Reliability Engineering

<style>¿ </style> <p style="margin:0px;">Chapter 1 Introduction 1</p> <p style="margin:0px;">What You Will Learn 1</p> <p style="margin:0px;">1.1 Uncertainty in Engineering 1</p> <p style="margin:0px;">1.2 Definition of Reliability 2</p> <p style="margin:0px;">1.3 Importance of Reliability 3</p> <p style="margin:0px;">1.4 Pattern of Failures 4</p> <p style="margin:0px;">1.4.1 Component Failures 4</p> <p style="margin:0px;">1.4.2 Mechanical and Structural Failures 11</p> <p style="margin:0px;">1.5 Factor of Safety and Reliability 15</p> <p style="margin:0px;">1.6 Reliability Analysis Procedure 18</p> <p style="margin:0px;">1.7 Reliability Management 18</p> <p style="margin:0px;">1.8 History of Reliability Engineering 19</p> <p style="margin:0px;">1.9 Some Examples of System Failures 21</p> <p style="margin:0px;">1.9.1 Collapse of Tacoma Narrows Bridge in 1940 21</p> <p style="margin:0px;">1.9.2 Crash of El Al Boeing 747-200 in 1992 22</p> <p style="margin:0px;">1.9.3 Disaster of Space Shuttle Challenger in 1986 22</p> <p style="margin:0px;">1.9.4 Chernobyl Nuclear Power Plant Accident in 1986 24</p> <p style="margin:0px;">1.9.5 Mississippi River Bridge 9340 Collapse in 2007 24</p> <p style="margin:0px;">1.9.6 Fukushima Nuclear Accident in 2011 25</p> <p style="margin:0px;">1.9.7 Explosion of the First Jet Airplane Comet 26</p> <p style="margin:0px;">1.9.8 Breaking of the Tanker S. S. Schenectady 27</p> <p style="margin:0px;">1.9.9 Crash of the Supersonic Aircraft Concorde 27</p> <p style="margin:0px;">1.10 Numerical Solutions Using Matlab and Excel 29</p> <p style="margin:0px;">1.11 Reliability Literature 32</p> <p style="margin:0px;">References and Bibliography 32</p> <p style="margin:0px;">Review Questions 44</p> <p style="margin:0px;">Problems 45</p> <p style="margin:0px;">&nbsp;</p> <p style="margin:0px;">Chapter 2 Basic Probability Theory 50</p> <p style="margin:0px;">What You Will Learn 50</p> <p style="margin:0px;">2.1 Introduction 50</p> <p style="margin:0px;">2.2 Mutually Exclusive Events 51</p> <p style="margin:0px;">2.3 Set Theory 51</p> <p style="margin:0px;">2.4 Sample Points and Sample Space 52</p> <p style="margin:0px;">2.5 Definition of Probability 55</p> <p style="margin:0px;">2.5.1 Relative Frequency (Statistical) Definition 55</p> <p style="margin:0px;">2.5.2 Axiomatic Definition 55</p> <p style="margin:0px;">2.6 Laws of Probability 56</p> <p style="margin:0px;">2.6.1 Union and Intersection of Two Events 56</p> <p style="margin:0px;">2.6.2 Mutually Exclusive Events 56</p> <p style="margin:0px;">2.6.3 Complementary Events 59</p> <p style="margin:0px;">2.6.4 Conditional Probability 62</p> <p style="margin:0px;">2.6.5 Statistically Independent Events 65</p> <p style="margin:0px;">2.6.6 General Laws 66</p> <p style="margin:0px;">2.7 Total Probability Theorem 68</p> <p style="margin:0px;">2.8 Bayes’ Rule 73</p> <p style="margin:0px;">References and Bibliography 75</p> <p style="margin:0px;">Review Questions 76</p> <p style="margin:0px;">Problems 79</p> <p style="margin:0px;">&nbsp;</p> <p style="margin:0px;">Chapter 3 Random Variables and Probability Distributions 87</p> <p style="margin:0px;">What You Will Learn 87</p> <p style="margin:0px;">3.1 Introduction 87</p> <p style="margin:0px;">3.2 Probability Mass Function for Discrete Random Variables 88</p> <p style="margin:0px;">3.3 Cumulative Distribution Function for Discrete Random Variables 88</p> <p style="margin:0px;">3.4 Probability Density Function for Continuous Random Variables 90</p> <p style="margin:0px;">3.5 Mean, Mode, and Median 94</p> <p style="margin:0px;">3.5.1 