MICHAEL TODINOV has a background in mechanical engineering, applied mathematics and computer science. He received his PhD and his higher doctorate (DEng) from the University of Birmingham and is currently a professor in mechanical engineering in Oxford Brookes University, UK. Professor Todinov is an internationally acclaimed expert in reliability and risk. In 2017, he received the prestige IMechE award in the area of risk reduction in mechanical engineering. He has published four research monographs and a large number of research papers in the area of reliability and risk. His name is associated with developing theoretical and computational frameworks for analysis and optimisation of repairable flow networks and for reliability analysis based on the cost of failure.

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• Preface xv1 Domain-Independent Methods for Reliability Improvement and Risk Reduction 11.1 The Domain-Specific Methods for Risk Reduction 11.2 The Statistical, Data-Driven Approach 31.3 The Physics-of-Failure Approach 41.4 Reliability Improvement and TRIZ 61.5 The Domain-Independent Methods for Reliability Improvement and Risk Reduction 62 Basic Concepts 92.1 Likelihood of Failure, Consequences from Failure, Potential Loss, and Risk of Failure 92.2 Drawbacks of the Expected Loss as a Measure of the Potential Loss from Failure 142.3 Potential Loss, Conditional Loss, and Risk of Failure 152.4 Improving Reliability and Reducing Risk 192.5 Resilience 213 Overview of Methods and Principles for Improving Reliability and Reducing Risk That Can Be Classified as Domain-Independent 233.1 Improving Reliability and Reducing Risk by Preventing Failure Modes 233.1.1 Techniques for Identifying and Assessing Failure Modes 233.1.2 Effective Risk Reduction Procedure Related to Preventing Failure Modes from Occurring 273.1.3 Reliability Improvement and Risk Reduction by Root Cause Analysis 283.1.3.1 Case Study: Improving the Reliability of Automotive Suspension Springs by Root Cause Analysis 283.1.4 Preventing Failure Modes by Removing Latent Faults 293.2 Improving Reliability and Reducing Risk by a Fault-Tolerant System Design and Fail-Safe Design 313.2.1 Building in Redundancy 313.2.1.1 Case Study: Improving Reliability by k-out-of-n redundancy 343.2.2 Fault-Tolerant Design 343.2.3 Fail-Safe Principle and Fail-Safe Design 353.2.4 Reducing Risk by Eliminating Vulnerabilities 363.2.4.1 Eliminating Design Vulnerabilities 363.2.4.2 Reducing the Negative Impact of Weak Links 373.2.4.3 Reducing the Likelihood of Unfavourable Combinations of Risk-Critical Random Factors 383.2.4.4 Reducing the Vulnerability of Computational Models 393.3 Improving Reliability and Reducing Risk by Protecting Against Common Cause 403.4 Improving Reliability and Reducing Risk by Simplifying at a System and Component Level 423.5 Improving Reliability and Reducing Risk by Reducing the Variability of Risk-Critical Parameters 443.5.1 Case Study: Interaction Between the Upper Tail of the Load Distribution and the Lower Tail of the Strength Distribution 463.6 Improving Reliability and Reducing Risk by Making the Design Robust 483.6.1 Case Study: Increasing the Robustness of a Spring Assembly with Constant Clamping Force 503.7 Improving Reliability and Reducing Risk by Built-in Reinforcement 513.7.1 Built-In Prevention Reinforcement 513.7.2 Built-In Protection Reinforcement 513.8 Improving Reliability and Reducing Risk by Condition Monitoring 523.9 Reducing the Risk of Failure by Improving Maintainability 563.10 Reducing Risk by Eliminating Factors Promoting Human Errors 573.11 Reducing Risk by Reducing the Hazard Potential 583.12 Reducing Risk by using Protective Barriers 593.13 Reducing Risk by Efficient Troubleshooting Procedures and Systems 603.14 Risk Planning and Training 604 Improving Reliability and Reducing Risk by Separation 614.1 The Method of Separation 614.2 Separation of Risk-Critical Factors 624.2.1 Time Separation by Scheduling 624.2.1.1 Case Study: Full Time Separation with Random Starts of the Events 624.2.2 Time and Space Separation by Using Interlocks 634.2.2.1 Case Study: A Time Separation by Using an Interlock 634.2.3 Time Separation in Distributed Systems by Using Logical Clocks 644.2.4 Space Separation of Information 654.2.5 Separation of Duties to Reduce the Risk of Compromised Safety, Errors, and Fraud 654.2.6 Logical Separation by Using a Shared Unique Key 664.2.6.1 Case Study: Logical Separation of X-ray Equipment by a Shared Unique Key 664.2.7 Separation by Providing Conditions for Independent Operation 674.3 Separation of Functions, Properties, or Behaviour 684.3.1 Separation of Functions 684.3.1.1 Separation of Functions to Optimise for Maximum Reliability 684.3.1.2 Separation of Functions to Reduce Load Magnitudes 704.3.1.3 Separation of a Single Function into Multiple Components to Reduce Vulnerability to a Single Failure 714.3.1.4 Separation of Functions to Compensate Deficiencies 714.3.1.5 Separation of Functions to Prevent Unwanted Interactions 714.3.1.6 Separation of Methods to Reduce the Risk Associated with Incorrect Mathematical Models 724.4 Separation of Properties to Counter Poor Performance Caused by Inhomogeneity 724.4.1 Separation of Strength Across Components and Zones According to the Intensity of the Stresses from Loading 724.4.2 Separation of Properties to Satisfy Conflicting Requirements 744.4.3 Separation in Geometry 754.4.3.1 Case Study: Separation in Geometry for a Cantilever Beam 754.5 Separation on a Parameter, Conditions, or Scale 764.5.1 Separation at Distinct Values of a Risk-Critical Parameter Through Deliberate Weaknesses and Stress Limiters 764.5.2 Separation by Using Phase Changes 774.5.3 Separation of Reliability Across Components and Assemblies According to Their Cost of Failure 774.5.3.1 Case Study: Separation of the Reliability of Components Based on the Cost of Failure 785 Reducing Risk by Deliberate Weaknesses 815.1 Reducing the Consequences from Failure Through Deliberate Weaknesses 815.2 Separation from Excessive Levels of Stress 825.2.1 Deliberate Weaknesses Disconnecting Excessive Load 825.2.2 Energy-Absorbing Deliberate Weaknesses 855.2.2.1 Case Study: Reducing the Maximum Stress from Dynamic Loading by Energy-Absorbing Elastic Components 855.2.3 Designing Frangible Objects or Weakly Fixed Objects 865.3 Separation from Excessive Levels of Damage 875.3.1 Deliberate Weaknesses Decoupling