability of Failure of a Stressed Component with Complex Shape 276\u003c\/p\u003e \u003cp\u003e13.4 Link between the Stress Hazard Density and the Conditional Individual Probability of Initiating Failure 278\u003c\/p\u003e \u003cp\u003e13.5 Probability of Failure Initiated by Defects in Components with Complex Shape 279\u003c\/p\u003e \u003cp\u003e13.6 Limiting the Vulnerability of Designs to Failure Caused by Flaws 280\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 A Comparative Method for Improving the Reliability and Availability of Components and Systems 283\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Advantages of the Comparative Method to Traditional Methods 283\u003c\/p\u003e \u003cp\u003e14.2 A Comparative Method for Improving the Reliability of Components Whose Failure is Initiated by Flaws 285\u003c\/p\u003e \u003cp\u003e14.3 A Comparative Method for Improving System Reliability 289\u003c\/p\u003e \u003cp\u003e14.4 A Comparative Method for Improving the Availability of Flow Networks 290\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Reliability Governed by the Relative Locations of Random Variables in a Finite Domain 293\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Reliability Dependent on the Relative Configurations of Random Variables 293\u003c\/p\u003e \u003cp\u003e15.2 A Generic Equation Related to Reliability Dependent on the Relative Locations of a Fixed Number of Random Variables 293\u003c\/p\u003e \u003cp\u003e15.3 A Given Number of Uniformly Distributed Random Variables in a Finite Interval (Conditional Case) 297\u003c\/p\u003e \u003cp\u003e15.4 Probability of Clustering of a Fixed Number Uniformly Distributed Random Events 298\u003c\/p\u003e \u003cp\u003e15.5 Probability of Unsatisfied Demand in the Case of One Available Source and Many Consumers 302\u003c\/p\u003e \u003cp\u003e15.6 Reliability Governed by the Relative Locations of Random Variables following a Homogeneous Poisson Process in a Finite Domain 304\u003c\/p\u003e \u003cp\u003eAppendix 15.1 305\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Reliability and Risk Dependent on the Existence of Minimum Separation Intervals between the Locations of Random Variables on a Finite Interval 307\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Applications Requiring Minimum Separation Intervals and Minimum Failure‐Free Operating Periods 307\u003c\/p\u003e \u003cp\u003e16.2 Minimum Separation Intervals and Rolling MFFOP Reliability Measures 309\u003c\/p\u003e \u003cp\u003e16.3 General Equations Related to Random Variables following a Homogeneous Poisson Process in a Finite Interval 310\u003c\/p\u003e \u003cp\u003e16.4 Application Examples 312\u003c\/p\u003e \u003cp\u003e\u003ci\u003e16.4.1 Setting Reliability Requirements to Guarantee a Specified MFFOP \u003c\/i\u003e312\u003c\/p\u003e \u003cp\u003e\u003ci\u003e16.4.2 Reliability Assurance That a Specified MFFOP Has Been Met \u003c\/i\u003e312\u003c\/p\u003e \u003cp\u003e0002547085.indd 13 8\/18\/2015 6:29:01 PM\u003c\/p\u003e \u003cp\u003e\u003cb\u003exiv \u003c\/b\u003eContents\u003c\/p\u003e \u003cp\u003e\u003ci\u003e16.4.3 Specifying a Number Density Envelope to Guarantee Probability\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eof Unsatisfied Random Demand below a Maximum Acceptable Level \u003c\/i\u003e314\u003c\/p\u003e \u003cp\u003e\u003ci\u003e16.4.4 Insensitivity of the Probability of Unsatisfied Demand to the Variance of the Demand Time \u003c\/i\u003e315\u003c\/p\u003e \u003cp\u003e16.5 Setting Reliability Requirements to Guarantee a Rolling MFFOP Followed by a Downtime 317\u003c\/p\u003e \u003cp\u003e16.6 Setting Reliability Requirements to Guarantee an Availability Target 320\u003c\/p\u003e \u003cp\u003e16.7 Closed-Form Expression for the Expected Fraction of the Time of Unsatisfied Demand 323\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Reliability Analysis and Setting Reliability Requirements Based on the Cost of Failure 327\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 The Need for a Cost‐of‐Failure‐Based Approach 327\u003c\/p\u003e \u003cp\u003e17.2 Risk of Failure 328\u003c\/p\u003e \u003cp\u003e17.3 Setting Reliability Requirements Based on a Constant Cost of Failure 330\u003c\/p\u003e \u003cp\u003e17.4 Drawbacks of the Expected Loss as a Measure of the Potential Loss from Failure 332\u003c\/p\u003e \u003cp\u003e17.5 Potential Loss, Conditional Loss and Risk of Failure 333\u003c\/p\u003e \u003cp\u003e17.6 Risk Associated with Multiple Failure Modes 336\u003c\/p\u003e \u003cp\u003e\u003ci\u003e17.6.1 An Important Special Case \u003c\/i\u003e337\u003c\/p\u003e \u003cp\u003e17.7 Expected Potential Loss Associated with Repairable Systems Whose Component Failures Follow a Homogeneous Poisson Process 338\u003c\/p\u003e \u003cp\u003e17.8 A Counterexample Related to Repairable Systems 341\u003c\/p\u003e \u003cp\u003e17.9 Guaranteeing Multiple Reliability Requirements for Systems with Components Logically Arranged in Series 342\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Potential Loss, Potential Profit and Risk 345\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Deficiencies of the Maximum Expected Profit Criterion in Selecting a Risky Prospect 345\u003c\/p\u003e \u003cp\u003e18.2 Risk of a Net Loss and Expected Potential Reward Associated with a Limited Number of Statistically Independent Risk–Reward Bets in a Risky Prospect 346\u003c\/p\u003e \u003cp\u003e18.3 Probability and Risk of a Net Loss Associated with a Small Number of Opportunity Bets 348\u003c\/p\u003e \u003cp\u003e18.4 Samuelson’s Sequence of Good Bets Revisited 351\u003c\/p\u003e \u003cp\u003e18.5 Variation of the Risk of a Net Loss Associated with a Small Number of Opportunity Bets 352\u003c\/p\u003e \u003cp\u003e18.6 Distribution of the Potential Profit from a Limited Number of Risk–Reward Activities 353\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Optimal Allocation of Limited Resources among Discrete Risk Reduction Options 357\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Statement of the Problem 357\u003c\/p\u003e \u003cp\u003e19.2 Weaknesses of the Standard (0‐1) Knapsack Dynamic Programming Approach 359\u003c\/p\u003e \u003cp\u003e\u003ci\u003e19.2.1 A Counterexample \u003c\/i\u003e359\u003c\/p\u003e \u003cp\u003e\u003ci\u003e19.2.2 The New Formulation of the Optimal Safety Budget Allocation Problem \u003c\/i\u003e360\u003c\/p\u003e \u003cp\u003e\u003ci\u003e19.2.3 Dependence of the Removed System Risk on the Appropriate Selection of Combinations of Risk Reduction Options \u003c\/i\u003e361\u003c\/p\u003e \u003cp\u003e\u003ci\u003e19.2.4 A Dynamic Algorithm for Solving the Optimal Safety Budget Allocation Problem \u003c\/i\u003e365\u003c\/p\u003e \u003cp\u003e19.3 Validation of the Model by a Recursive Backtracking 369\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A 373\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Random Events 373\u003c\/p\u003e \u003cp\u003eA.2 Union of Events 375\u003c\/p\u003e \u003cp\u003eA.3 Intersection of Events 376\u003c\/p\u003e \u003cp\u003eA.4 Probability 378\u003c\/p\u003e \u003cp\u003eA.5 Probability of a Union and Intersection of Mutually Exclusive Events 379\u003c\/p\u003e \u003cp\u003eA.6 Conditional Probability 380\u003c\/p\u003e \u003cp\u003eA.7 Probability of a Union of Non‐disjoint Events 383\u003c\/p\u003e \u003cp\u003eA.8 Statistically Dependent Events 384\u003c\/p\u003e \u003cp\u003eA.9 Statistically Independent Events 384\u003c\/p\u003e \u003cp\u003eA.10 Probability of a Union of Independent Events 385\u003c\/p\u003e \u003cp\u003eA.11 Boolean Variables and Boolean Algebra 385\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B 391\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB.1 Random Variables: Basic Properties 391\u003c\/p\u003e \u003cp\u003eB.2 Boolean Random Variables 392\u003c\/p\u003e \u003cp\u003eB.3 Continuous Random Variables 392\u003c\/p\u003e \u003cp\u003eB.4 Probability Density Function 392\u003c\/p\u003e \u003cp\u003eB.5 Cumulative Distribution Function 393\u003c\/p\u003e \u003cp\u003eB.6 Joint Distribution of Continuous Random Variables 393\u003c\/p\u003e \u003cp\u003eB.7 Correlated Random Variables 394\u003c\/p\u003e \u003cp\u003eB.8 Statistically Independent Random Variables 395\u003c\/p\u003e \u003cp\u003eB.9 Properties of the Expectations and Variances of Random Variables 396\u003c\/p\u003e \u003cp\u003eB.10 Important Theoretical Results Regarding the Sample Mean 397\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix C: Cumulative Distribution Function of the Standard Normal Distribution 399\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix D: \u003c\/b\u003e\u003ci\u003eχ\u003c\/i\u003e\u003cb\u003e2\u003c\/b\u003e\u003cb\u003e‐\u003c\/b\u003e\u003cb\u003eDistribution 401\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eReferences 407\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIndex 413\u003c\/b\u003e\u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49528839438679,"sku":"9781118873328","price":107.95,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118873328.jpg?v=1731873224","url":"https:\/\/bookcurl.com\/products\/reliability-and-risk-models-9781118873328","provider":"Book Curl","version":"1.0","type":"link"}