Maintenance, Replacement, and Reliability Theory and Applications SECOND EDITION Andrew K.S. Jardine Albert H.C. Tsang (cfc CRC Press Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Croup, an informa business
Contents Preface for the First Edition Preface for the Second Edition Acknowledgments for the First Edition xix Acknowledgments for the Second Edition xxi Authors Abstract xv xvii xxiii xxv Chapter 1 Introduction 1 1.1 From Maintenance Management to Physical Asset Management 1 1.2 Challenges of PAM 2 1.2.1 Emerging Trends of Operation Strategies 2 1.2.2 Toughening Societal Expectations 2 1.2.3 Technological Changes 2 1.2.4 Increased Emphasis on Sustainability 3 1.3 Improving PAM 4 1.3.1 Maintenance Excellence 4 1.3.1.1 Strategic 5 1.3.1.2 Tactical 5 1.3.1.3 Continuous Improvements 6 1.3.2 Quantum Leaps 6 1.4 PAS 55 A Framework for Optimized Management of Physical Assets 6 1.5 Reliability through the Operator: TPM 7 1.6 Reliability by Design: RCM 9 1.7 Optimizing Maintenance and Replacement Decisions 13 1.8 The Quantitative Approach 16 1.8.1 Setting Objectives 17 1.8.2 Models 18 1.8.3 Obtaining Solutions from Models 21 1.8.4 Maintenance Control and Mathematical Models 22 1.9 Data Requirements for Modeling 24 References 24 Chapter 2 Component Replacement Decisions 27 2.1 Introduction 27 2.2 Optimal Replacement Times for Equipment Whose Operating Cost Increases with Use 30 2.2.1 Statement of the Problem 30
viii Contents 2.2.2 Construction of the Model 31 2.2.3 Numerical Example 33 2.2.4 Further Comments 34 2.2.5 Applications 36 2.2.5.1 Replacing the Air Filter in an Automobile... 36 2.2.5.2 Overhauling a Boiler Plant 37 2.3 Stochastic Preventive Replacement: Some Introductory Comments 38 2.4 Optimal Preventive Replacement Interval of Items Subject to Breakdown (Also Known as the Group or Block Policy) 39 2.4.1 Statement of the Problem 39 2.4.2 Construction of the Model 40 2.4.3 Determination of H(t) 41 2.4.3.1 Renewal Theory Approach 41 2.4.3.2 Discrete Approach 43 2.4.4 Numerical Example 46 2.4.5 Further Comments 47 2.4.6 An Application: Optimal Replacement Interval for a Left-Hand Steering Clutch 48 2.5 Optimal Preventive Replacement Age of an Item Subject to Breakdown 48 2.5.1 Statement of the Problem 48 2.5.2 Construction of the Model 49 2.5.3 Numerical Example 52 2.5.4 Further Comments 53 2.5.5 An Application: Optimal Bearing Replacement Age 54 2.6 Optimal Preventive Replacement Age of an Item Subject to Breakdown, Taking Account of the Times Required to Carry Out Failure and Preventive Replacements 55 2.6.1 Statement of the Problem 55 2.6.2 Construction of the Model 55 2.6.3 Numerical Example 56 2.7 Optimal Preventive Replacement Interval or Age of an Item Subject to Breakdown: Minimization of Downtime 57 2.7.1 Statement of the Problem 57 2.7.2 Construction of the Models 58 2.7.2.1 Model 1: Determination of Optimal Preventive Replacement Interval 58 2.7.2.2 Model 2: Determination of Optimal Preventive Replacement Age 59 2.7.3 Numerical Examples 59 2.7.3.1 Model 1: Replacement Interval 59 2.7.3.2 Model 2: Replacement Age 60 2.7.4 Further Comments 61
Contents lx 2.7.5 Applications 61 2.7.5.1 Replacement of Sugar Refinery Cloths 61 2.7.5.2 Replacement of Sugar Feeds in a Sugar Refinery 62 2.8 Group Replacement: Optimal Interval between Group Replacements of Items Subject to Failure The Lamp Replacement Problem 62 2.8.1 Statement of the Problem 62 2.8.2 Construction of the Model 63 2.8.3 Numerical Example 64 2.8.4 Further Comments 64 2.8.5 An Application: Optimal Replacement Interval for a Group of 40 Valves in a Compressor 64 2.9 Further Replacement Models 65 2.9.1 Multistage Replacement 65 2.9.2 Optional Policies 66 2.9.3 Repairable Systems 67 2.10 Case Study on Project Prioritization, Trend Tests, Weibull Analysis, and Optimizing Component Replacement Intervals 70 