Damaged Regions and Limiting the Spread of Damage 875.3.2 Deliberate Weaknesses Providing Stress and Strain Relaxation 885.3.3 Deliberate Weaknesses Separating from Excessive Levels of Damage Accumulation 905.4 Deliberate Weaknesses Deflecting the Failure Location or Damage Propagation 915.4.1 Deflecting the Failure Location from Places Where the Cost of Failure is High 915.4.2 Deflecting the Failure Location from Places Where the Cost of Intervention for Repair is High 925.4.3 Deliberate Weaknesses Deflecting the Propagation of Damage 925.5 Deliberate Weaknesses Designed to Provide Warning 925.6 Deliberate Weaknesses Designed to Provide Quick Access or Activate Protection 945.7 Deliberate Weaknesses and Stress Limiters 946 Improving Reliability and Reducing Risk by Stochastic Separation 976.1 Stochastic Separation of Risk-Critical Factors 976.1.1 Real-Life Applications that Require Stochastic Separation 976.1.2 Stochastic Separation of a Fixed Number of Random Events with Different Duration Times 996.1.2.1 Case Study: Stochastic Separation of Consumers by Proportionally Reducing Their Demand Times 1026.1.3 Stochastic Separation of Random Events Following a Homogeneous Poisson Process 1056.1.3.1 Case Study: Stochastic Separation of Random Demands Following a Homogeneous Poisson Process 1066.1.4 Stochastic Separation Based on the Probability of Overlapping of Random Events for More than a Single Source Servicing the Random Demands 1066.1.5 Computer Simulation Algorithm Determining the Probability of Overlapping for More than a Single Source Servicing the Demands 1086.2 Expected Time Fraction of Simultaneous Presence of Critical Events 1106.2.1 Case Study: Expected Fraction of Unsatisfied Demand at a Constant Sum of the Time Fractions of User Demands 1126.2.2 Case Study: Servicing Random Demands from Ten Different Users, Each Characterised by a Distinct Demand Time Fraction 1146.3 Analytical Method for Determining the Expected Fraction of Unsatisfied Demand for Repair 1146.3.1 Case Study: Servicing Random Repairs from a System Including Components of Three Different Types, Each Characterised by a Distinct Repair Time 1156.4 Expected Time Fraction of Simultaneous Presence of Critical Events that have been Initiated with Specified Probabilities 1166.4.1 Case Study: Servicing Random Demands from Patients in a Hospital 1176.4.2 Case Study: Servicing Random Demands from Four Different Types of Users, Each Issuing a Demand with Certain Probability 1186.5 Stochastic Separation Based on the Expected Fraction of Unsatisfied Demand 1196.5.1 Fixed Number of Random Demands on a Time Interval 1196.5.2 Random Demands Following a Poisson Process on a Time Interval 1206.5.2.1 Case Study: Servicing Random Failures from Circular Knitting Machines by an Optimal Number of Repairmen 1227 Improving Reliability and Reducing Risk by Segmentation 1257.1 Segmentation as a Problem-Solving Strategy 1257.2 Creating a Modular System by Segmentation 1277.3 Preventing Damage Accumulation and Limiting Damage Propagation by Segmentation 1297.3.1 Creating Barriers Containing Damage 1297.3.2 Creating Weak Interfaces Dissipating or Deflecting Damage 1317.3.3 Reducing Deformations and Stresses by Segmentation 1317.3.4 Reducing Hazard Potential by Segmentation 1317.3.5 Reducing the Likelihood of Errors by Segmenting Operations 1327.3.6 Limiting the Presence of Flaws by Segmentation 1327.4 Improving Fault Tolerance and Reducing Vulnerability to a Single Failure by Segmentation 1337.4.1 Case Study: Improving Fault Tolerance of a Column Loaded in Compression by Segmentation 1337.4.2 Reducing the Vulnerability to a Single Failure by Segmentation 1367.5 Reducing Loading Stresses by Segmentation 1387.5.1 Improving Load Distribution by Segmentation 1387.5.2 Improving Heat Dissipation by Segmentation 1397.5.3 Case Study: Reducing Stress by Increasing the Perimeter to Cross-Sectional Area Ratio Through Segmentation 1407.6 Reducing the Probability of a Loss/Error by Segmentation 1427.6.1 Reducing the Likelihood of a Loss by Segmenting Opportunity Bets 1427.6.1.1 Case Study: Reducing the Risk of a Loss from a Risky Prospect Involving a Single Opportunity Bet 1437.6.2 Reducing the Likelihood of a Loss by Segmenting an Investment Portfolio 1447.6.3 Reducing the Likelihood of Erroneous Conclusion from Imperfect Tests by Segmentation 1457.7 Decreasing the Variation of Properties by Segmentation 1467.8 Improved Control and Condition Monitoring by Time Segmentation 1488 Improving Reliability and Reducing Risk by Inversion 1498.1 The Method of Inversion 1498.2 Improving Reliability by Inverting Functions, Relative Position, and Motion 1508.2.1 Case Study: Eliminating Failure Modes of an Alarm Circuit by Inversion of Functions 1518.2.2 Improving Reliability by Inverting the Relative Position of Objects 1528.2.2.1 Case Study: Inverting the Position of an Object with Respect to its Support to Improve Reliability 1538.3 Improving Reliability by Inverting Properties and Geometry 1558.3.1 Case Study: Improving Reliability by Inverting Mechanical Properties Whilst Maintaining an Invariant 1558.3.2 Case Study: Improving Reliability by Inverting Geometry Whilst Maintaining an Invariant 1568.4 Improving Reliability and Reducing Risk by Introducing Inverse States 1588.4.1 Inverse States Cancelling Anticipated Undesirable Effects 1588.4.2 Inverse States Buffering Anticipated Undesirable Effects 1598.4.3 Inverse States Reducing the Likelihood of an Erroneous Action 1608.5 Improving Reliability and Reducing Risk by Inverse Thinking 1618.5.1 Inverting the Problem Related to Reliability Improvement and Risk Reduction 1618.5.1.1 Case Study: Reducing the Risk of High Employee Turnover 1628.5.2 Improving Reliability and Reducing Risk by Inverting the Focus 1638.5.2.1 Shifting the Focus from the Components to the System 1638.5.2.2 Starting from the Desired Ideal End Result 1638.5.2.3 Focusing on Events that are Missing 1648.5.3 Improving Reliability and Reducing Risk by Moving Backwards to Contributing Factors 1648.5.3.1 Case Study: Identifying Failure Modes of a Lubrication System by Moving Backwards to Contributing Factors 1658.5.4 Inverse Thinking in Mathematical Models Evaluating or Reducing Risk 1668.5.4.1 Case Study: Using the Method of Inversion for Fast Evaluation of the Production Availability of a Complex System 1678.5.4.2 Case Study: Repeated Inversion for Evaluating the Risk of Collision of