Mean 95</p> <p style="margin:0px;">3.5.2 Mode 96</p> <p style="margin:0px;">3.5.3 Median 96</p> <p style="margin:0px;">3.6 Standard Deviation and Skewness Coefficient 98</p> <p style="margin:0px;">3.6.1 Standard Deviation 99</p> <p style="margin:0px;">3.6.2 Skewness Coefficient 103</p> <p style="margin:0px;">3.7 Moments of Random Variables 105</p> <p style="margin:0px;">3.8 Importance of Moment Functions– Chebyshev Inequality 106</p> <p style="margin:0px;">3.9 Jointly Distributed Random Variables 108</p> <p style="margin:0px;">3.9.1 Joint Density and Distribution Functions 108</p> <p style="margin:0px;">3.9.2 Obtaining the Marginal or Individual Density Function from the Joint Density Function 109</p> <p style="margin:0px;">3.10 Moments of Jointly Distributed Random Variables 111</p> <p style="margin:0px;">3.11 Probability Distributions 112</p> <p style="margin:0px;">3.11.1 Binomial Distribution 116</p> <p style="margin:0px;">3.11.2 Poisson Distribution 119</p> <p style="margin:0px;">3.11.3 Normal Distribution 122</p> <p style="margin:0px;">3.11.3 Lognormal Distribution 130</p> <p style="margin:0px;">3.12 Central Limit Theorem 134</p> <p style="margin:0px;">3.13 Normal Approximation to Binomial Distribution 134</p> <p style="margin:0px;">3.14 Numerical Solutions Using MATLAB and Excel 135</p> <p style="margin:0px;">3.14.1 MATLAB Functions for Discrete and Continuous Probability Distributions 135</p> <p style="margin:0px;">3.14.2 Random Numbers, Fitting Data to Distributions and Confidence Intervals 140</p> <p style="margin:0px;">3.14.3 Solutions Using Excel 142 </p> <p style="margin:0px;">References and Bibliography 144</p> <p style="margin:0px;">Review Questions 145</p> <p style="margin:0px;">Problems 148</p> <p style="margin:0px;">&nbsp;</p> <p style="margin:0px;">Chapter 4 Extremal Distributions 161</p> <p style="margin:0px;">What You Will Learn 161</p> <p style="margin:0px;">4.1 Introduction 161</p> <p style="margin:0px;">4.2 Extreme Value Distributions in Terms of Parent Distribution 163</p> <p style="margin:0px;">4.3 Asymptotic Distributions 166</p> <p style="margin:0px;">4.4 Type-I Asymptotic Distributions 167</p> <p style="margin:0px;">4.4.1 Maximum Value 167</p> <p style="margin:0px;">4.4.2 Smallest Value 167</p> <p style="margin:0px;">4.5 Type-II Asymptotic Distributions 168</p> <p style="margin:0px;">4.5.1 Maximum Value 168</p> <p style="margin:0px;">4.5.2 Smallest Value 169</p> <p style="margin:0px;">4.6 Type-III Asymptotic Distributions 170</p> <p style="margin:0px;">4.6.1 Maximum Value 170</p> <p style="margin:0px;">4.6.2 Smallest Value 170</p> <p style="margin:0px;">4.7 Return Period 171</p> <p style="margin:0px;">4.8 Characteristic Value 172</p> <p style="margin:0px;">4.9 Fitting Extremal Distributions to Experimental Data 173</p> <p style="margin:0px;">4.9.1 Least-squares Fit 174</p> <p style="margin:0px;">4.10 Generalized Extreme Value Distribution 176</p> <p style="margin:0px;">4.11 Numerical Solutions Using MATLAB and Excel 178</p> <p style="margin:0px;">References and Bibliography 183</p> <p style="margin:0px;">Review Questions 184</p> <p style="margin:0px;">Problems 186</p> <p style="margin:0px;">&nbsp;</p> <p style="margin:0px;">Chapter 5 Functions of Random Variables 191</p> <p style="margin:0px;">What You Will Learn 191</p> <p style="margin:0px;">5.1 Introduction 191</p> <p style="margin:0px;">5.2 Functions of a Single Random Variable 192</p> <p style="margin:0px;">5.3 Functions of Two Random Variables 197</p> <p style="margin:0px;">5.3.1 Sum of Two Random Variables 198</p> <p style="margin:0px;">5.3.2 Product of Two Random