2.10.1 Introduction 70 2.10.2 Optimal Preventive Replacement Age for Major Components 70 2.10.3 Optimal Preventive Replacement Age for Item Parts (Minor Components) 71 2.10.4 Conclusion for Item Parts 76 2.11 Spare Parts Provisioning: Preventive Replacement Spares 76 2.11.1 Introduction 76 2.11.2 Construction of the Model 77 2.11.2.1 The Constant Interval Model 77 2.11.2.2 The Age-Based Preventive Replacement Model 77 2.11.3 Numerical Example 77 2.11.3.1 Constant-Interval Policy 77 2.11.3.2 Age-Based Policy 78 2.11.4 Further Comments 78 2.11.5 An Application: Cylinder Head Replacement Constant-Interval Policy 78 2.12 Spare Parts Provisioning: Insurance Spares 78 2.12.1 Introduction 78 2.12.2 Classes of Components 79 2.12.2.1 Nonrepairable Components 79 2.12.2.2 Normal Distribution Approach 80 2.12.2.3 Poisson Distribution Approach 80 2.12.2.4 Repairable Components 81 2.12.3 Cost Model 83
X Contents 2.12.4 Further Comments 83 2.12.5 An Application: Electric Motors 83 2.13 Solving the Constant-Interval and Age-Based Models Graphically: Use of Glasser's Graphs 85 2.13.1 Introduction 85 2.13.2 Using Glasser's Graphs 86 2.13.3 Numerical Example 87 2.13.4 Calculation of the Savings 88 2.14 Solving the Constant-Interval and Age-Based Models Using OREST Software 89 2.14.1 Introduction 89 2.14.2 Using OREST 89 2.14.3 Further Comments 91 Problems 91 References 99 Chapter 3 Inspection Decisions 101 3.1 Introduction 101 3.2 Optimal Inspection Frequency: Maximization of Profit 101 3.2.1 Statement of the Problem 101 3.2.2 Construction of the Model 103 3.2.3 Numerical Example 106 3.2.4 Further Comments 107 3.3 Optimal Inspection Frequency: Minimization of Downtime... 108 3.3.1 Statement of the Problem 108 3.3.2 Construction of the Model 108 3.3.3 Numerical Example 109 3.3.4 Further Comments 109 3.3.5 An Application: Optimal Vehicle Fleet Inspection Schedule 110 3.4 Optimal Inspection Interval to Maximize the Availability of Equipment Used in Emergency Conditions, Such as a Protective Device 112 3.4.1 Statement of the Problem 112 3.4.2 Construction of the Model 113 3.4.3 Numerical Example 114 3.4.4 Further Comments 115 3.4.5 Exponential Failure Distribution and Negligible Time Required to Perform Inspections and Repairs/Replacements 116 3.4.6 An Application: Pressure Safety Valves in an Oil and Gas Field 116 3.5 Optimizing CBM Decisions 118 3.5.1 Introduction 118 3.5.2 The Proportional Hazards Model 119
Contents xl 3.5.3 Blending Hazard and Economics: Optimizing the CBM Decision 120 3.5.4 Applications 122 3.5.4.1 Food Processing: Use of Vibration Monitoring 122 3.5.4.2 Coal Mining: Use of Oil Analysis 123 3.5.4.3 Transportation: Use of Visual Inspection... 123 3.5.5 Further Comments 123 3.5.6 Software for CBM Optimization 125 3.5.6.1 Event Data 127 Problems 129 References 133 Chapter 4 Capital Equipment Replacement Decisions 135 4.1 Introduction 135 4.2 Optimal Replacement Interval for Capital Equipment: Minimization of Total Cost 137 4.2.1 Statement of the Problem 137 4.2.2 Construction of the Model 137 4.2.3 Numerical Example 138 4.2.4 Further Comments 139 4.2.5 Applications 141 4.2.5.1 Mobile Equipment: Vehicle Fleet Replacement 141 4.2.5.2 Fixed Equipment: Internal Combustion Engine 143 4.3 Optimal Replacement Interval for Capital Equipment: Maximization of Discounted Benefits 144 4.3.1 Statement of the Problem 144 4.3.2 Construction of the Model 144 4.3.2.1 First Cycle of Operation 146 4.3.2.2 Second Cycle of Operation 146 4.3.2.3 Third Cycle of Operation 147 4.3.2.4 nth Cycle of Operation 147 4.3.3 Numerical Example 148 4.3.4 Further Comments 149 4.3.5 Proof that Optimization over a Long Period Is Not Equivalent to Optimization per Unit Time When Discounting Is Included 150 4.4 Optimal Replacement Interval for Capital Equipment Whose Planned Utilization Pattern Is Variable: Minimization of Total Cost 151 4.4.1 Statement of the Problem 151 4.4.2 Construction of the Model 151 4.4.2.1 Consider a Replacement Cycle of n Years... 152