Ships 1709 Reliability Improvement and Risk Reduction Through Self-Reinforcement 1779.1 Self-Reinforcement Mechanisms 1779.2 Self-Reinforcement Relying on a Proportional Compensating Factor 1799.2.1 Transforming Forces and Pressure into a Self-Reinforcing Response 1799.2.1.1 Capturing a Self-Reinforcing Proportional Response from Friction Forces 1799.2.1.2 Case Study: Transforming Friction Forces into a Proportional Response in the Design of a Friction Grip 1809.2.1.3 Transforming Pressure into a Self-Reinforcing Response 1829.2.1.4 Transforming Weight into a Self-Reinforcing Response 1829.2.1.5 Transforming Moments into a Self-Reinforcing Response 1829.2.1.6 Self-Reinforcement by Self-Balancing 1839.2.1.7 Self-Reinforcement by Self-Anchoring 1849.2.2 Transforming Motion into a Self-Reinforcing Response 1869.2.3 Self-Reinforcement by Self-Alignment 1869.2.3.1 Case Study: Self-Reinforcement by Self-Alignment of a Rectangular Panel Under Wind Pressure 1879.2.4 Self-Reinforcement Through Modified Geometry and Strains 1889.3 Self-Reinforcement by Feedback Loops 1889.3.1 Self-Reinforcement by Creating Negative Feedback Loops 1889.3.2 Positive Feedback Loops 1899.3.3 Reducing Risk by Eliminating or Inhibiting Positive Feedback Loops with Negative Impact 1909.3.3.1 Case Study: Growth of Damage Sustained by a Positive Feedback Loop with Negative Impact 1929.3.4 Self-Reinforcement by Creating Positive Feedback Loops with Positive Impact 1949.3.4.1 Case Study: Positive Feedback Loop Providing Self-Reinforcement by Self-Energising 19510 Improving Reliability and Reducing Risk by Minimising the Rate of Damage Accumulation and by a Substitution 19710.1 Improving Reliability and Reducing Risk by Minimising the Rate of Damage Accumulation 19710.1.1 Classification of Failures Caused by Accumulation of Damage 19710.1.2 Minimising the Rate of Damage Accumulation by Optimal Replacement 19810.1.3 Minimising the Rate of Damage Accumulation by Selecting the Optimal Variation of the Damage-Inducing Factors 20310.1.3.1 A Case Related to a Single Damage-Inducing Factor 20310.1.3.2 A Case Related to Multiple Damage-Inducing Factors 20610.1.3.3 Reducing the Rate of Damage Accumulation by Derating 20910.1.4 Reducing the Rate of Damage Accumulation by Deliberate Weaknesses 21010.1.5 Reducing the Rate of Damage Accumulation by Reducing Exposure to Acceleration Stresses 21110.1.5.1 Reducing Exposure to Acceleration Stresses by Reducing the Magnitude of the Acceleration Stresses 21110.1.5.2 Reducing Exposure to Acceleration Stresses by Modifying or Replacing the Working Environment 21110.1.6 Reducing the Rate of Damage Accumulation by Appropriate Materials Selection, Design, and Manufacturing 21210.2 Improving Reliability and Reducing Risk by Substitution with Assemblies Working on Different Physical Principles 21310.2.1 Increasing Reliability by a Substitution with Magnetic Assemblies 21510.2.2 Increasing Reliability by a Substitution with Electrical Systems 21510.2.3 Increasing Reliability by a Substitution with Optical Assemblies 21610.2.4 Increasing Reliability and Reducing Risk by a Substitution with Software 21711 Improving Reliability by Comparative Models, Permutations, and by Reducing the Time/Space Exposure 21911.1 A Comparative Method for Improving System Reliability 21911.1.1 Comparative Method for Improving System Reliability Based on Proving an Inequality 22011.1.2 The Method of Biased Coins for Proving System Reliability Inequalities 22111.1.2.1 Case Study: Comparative Method for Improving System Reliability by the Method of Biased Coins 22311.1.3 A Comparative Method Based on Computer Simulation for Production Networks 22511.2 Improving Reliability and Reducing Risk by Permutations of Interchangeable Components and Processes 22611.3 Improving Reliability and Availability by Appropriate Placement of the Condition Monitoring Equipment 22911.4 Improving Reliability and Reducing Risk by Reducing Time/Space Exposure 23111.4.1 Reducing the Time of Exposure 23111.4.2 Reducing the Space of Exposure 23211.4.2.1 Case Study: Reducing the Risk of Failure of Wires by Simultaneously Reducing the Cost 23211.4.2.2 Case Study: Evaluating the Risk of Failure of Components with Complex Shape 23312 Reducing Risk by Determining the Exact Upper Bound of Uncertainty 23512.1 Uncertainty Associated with Properties from Multiple Sources 23512.2 Quantifying Uncertainty in the Case of Known Mixing Proportions 23712.2.1 Variance of a Property from Multiple Sources in the Case Where the Mixing Proportions are Known 23912.2.1.1 Case Study: Estimating the Uncertainty in Setting Positioning Distance 23912.3 A Tight Upper Bound for the Uncertainty in the Case of Unknown Mixing Proportions 24212.3.1 Variance Upper Bound Theorem 24212.3.2 An Algorithm for Determining the Exact Upper Bound of the Variance of Properties from Multiple Sources 24312.3.3 Determining the Source Whose Removal Results in the Largest Decrease of the Exact Variance Upper Bound 24412.4 Applications of the Variance Upper Bound 24512.4.1 Using the Variance Upper Bound for Increasing the Robustness of Products and Processes 24512.4.2 Using the Variance Upper Bound for Increasing the Robustness of Electronic Devices 24612.4.2.1 Case Study: Calculating the Worst-Case Variation by the Variance Upper Bound Theorem 24612.4.3 Using the Variance Upper Bound Theorem for Delivering Conservative Designs 24712.4.3.1 Case Study: Identifying the Distributions Associated with the Worst-Case Variation During Virtual Testing 24712.5 Using Standard Inequalities to Obtain a Tight Upper Bound for the Uncertainty in Mechanical Properties 248References 251Index 261

MICHAEL TODINOV has a background in mechanical engineering, applied mathematics and computer science. He received his PhD and his higher doctorate (DEng) from the University of Birmingham and is currently a professor in mechanical engineering in Oxford Brookes University, UK. Professor Todinov is an internationally acclaimed expert in reliability and risk. In 2017, he received the prestige IMechE award in the area of risk reduction in mechanical engineering. He has published four research monographs and a large number of research papers in the area of reliability and risk. His name is associated with developing theoretical and computational frameworks for analysis and optimisation of repairable flow networks and for reliability analysis based on the cost of failure.

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• Preface xv1 Domain-Independent Methods for Reliability Improvement and Risk Reduction 11.1 The Domain-Specific Methods for Risk Reduction 11.2 The Statistical, Data-Driven Approach 31.3 The Physics-of-Failure Approach 41.4 Reliability Improvement and TRIZ 61.5 The Domain-Independent Methods for Reliability Improvement and Risk Reduction 62 Basic Concepts 92.1 Likelihood of Failure, Consequences from Failure, Potential Loss, and Risk of Failure 92.2 Drawbacks of the Expected Loss as a Measure of the Potential Loss from Failure 142.3 Potential Loss, Conditional Loss, and Risk of Failure 152.4 Improving Reliability and Reducing Risk 192.5 Resilience 213 Overview of Methods and Principles for Improving Reliability and Reducing Risk That Can Be Classified as Domain-Independent 233.1 Improving Reliability and Reducing Risk by Preventing Failure Modes 233.1.1 Techniques for Identifying and Assessing Failure Modes 233.1.2 Effective Risk Reduction Procedure Related to Preventing Failure Modes from Occurring 273.1.3 Reliability Improvement and Risk Reduction by Root Cause Analysis 283.1.3.1 Case Study: Improving the Reliability of Automotive Suspension Springs by Root Cause Analysis 283.1.4 Preventing Failure Modes by Removing Latent Faults 293.2 Improving Reliability and Reducing Risk by a Fault-Tolerant System Design and Fail-Safe Design 313.2.1 Building in Redundancy 313.2.1.1 Case Study: Improving Reliability by k-out-of-n redundancy 343.2.2 Fault-Tolerant Design 343.2.3 Fail-Safe Principle and Fail-Safe Design 353.2.4 Reducing Risk by Eliminating Vulnerabilities 363.2.4.1 Eliminating Design Vulnerabilities 363.2.4.2 Reducing the Negative Impact of Weak Links 373.2.4.3 Reducing the Likelihood of Unfavourable Combinations of Risk-Critical Random Factors 383.2.4.4 Reducing the Vulnerability of Computational Models 393.3 Improving Reliability and Reducing Risk by Protecting Against Common Cause 403.4 Improving Reliability and Reducing Risk by Simplifying at a System and Component Level 423.5 Improving Reliability and Reducing Risk by Reducing the Variability of Risk-Critical Parameters 443.5.1 Case Study: Interaction Between the Upper Tail of the Load Distribution and the Lower Tail of the Strength Distribution 463.6 Improving Reliability and Reducing Risk by Making the Design Robust 483.6.1 Case Study: Increasing the Robustness of a Spring Assembly with Constant Clamping Force 503.7 Improving Reliability and Reducing Risk by Built-in Reinforcement 513.7.1 Built-In Prevention Reinforcement 513.7.2 Built-In Protection Reinforcement 513.8 Improving Reliability and Reducing Risk by Condition Monitoring 523.9 Reducing the Risk of Failure by Improving Maintainability 563.10 Reducing Risk by Eliminating Factors Promoting Human Errors 573.11 Reducing Risk by Reducing the Hazard Potential 583.12 Reducing Risk by using Protective Barriers 593.13 Reducing Risk by Efficient Troubleshooting Procedures and Systems 603.14 Risk Planning and Training 604 Improving Reliability and Reducing Risk by Separation 614.1 The Method of Separation 614.2 Separation of Risk-Critical Factors 624.2.1 Time Separation by Scheduling 624.2.1.1 Case Study: Full Time Separation with Random Starts of the Events 624.2.2 Time and Space Separation by Using Interlocks 634.2.2.1 Case Study: A Time Separation by Using an Interlock 634.2.3 Time Separation in Distributed Systems by Using Logical Clocks 644.2.4 Space Separation of Information 654.2.5 Separation of Duties to Reduce the Risk of Compromised Safety, Errors, and Fraud 654.2.6 Logical Separation by Using a Shared Unique Key 664.2.6.1 Case Study: Logical Separation of X-ray Equipment by a Shared Unique Key 664.2.7 Separation by Providing Conditions for Independent Operation 674.3 Separation of Functions, Properties, or Behaviour 684.3.1 Separation of Functions 684.3.1.1 Separation of Functions to Optimise for Maximum Reliability 684.3.1.2 Separation of Functions to Reduce Load Magnitudes 704.3.1.3 Separation of a Single Function into Multiple Components to Reduce Vulnerability to a Single Failure 714.3.1.4 Separation of Functions to Compensate Deficiencies 714.3.1.5 Separation of Functions to Prevent Unwanted Interactions 714.3.1.6 Separation of Methods to Reduce the Risk Associated with Incorrect Mathematical Models 724.4 Separation of Properties to Counter Poor Performance Caused by Inhomogeneity 724.4.1 Separation of Strength Across Components and Zones According to the Intensity of the Stresses from Loading 724.4.2 Separation of Properties to Satisfy Conflicting Requirements 744.4.3 Separation in Geometry 754.4.3.1 Case Study: Separation in Geometry for a Cantilever Beam 754.5 Separation on a Parameter, Conditions, or Scale 764.5.1 Separation at Distinct Values of a Risk-Critical Parameter Through Deliberate Weaknesses and Stress Limiters 764.5.2 Separation by Using Phase Changes 774.5.3 Separation of Reliability Across Components and Assemblies According to Their Cost of Failure 774.5.3.1 Case Study: Separation of the Reliability of Components Based on the Cost of Failure 785 Reducing Risk by Deliberate Weaknesses 815.1 Reducing the Consequences from Failure Through Deliberate Weaknesses 815.2 Separation from Excessive Levels of Stress 825.2.1 Deliberate Weaknesses Disconnecting Excessive Load 825.2.2 Energy-Absorbing Deliberate Weaknesses 855.2.2.1 Case Study: Reducing the Maximum Stress from Dynamic Loading by Energy-Absorbing Elastic Components 855.2.3 Designing Frangible Objects or Weakly Fixed Objects 865.3 Separation from Excessive Levels of Damage 875.3.1 Deliberate Weaknesses Decoupling Damaged Regions and Limiting the Spread of Damage 875.3.2 Deliberate Weaknesses Providing Stress and Strain Relaxation 885.3.3 Deliberate Weaknesses Separating from Excessive Levels of Damage Accumulation 905.4 Deliberate Weaknesses Deflecting the Failure Location or Damage Propagation 915.4.1 Deflecting the Failure Location from Places Where the Cost of Failure is High 915.4.2 Deflecting the Failure Location from Places Where the Cost of Intervention for Repair is High 925.4.3 Deliberate Weaknesses Deflecting the Propagation of Damage 925.5 Deliberate Weaknesses Designed to Provide Warning 925.6 Deliberate Weaknesses Designed to Provide Quick Access or Activate Protection 945.7 Deliberate Weaknesses and Stress Limiters 946 Improving Reliability and Reducing Risk by Stochastic Separation 976.1 Stochastic Separation of Risk-Critical Factors 976.1.1 Real-Life Applications that Require Stochastic Separation 976.1.2 Stochastic Separation of a Fixed Number of Random Events with Different Duration Times 996.1.2.1 Case Study: Stochastic Separation of Consumers by Proportionally Reducing Their Demand Times 1026.1.3 Stochastic Separation of Random Events Following a Homogeneous Poisson Process 1056.1.3.1 Case Study: Stochastic Separation of Random Demands Following a Homogeneous Poisson Process 1066.1.4 Stochastic Separation Based on the Probability of Overlapping of Random Events for More than a Single Source Servicing the Random Demands 1066.1.5 Computer Simulation Algorithm Determining the Probability of Overlapping for More than a Single Source Servicing the Demands 1086.2 Expected