;ii Contents 4.4.3 Numerical Example 153 4.4.4 Further Comments 156 4.4.5 An Application: Establishing the Economic Life of a Fleet of Buses 156 4.5 Optimal Replacement Policy for Capital Equipment Taking into Account Technological Improvement: Finite Planning Horizon 157 4.5.1 Statement of the Problem 157 4.5.2 Construction of the Model 157 4.5.3 Numerical Example 159 4.5.4 Further Comments 161 4.5.5 An Application: Replacing Current Mining Equipment with a Technologically Improved Version 161 4.6 Optimal Replacement Policy for Capital Equipment Taking into Account Technological Improvement: Infinite Planning Horizon 161 4.6.1 Statement of the Problem 161 4.6.2 Construction of the Model 162 4.6.3 Numerical Example 163 4.6.4 Further Comments 164 4.6.5 An Application: Repair versus Replace of a Front-End Loader 164 4.7 Software for Economic Life Optimization 166 4.7.1 Introduction 166 4.7.2 Using PERDEC and AGE/CON 167 4.7.3 Further Comments 167 Problems 168 References 177 Chapter 5 Maintenance Resource Requirements 179 5.1 Introduction 179 5.1.1 Facilities for Maintenance within an Organization... 179 5.1.2 The Combined Use of the Facilities within an Organization and Outside Resources 180 5.2 Queuing Theory Preliminaries 181 5.2.1 Queuing Systems 182 5.2.2 Queuing Theory Results 183 5.2.2.1 Single-Channel Queuing System 183 5.2.2.2 Multichannel Queuing Systems 183 5.3 Optimal Number of Workshop Machines to Meet a Fluctuating Workload 183 5.3.1 Statement of the Problem 183 5.3.2 Construction of the Model 184 5.3.3 Numerical Example 185
Contents xiii 5.3.4 Further Comments 188 5.3.5 Applications 188 5.3.5.1 Optimizing the Backlog 188 5.3.5.2 Crew Size Optimization 189 5.4 Optimal Mix of Two Classes of Similar Equipment (Such as Medium/Large Lathes) to Meet a Fluctuating Workload 190 5.4.1 Statement of the Problem 190 5.4.2 Construction of the Model 190 5.4.2.1 Logic Flowchart 191 5.4.2.2 Obtaining Necessary Information and Constructing the Model 191 5.4.3 Numerical Example 193 5.4.4 Further Comments 200 5.4.5 Applications 201 5.4.5.1 Establishing the Optimal Number of Lathes in a Steel Mill 201 5.4.5.2 Balancing Maintenance Cost and Reliability in Thermal Generating Station 203 5.5 Rightsizing a Fleet of Equipment: An Application 205 5.5.1 An Application: Fleet Size in an Open-Pit Mine 205 5.6 Optimal Size of a Maintenance Workforce to Meet a Fluctuating Workload, Taking Account of Subcontracting Opportunities 206 5.6.1 Statement of the Problem 206 5.6.2 Construction of the Model 207 5.6.3 Numerical Example 210 5.6.4 Further Comments 211 5.6.5 An Example: Number of Vehicles to Have in a Fleet (Such as a Courier Fleet) 212 5.7 The Lease or Buy Decision 213 5.7.1 Statement of the Problem 213 5.7.2 Solution of the Problem 213 5.7.2.1 Use of Retained Earnings 213 5.7.2.2 Use of Borrowed Funds 214 5.7.2.3 Leasing 215 5.7.2.4 Conclusion 216 5.7.3 Further Comments 216 Problems 216 References 217 Appendix 1: Statistics Primer 219 Appendix 2: WeibuII Analysis 233 Appendix 3: Maximum Likelihood Estimator 275 Appendix 4: Markov Chains 279
xiv Contents Appendix 5: Knowledge Elicitation 283 Appendix 6: Time Value of Money Discounted Cash Flow Analysis 295 Appendix 7: List of Applications of Maintenance Decision Optimization Models 305 Appendix 8: Ordinates of the Standard Normal Distribution 309 Appendix 9: Areas in the Tail of the Standard Normal Distribution 311 Appendix 10: Values of Gamma Function 315 Appendix 11: Median Ranks Table 317 Appendix 12: Five Percent Ranks Table 319 Appendix 13: Ninety-Five Percent Ranks Table 321 Appendix 14: Critical Values for the Kolmogorov-Smirnov Statistic (da) 323 Appendix 15: Answers to Problems 325 Index 331