Time Fraction of Simultaneous Presence of Critical Events 1106.2.1 Case Study: Expected Fraction of Unsatisfied Demand at a Constant Sum of the Time Fractions of User Demands 1126.2.2 Case Study: Servicing Random Demands from Ten Different Users, Each Characterised by a Distinct Demand Time Fraction 1146.3 Analytical Method for Determining the Expected Fraction of Unsatisfied Demand for Repair 1146.3.1 Case Study: Servicing Random Repairs from a System Including Components of Three Different Types, Each Characterised by a Distinct Repair Time 1156.4 Expected Time Fraction of Simultaneous Presence of Critical Events that have been Initiated with Specified Probabilities 1166.4.1 Case Study: Servicing Random Demands from Patients in a Hospital 1176.4.2 Case Study: Servicing Random Demands from Four Different Types of Users, Each Issuing a Demand with Certain Probability 1186.5 Stochastic Separation Based on the Expected Fraction of Unsatisfied Demand 1196.5.1 Fixed Number of Random Demands on a Time Interval 1196.5.2 Random Demands Following a Poisson Process on a Time Interval 1206.5.2.1 Case Study: Servicing Random Failures from Circular Knitting Machines by an Optimal Number of Repairmen 1227 Improving Reliability and Reducing Risk by Segmentation 1257.1 Segmentation as a Problem-Solving Strategy 1257.2 Creating a Modular System by Segmentation 1277.3 Preventing Damage Accumulation and Limiting Damage Propagation by Segmentation 1297.3.1 Creating Barriers Containing Damage 1297.3.2 Creating Weak Interfaces Dissipating or Deflecting Damage 1317.3.3 Reducing Deformations and Stresses by Segmentation 1317.3.4 Reducing Hazard Potential by Segmentation 1317.3.5 Reducing the Likelihood of Errors by Segmenting Operations 1327.3.6 Limiting the Presence of Flaws by Segmentation 1327.4 Improving Fault Tolerance and Reducing Vulnerability to a Single Failure by Segmentation 1337.4.1 Case Study: Improving Fault Tolerance of a Column Loaded in Compression by Segmentation 1337.4.2 Reducing the Vulnerability to a Single Failure by Segmentation 1367.5 Reducing Loading Stresses by Segmentation 1387.5.1 Improving Load Distribution by Segmentation 1387.5.2 Improving Heat Dissipation by Segmentation 1397.5.3 Case Study: Reducing Stress by Increasing the Perimeter to Cross-Sectional Area Ratio Through Segmentation 1407.6 Reducing the Probability of a Loss/Error by Segmentation 1427.6.1 Reducing the Likelihood of a Loss by Segmenting Opportunity Bets 1427.6.1.1 Case Study: Reducing the Risk of a Loss from a Risky Prospect Involving a Single Opportunity Bet 1437.6.2 Reducing the Likelihood of a Loss by Segmenting an Investment Portfolio 1447.6.3 Reducing the Likelihood of Erroneous Conclusion from Imperfect Tests by Segmentation 1457.7 Decreasing the Variation of Properties by Segmentation 1467.8 Improved Control and Condition Monitoring by Time Segmentation 1488 Improving Reliability and Reducing Risk by Inversion 1498.1 The Method of Inversion 1498.2 Improving Reliability by Inverting Functions, Relative Position, and Motion 1508.2.1 Case Study: Eliminating Failure Modes of an Alarm Circuit by Inversion of Functions 1518.2.2 Improving Reliability by Inverting the Relative Position of Objects 1528.2.2.1 Case Study: Inverting the Position of an Object with Respect to its Support to Improve Reliability 1538.3 Improving Reliability by Inverting Properties and Geometry 1558.3.1 Case Study: Improving Reliability by Inverting Mechanical Properties Whilst Maintaining an Invariant 1558.3.2 Case Study: Improving Reliability by Inverting Geometry Whilst Maintaining an Invariant 1568.4 Improving Reliability and Reducing Risk by Introducing Inverse States 1588.4.1 Inverse States Cancelling Anticipated Undesirable Effects 1588.4.2 Inverse States Buffering Anticipated Undesirable Effects 1598.4.3 Inverse States Reducing the Likelihood of an Erroneous Action 1608.5 Improving Reliability and Reducing Risk by Inverse Thinking 1618.5.1 Inverting the Problem Related to Reliability Improvement and Risk Reduction 1618.5.1.1 Case Study: Reducing the Risk of High Employee Turnover 1628.5.2 Improving Reliability and Reducing Risk by Inverting the Focus 1638.5.2.1 Shifting the Focus from the Components to the System 1638.5.2.2 Starting from the Desired Ideal End Result 1638.5.2.3 Focusing on Events that are Missing 1648.5.3 Improving Reliability and Reducing Risk by Moving Backwards to Contributing Factors 1648.5.3.1 Case Study: Identifying Failure Modes of a Lubrication System by Moving Backwards to Contributing Factors 1658.5.4 Inverse Thinking in Mathematical Models Evaluating or Reducing Risk 1668.5.4.1 Case Study: Using the Method of Inversion for Fast Evaluation of the Production Availability of a Complex System 1678.5.4.2 Case Study: Repeated Inversion for Evaluating the Risk of Collision of Ships 1709 Reliability Improvement and Risk Reduction Through Self-Reinforcement 1779.1 Self-Reinforcement Mechanisms 1779.2 Self-Reinforcement Relying on a Proportional Compensating Factor 1799.2.1 Transforming Forces and Pressure into a Self-Reinforcing Response 1799.2.1.1 Capturing a Self-Reinforcing Proportional Response from Friction Forces 1799.2.1.2 Case Study: Transforming Friction Forces into a Proportional Response in the Design of a Friction Grip 1809.2.1.3 Transforming Pressure into a Self-Reinforcing Response 1829.2.1.4 Transforming Weight into a Self-Reinforcing Response 1829.2.1.5 Transforming Moments into a Self-Reinforcing Response 1829.2.1.6 Self-Reinforcement by Self-Balancing 1839.2.1.7 Self-Reinforcement by Self-Anchoring 1849.2.2 Transforming Motion into a Self-Reinforcing Response 1869.2.3 Self-Reinforcement by Self-Alignment 1869.2.3.1 Case Study: Self-Reinforcement by Self-Alignment of a Rectangular Panel Under Wind Pressure 1879.2.4 Self-Reinforcement Through Modified Geometry and Strains 1889.3 Self-Reinforcement by Feedback Loops 1889.3.1 Self-Reinforcement by Creating Negative Feedback Loops 1889.3.2 Positive Feedback Loops 1899.3.3 Reducing Risk by Eliminating or Inhibiting Positive Feedback Loops with Negative Impact 1909.3.3.1 Case Study: Growth of Damage Sustained by a Positive Feedback Loop with Negative Impact 1929.3.4 Self-Reinforcement by Creating Positive Feedback Loops with Positive Impact 1949.3.4.1 Case Study: Positive Feedback Loop Providing Self-Reinforcement by Self-Energising 19510 Improving Reliability and Reducing Risk by Minimising the Rate of Damage Accumulation and by a Substitution 19710.1 Improving Reliability and Reducing Risk by Minimising the Rate of Damage Accumulation 19710.1.1 Classification of Failures Caused by Accumulation of Damage 19710.1.2 Minimising the Rate of Damage Accumulation by Optimal Replacement 19810.1.3 Minimising the Rate of Damage Accumulation by Selecting the Optimal Variation of the Damage-Inducing Factors 20310.1.3.1 A Case Related to a Single Damage-Inducing Factor 20310.1.3.2 A Case Related to Multiple Damage-Inducing Factors 20610.1.3.3 Reducing the Rate of Damage Accumulation by Derating 20910.1.4 Reducing the Rate of Damage Accumulation by Deliberate Weaknesses 21010.1.5 Reducing the Rate of Damage Accumulation by Reducing Exposure to Acceleration Stresses 21110.1.5.1 Reducing Exposure to Acceleration Stresses by Reducing the Magnitude of the Acceleration Stresses 21110.1.5.2 Reducing Exposure to Acceleration Stresses by Modifying or Replacing the Working Environment 21110.1.6 Reducing the Rate of Damage Accumulation by Appropriate Materials Selection, Design, and Manufacturing 21210.2 Improving Reliability and Reducing Risk by Substitution with Assemblies Working on Different Physical Principles 21310.2.1 Increasing Reliability by a Substitution with Magnetic Assemblies 21510.2.2 Increasing Reliability by a Substitution with Electrical Systems 21510.2.3 Increasing Reliability by a Substitution with Optical Assemblies 21610.2.4 Increasing Reliability and Reducing Risk by a Substitution with Software 21711 Improving Reliability by Comparative Models, Permutations, and by Reducing the Time/Space Exposure 21911.1 A Comparative Method for Improving System Reliability 21911.1.1 Comparative Method for Improving System Reliability Based on Proving an Inequality 22011.1.2 The Method of Biased Coins for Proving System Reliability Inequalities 22111.1.2.1 Case Study: Comparative Method for Improving System Reliability by the Method of Biased Coins 22311.1.3 A Comparative Method Based on Computer Simulation for Production Networks 22511.2 Improving Reliability and Reducing Risk by Permutations of Interchangeable Components and Processes 22611.3 Improving Reliability and Availability by Appropriate Placement of the Condition Monitoring Equipment 22911.4 Improving Reliability and Reducing Risk by Reducing Time/Space Exposure 23111.4.1 Reducing the Time of Exposure 23111.4.2 Reducing the Space of Exposure 23211.4.2.1 Case Study: Reducing the Risk of Failure of Wires by Simultaneously Reducing the Cost 23211.4.2.2 Case Study: Evaluating the Risk of Failure of Components with Complex Shape 23312 Reducing Risk by Determining the Exact Upper Bound of Uncertainty 23512.1 Uncertainty Associated with Properties from Multiple Sources 23512.2 Quantifying Uncertainty in the Case of Known Mixing Proportions 23712.2.1 Variance of a Property from Multiple Sources in the Case Where the Mixing Proportions are Known 23912.2.1.1 Case Study: Estimating the Uncertainty in Setting Positioning Distance 23912.3 A Tight Upper Bound for the Uncertainty in the Case of Unknown Mixing Proportions 24212.3.1 Variance Upper Bound Theorem 24212.3.2 An Algorithm for Determining the Exact Upper Bound of the Variance of Properties from Multiple Sources 24312.3.3 Determining the Source Whose Removal Results in the Largest Decrease of the Exact Variance Upper Bound 24412.4 Applications of the Variance Upper Bound 24512.4.1 Using the Variance Upper Bound for Increasing the Robustness of Products and Processes 24512.4.2 Using the Variance Upper Bound for Increasing the Robustness of Electronic Devices 24612.4.2.1 Case Study: Calculating the Worst-Case Variation by the Variance Upper Bound Theorem 24612.4.3 Using the Variance Upper Bound Theorem for Delivering Conservative Designs 24712.4.3.1 Case Study: Identifying the Distributions Associated with the Worst-Case Variation During Virtual Testing 24712.5 Using Standard Inequalities to Obtain a Tight Upper Bound for the Uncertainty in Mechanical Properties 248References 251Index 261

MICHAEL TODINOV has a background in mechanical engineering, applied mathematics and computer science. He received his PhD and his higher doctorate (DEng) from the University of Birmingham and is currently a professor in mechanical engineering in Oxford Brookes University, UK. Professor Todinov is an internationally acclaimed expert in reliability and risk. In 2017, he received the prestige IMechE award in the area of risk reduction in mechanical engineering. He has published four research monographs and a large number of research papers in the area of reliability and risk. His name is associated with developing theoretical and computational frameworks for analysis and optimisation of repairable flow networks and for reliability analysis based on the cost of failure.

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• Preface xv1 Domain-Independent Methods for Reliability Improvement and Risk Reduction 11.1 The Domain-Specific Methods for Risk Reduction 11.2 The Statistical, Data-Driven Approach 31.3 The Physics-of-Failure Approach 41.4 Reliability Improvement and TRIZ 61.5 The Domain-Independent Methods for Reliability Improvement and Risk Reduction 62 Basic Concepts 92.1 Likelihood of Failure, Consequences from Failure, Potential Loss, and Risk of Failure 92.2 Drawbacks of the Expected Loss as a Measure of the Potential Loss from Failure 142.3 Potential Loss, Conditional Loss, and Risk of Failure 152.4 Improving Reliability and Reducing Risk 192.5 Resilience 213 Overview of Methods and Principles for Improving Reliability and Reducing Risk That Can Be Classified as Domain-Independent 233.1 Improving Reliability and Reducing Risk by Preventing Failure Modes 233.1.1 Techniques for Identifying and Assessing Failure Modes 233.1.2 Effective Risk Reduction Procedure Related to Preventing Failure Modes from Occurring 273.1.3 Reliability Improvement and Risk Reduction by Root Cause Analysis 283.1.3.1 Case Study: Improving the Reliability of Automotive Suspension Springs by Root Cause Analysis 283.1.4 Preventing Failure Modes by Removing Latent Faults 293.2 Improving Reliability and Reducing Risk by a Fault-Tolerant System Design and Fail-Safe Design 313.2.1 Building in Redundancy 313.2.1.1 Case Study: Improving Reliability by k-out-of-n redundancy 343.2.2 Fault-Tolerant Design 343.2.3 Fail-Safe Principle and Fail-Safe Design 353.2.4 Reducing Risk by Eliminating Vulnerabilities 363.2.4.1 Eliminating Design Vulnerabilities 363.2.4.2 Reducing the Negative Impact of Weak Links 373.2.4.3 Reducing the Likelihood of Unfavourable Combinations of Risk-Critical Random Factors 383.2.4.4 Reducing the Vulnerability of Computational Models 393.3 Improving Reliability and Reducing Risk by Protecting Against Common Cause 403.4 Improving Reliability and Reducing Risk by Simplifying at a System and Component Level 423.5 Improving Reliability and Reducing Risk by Reducing the Variability of Risk-Critical Parameters 443.5.1 Case Study: Interaction Between the Upper Tail of the Load Distribution and the Lower Tail of the Strength Distribution 463.6 Improving Reliability and Reducing Risk by Making the Design Robust 483.6.1 Case Study: Increasing the Robustness of a Spring Assembly with Constant Clamping Force 503.7 Improving Reliability and Reducing Risk by Built-in Reinforcement 513.7.1 Built-In Prevention Reinforcement 513.7.2 Built-In Protection Reinforcement 513.8 Improving Reliability and Reducing Risk by Condition Monitoring 523.9 Reducing the Risk of Failure by Improving Maintainability 563.10 Reducing Risk by Eliminating Factors Promoting Human Errors 573.11 Reducing Risk by Reducing the Hazard Potential 583.12 Reducing Risk by using Protective Barriers 593.13 Reducing Risk by Efficient Troubleshooting Procedures and Systems 603.14 Risk Planning and Training 604 Improving Reliability and Reducing Risk by Separation 614.1 The Method of Separation 614.2 Separation of Risk-Critical Factors 624.2.1 Time Separation by Scheduling 624.2.1.1 Case Study: Full Time Separation with Random Starts of the Events 624.2.2 Time and Space Separation by Using Interlocks 634.2.2.1 Case Study: A Time Separation by Using an Interlock 634.2.3 Time Separation in Distributed Systems by Using Logical Clocks 644.2.4 Space Separation of Information 654.2.5 Separation of Duties to Reduce the Risk of Compromised Safety, Errors, and Fraud 654.2.6 Logical Separation by Using a Shared Unique Key 664.2.6.1 Case Study: Logical Separation of X-ray Equipment by a Shared Unique Key 664.2.7 Separation by Providing Conditions for Independent Operation 674.3 Separation of Functions, Properties, or Behaviour 684.3.1 Separation of Functions 684.3.1.1 Separation of Functions to Optimise for Maximum Reliability 684.3.1.2 Separation of Functions to Reduce Load Magnitudes 704.3.1.3 Separation of a Single Function into Multiple Components to Reduce Vulnerability to a Single Failure 714.3.1.4 Separation of Functions to Compensate Deficiencies 714.3.1.5 Separation of Functions to Prevent Unwanted Interactions 714.3.1.6 Separation of Methods to Reduce the Risk Associated with Incorrect Mathematical Models 724.4 Separation of Properties to Counter Poor Performance Caused by Inhomogeneity 724.4.1 Separation of Strength Across Components and Zones According to the Intensity of the Stresses from Loading 724.4.2 Separation of Properties to Satisfy Conflicting Requirements 744.4.3 Separation in Geometry 754.4.3.1 Case Study: Separation in Geometry for a Cantilever Beam 754.5 Separation on a Parameter, Conditions, or Scale 764.5.1 Separation at Distinct Values of a Risk-Critical Parameter Through Deliberate Weaknesses and Stress Limiters 764.5.2 Separation by Using Phase Changes 774.5.3 Separation of Reliability Across Components and Assemblies According to Their Cost of Failure 774.5.3.1 Case Study: Separation of the Reliability of Components Based on the Cost of Failure 785 Reducing Risk by Deliberate Weaknesses 815.1 Reducing the Consequences from Failure Through Deliberate Weaknesses 815.2 Separation from Excessive Levels of Stress 825.2.1 Deliberate Weaknesses Disconnecting Excessive Load 825.2.2 Energy-Absorbing Deliberate Weaknesses 855.2.2.1 Case Study: Reducing the Maximum Stress from Dynamic Loading by Energy-Absorbing Elastic Components 855.2.3 Designing Frangible Objects or Weakly Fixed Objects 865.3 Separation from Excessive Levels of Damage 875.3.1 Deliberate Weaknesses Decoupling Damaged Regions and Limiting the Spread of Damage 875.3.2 Deliberate Weaknesses Providing Stress and Strain Relaxation 885.3.3 Deliberate Weaknesses Separating from Excessive Levels of Damage Accumulation 905.4 Deliberate Weaknesses Deflecting the Failure Location or Damage Propagation 915.4.1 Deflecting the Failure Location from Places Where the Cost of Failure is High 915.4.2 Deflecting the Failure Location from Places Where the Cost of Intervention for Repair is High 925.4.3 Deliberate Weaknesses Deflecting the Propagation of Damage 925.5 Deliberate Weaknesses Designed to Provide Warning 925.6 Deliberate Weaknesses Designed to Provide Quick Access or Activate Protection 945.7 Deliberate Weaknesses and Stress Limiters 946 Improving Reliability and Reducing Risk by Stochastic Separation 976.1 Stochastic Separation of Risk-Critical Factors 976.1.1 Real-Life Applications that Require Stochastic Separation 976.1.2 Stochastic Separation of a Fixed Number of Random Events with Different Duration Times 996.1.2.1 Case Study: Stochastic Separation of Consumers by Proportionally Reducing Their Demand Times 1026.1.3 Stochastic Separation of Random Events Following a Homogeneous Poisson Process 1056.1.3.1 Case Study: Stochastic Separation of Random Demands Following a Homogeneous Poisson Process 1066.1.4 Stochastic Separation Based on the Probability of Overlapping of Random Events for More than a Single Source Servicing the Random Demands 1066.1.5 Computer Simulation Algorithm Determining the Probability of Overlapping for More than a Single Source Servicing the Demands 1086.2 Expected Time Fraction of Simultaneous Presence of Critical Events 1106.2.1 Case Study: Expected Fraction of Unsatisfied Demand at a Constant Sum of the Time Fractions of User Demands 1126.2.2 Case Study: Servicing Random Demands from Ten Different Users, Each Characterised by a Distinct Demand Time Fraction 1146.3 Analytical Method for Determining the Expected Fraction of Unsatisfied Demand for Repair 1146.3.1 Case Study: Servicing Random Repairs from a System Including Components of Three Different Types, Each Characterised by a Distinct Repair Time 1156.4 Expected Time Fraction of Simultaneous Presence of Critical Events that have been Initiated with Specified Probabilities 1166.4.1 Case Study: Servicing Random Demands from Patients in a Hospital 1176.4.2 Case Study: Servicing Random Demands from Four Different Types of Users, Each Issuing a Demand with Certain Probability 1186.5 Stochastic Separation Based on the Expected Fraction of Unsatisfied Demand 1196.5.1 Fixed Number of Random Demands on a Time Interval 1196.5.2 Random Demands Following a Poisson Process on a Time Interval 1206.5.2.1 Case Study: Servicing Random Failures from Circular Knitting Machines by an Optimal Number of Repairmen 1227 Improving Reliability and Reducing Risk by Segmentation 1257.1 Segmentation as a Problem-Solving Strategy 1257.2 Creating a Modular System by Segmentation 1277.3 Preventing Damage Accumulation and Limiting Damage Propagation by Segmentation 1297.3.1 Creating Barriers Containing Damage 1297.3.2 Creating Weak Interfaces Dissipating or Deflecting Damage 1317.3.3 Reducing Deformations and Stresses by Segmentation 1317.3.4 Reducing Hazard Potential by Segmentation 1317.3.5 Reducing the Likelihood of Errors by Segmenting Operations 1327.3.6 Limiting the Presence of Flaws by Segmentation 1327.4 Improving Fault Tolerance and Reducing Vulnerability to a Single Failure by Segmentation 1337.4.1 Case Study: Improving Fault Tolerance of a Column Loaded in Compression by Segmentation 1337.4.2 Reducing the Vulnerability to a Single Failure by Segmentation 1367.5 Reducing Loading Stresses by Segmentation 1387.5.1 Improving Load Distribution by Segmentation 1387.5.2 Improving Heat Dissipation by Segmentation 1397.5.3 Case Study: Reducing Stress by Increasing the Perimeter to Cross-Sectional Area Ratio Through Segmentation 1407.6 Reducing the Probability of a Loss/Error by Segmentation 1427.6.1 Reducing the Likelihood of a Loss by Segmenting Opportunity Bets 1427.6.1.1 Case Study: Reducing the Risk of a Loss from a Risky Prospect Involving a Single Opportunity Bet 1437.6.2 Reducing the Likelihood of a Loss by Segmenting an Investment Portfolio 1447.6.3 Reducing the Likelihood of Erroneous Conclusion from Imperfect Tests by Segmentation 1457.7 Decreasing the Variation of Properties by Segmentation 1467.8 Improved Control and Condition Monitoring by Time Segmentation 1488 Improving Reliability and Reducing Risk by Inversion 1498.1 The Method of Inversion 1498.2 Improving Reliability by Inverting Functions, Relative Position, and Motion 1508.2.1 Case Study: Eliminating Failure Modes of an Alarm Circuit by Inversion of Functions 1518.2.2 Improving Reliability by Inverting the Relative Position of Objects 1528.2.2.1 Case Study: Inverting the Position of an Object with Respect to its Support to Improve Reliability 1538.3 Improving Reliability by Inverting Properties and Geometry 1558.3.1 Case Study: Improving Reliability by Inverting Mechanical Properties Whilst Maintaining an Invariant 1558.3.2 Case Study: Improving Reliability by Inverting Geometry Whilst Maintaining an Invariant 1568.4 Improving Reliability and Reducing Risk by Introducing Inverse States 1588.4.1 Inverse States Cancelling Anticipated Undesirable Effects 1588.4.2 Inverse States Buffering Anticipated Undesirable Effects 1598.4.3 Inverse States Reducing the Likelihood of an Erroneous Action 1608.5 Improving Reliability and Reducing Risk by Inverse Thinking 1618.5.1 Inverting the Problem Related to Reliability Improvement and Risk Reduction 1618.5.1.1 Case Study: Reducing the Risk of High Employee Turnover 1628.5.2 Improving Reliability and Reducing Risk by Inverting the Focus 1638.5.2.1 Shifting the Focus from the Components to the System 1638.5.2.2 Starting from the Desired Ideal End Result 1638.5.2.3 Focusing on Events that are Missing 1648.5.3 Improving Reliability and Reducing Risk by Moving Backwards to Contributing Factors 1648.5.3.1 Case Study: Identifying Failure Modes of a Lubrication System by Moving Backwards to Contributing Factors 1658.5.4 Inverse Thinking in Mathematical Models Evaluating or Reducing Risk 1668.5.4.1 Case Study: Using the Method of Inversion for Fast Evaluation of the Production Availability of a Complex System 1678.5.4.2 Case Study: Repeated Inversion for Evaluating the Risk of Collision of Ships 1709 Reliability Improvement and Risk Reduction Through Self-Reinforcement 1779.1 Self-Reinforcement Mechanisms 1779.2 Self-Reinforcement Relying on a Proportional Compensating Factor 1799.2.1 Transforming Forces and Pressure into a Self-Reinforcing Response 1799.2.1.1 Capturing a Self-Reinforcing Proportional Response from Friction Forces 1799.2.1.2 Case Study: Transforming Friction Forces into a Proportional Response in the Design of a Friction Grip 1809.2.1.3 Transforming Pressure into a Self-Reinforcing Response 1829.2.1.4 Transforming Weight into a Self-Reinforcing Response 1829.2.1.5 Transforming Moments into a Self-Reinforcing Response 1829.2.1.6 Self-Reinforcement by Self-Balancing 1839.2.1.7 Self-Reinforcement by Self-Anchoring 1849.2.2 Transforming Motion into a Self-Reinforcing Response 1869.2.3 Self-Reinforcement by Self-Alignment 1869.2.3.1 Case Study: Self-Reinforcement by Self-Alignment of a Rectangular Panel Under Wind Pressure 1879.2.4 Self-Reinforcement Through Modified Geometry and Strains 1889.3 Self-Reinforcement by Feedback Loops 1889.3.1 Self-Reinforcement by Creating Negative Feedback Loops 1889.3.2 Positive Feedback Loops 1899.3.3 Reducing Risk by Eliminating or Inhibiting Positive Feedback Loops with Negative Impact 1909.3.3.1 Case Study: Growth of Damage Sustained by a Positive Feedback Loop with Negative Impact 1929.3.4 Self-Reinforcement by Creating Positive Feedback Loops with Positive Impact 1949.3.4.1 Case Study: Positive Feedback Loop Providing Self-Reinforcement by Self-Energising 19510 Improving Reliability and Reducing Risk by Minimising the Rate of Damage Accumulation and by a Substitution 19710.1 Improving Reliability and Reducing Risk by Minimising the Rate of Damage Accumulation 19710.1.1 Classification of Failures Caused by Accumulation of Damage 19710.1.2 Minimising the Rate of Damage Accumulation by Optimal Replacement 19810.1.3 Minimising the Rate of Damage Accumulation by Selecting the Optimal Variation of the Damage-Inducing Factors 20310.1.3.1 A Case Related to a Single Damage-Inducing Factor 20310.1.3.2 A Case Related to Multiple Damage-Inducing Factors 20610.1.3.3 Reducing the Rate of Damage Accumulation by Derating 20910.1.4 Reducing the Rate of Damage Accumulation by Deliberate Weaknesses 21010.1.5 Reducing the Rate of Damage Accumulation by Reducing Exposure to Acceleration Stresses 21110.1.5.1 Reducing Exposure to Acceleration Stresses by Reducing the Magnitude of the Acceleration Stresses 21110.1.5.2 Reducing Exposure to Acceleration Stresses by Modifying or Replacing the Working Environment 21110.1.6 Reducing the Rate of Damage Accumulation by Appropriate Materials Selection, Design, and Manufacturing 21210.2 Improving Reliability and Reducing Risk by Substitution with Assemblies Working on Different Physical Principles 21310.2.1 Increasing Reliability by a Substitution with Magnetic Assemblies 21510.2.2 Increasing Reliability by a Substitution with Electrical Systems 21510.2.3 Increasing Reliability by a Substitution with Optical Assemblies 21610.2.4 Increasing Reliability and Reducing Risk by a Substitution with Software 21711 Improving Reliability by Comparative Models, Permutations, and by Reducing the Time/Space Exposure 21911.1 A Comparative Method for Improving System Reliability 21911.1.1 Comparative Method for Improving System Reliability Based on Proving an Inequality 22011.1.2 The Method of Biased Coins for Proving System Reliability Inequalities 22111.1.2.1 Case Study: Comparative Method for Improving System Reliability by the Method of Biased Coins 22311.1.3 A Comparative Method Based on Computer Simulation for Production Networks 22511.2 Improving Reliability and Reducing Risk by Permutations of Interchangeable Components and Processes 22611.3 Improving Reliability and Availability by Appropriate Placement of the Condition Monitoring Equipment 22911.4 Improving Reliability and Reducing Risk by Reducing Time/Space Exposure 23111.4.1 Reducing the Time of Exposure 23111.4.2 Reducing the Space of Exposure 23211.4.2.1 Case Study: Reducing the Risk of Failure of Wires by Simultaneously Reducing the Cost 23211.4.2.2 Case Study: Evaluating the Risk of Failure of Components with Complex Shape 23312 Reducing Risk by Determining the Exact Upper Bound of Uncertainty 23512.1 Uncertainty Associated with Properties from Multiple Sources 23512.2 Quantifying Uncertainty in the Case of Known Mixing Proportions 23712.2.1 Variance of a Property from Multiple Sources in the Case Where the Mixing Proportions are Known 23912.2.1.1 Case Study: Estimating the Uncertainty in Setting Positioning Distance 23912.3 A Tight Upper Bound for the Uncertainty in the Case of Unknown Mixing Proportions 24212.3.1 Variance Upper Bound Theorem 24212.3.2 An Algorithm for Determining the Exact Upper Bound of the Variance of Properties from Multiple Sources 24312.3.3 Determining the Source Whose Removal Results in the Largest Decrease of the Exact Variance Upper Bound 24412.4 Applications of the Variance Upper Bound 24512.4.1 Using the Variance Upper Bound for Increasing the Robustness of Products and Processes 24512.4.2 Using the Variance Upper Bound for Increasing the Robustness of Electronic Devices 24612.4.2.1 Case Study: Calculating the Worst-Case Variation by the Variance Upper Bound Theorem 24612.4.3 Using the Variance Upper Bound Theorem for Delivering Conservative Designs 24712.4.3.1 Case Study: Identifying the Distributions Associated with the Worst-Case Variation During Virtual Testing 24712.5 Using Standard Inequalities to Obtain a Tight Upper Bound for the Uncertainty in Mechanical Properties 248References 251Index 261