Variables 202</p> <p style="margin:0px;">5.3.3 Quotient of Two Random Variables 203</p> <p style="margin:0px;">5.4 Function of Several Random Variables 205</p> <p style="margin:0px;">5.5 Moments of a Function of Several Random Variables 205</p> <p style="margin:0px;">5.5.1 Mean and Variance of a Linear Function 206</p> <p style="margin:0px;">5.5.2 Mean and Variance of Sum of Two Random Variables 207</p> <p style="margin:0px;">5.5.3 Mean and Variance of Product of Two Random Variables 207</p> <p style="margin:0px;">5.5.4 Mean and Variance of Quotient of Two Random Variables 208</p> <p style="margin:0px;">5.5.5 Mean and Variance of a General Nonlinear Function of Several Random Variables 208</p> <p style="margin:0px;">5.6 Moment-Generating Function 212</p> <p style="margin:0px;">5.6.1 Moments of Normally Distributed Variables 213</p> <p style="margin:0px;">5.7 Functions of Several Random Variables 215</p> <p style="margin:0px;">5.8 Numerical Solutions Using MATLAB 217</p> <p style="margin:0px;">References and Bibliography 220</p> <p style="margin:0px;">Review Questions 220</p> <p style="margin:0px;">Problems 222</p> <p style="margin:0px;">&nbsp;</p> <p style="margin:0px;">Chapter 6 Time-Dependent Reliability of Components and Systems 232</p> <p style="margin:0px;">What You Will Learn 232</p> <p style="margin:0px;">6.1 Introduction 232</p> <p style="margin:0px;">6.2 Failure Rate versus Time Curve 233</p> <p style="margin:0px;">6.3 Reliability and Hazard Functions 234</p> <p style="margin:0px;">6.4 Modeling of Failure Rates 236</p> <p style="margin:0px;">6.5 Estimation of Failure Rate from Empirical Data 237</p> <p style="margin:0px;">6.6 Mean Time to Failure (MTTF) 239</p> <p style="margin:0px;">6.7 Reliability and Hazard Functions for Different Distributions 241</p> <p style="margin:0px;">6.7.1 Exponential Distribution 241</p> <p style="margin:0px;">6.7.2 Normal Distribution 244</p> <p style="margin:0px;">6.7.3 Lognormal Distribution 246</p> <p style="margin:0px;">6.7.4 Weibull Distribution 251</p> <p style="margin:0px;">6.7.5 Gamma Distribution 256</p> <p style="margin:0px;">6.7.6 Rayleigh Distribution 258</p> <p style="margin:0px;">6.7.7 Uniform Distribution 260</p> <p style="margin:0px;">6.8 Expected Residual Life 262</p> <p style="margin:0px;">6.9 Series Systems 265</p> <p style="margin:0px;">6.9.1 Failure Rate of the System 267</p> <p style="margin:0px;">6.9.2 MTBF of the System 267</p> <p style="margin:0px;">6.10 Parallel Systems 268</p> <p style="margin:0px;">6.10.1 Failure Rate of the System 270</p> <p style="margin:0px;">6.10.2 MTBF of the System 270</p> <p style="margin:0px;">6.11 (k, n) Systems 271</p> <p style="margin:0px;">6.11.1 MTBF of the System 272</p> <p style="margin:0px;">6.12 Mixed Series and Parallel Systems 272</p> <p style="margin:0px;">6.13 Complex Systems 273</p> <p style="margin:0px;">6.13.1 Enumeration Method 274</p> <p style="margin:0px;">6.13.2 Conditional Probability Method 276</p> <p style="margin:0px;">6.13.3 Cut-set Method 278</p> <p style="margin:0px;">6.14 Reliability Enhancement 280</p> <p style="margin:0px;">6.14.1 Series System 280</p> <p style="margin:0px;">6.14.2 Parallel System 282</p> <p style="margin:0px;">6.15 Reliability Allocation–AGREE Method 283</p> <p style="margin:0px;">6.16 Numerical Solutions Using MATLAB and Excel 286</p> <p style="margin:0px;">References and Bibliography 289</p> <p style="margin:0px;">Review Questions 289</p> <p style="margin:0px;">Problems 292</p> <p style="margin:0px;">&nbsp;</p> <p style="margin:0px;">Chapter 7 Modeling of Geometry, Material Strength, and Loads 301</p> <p style="margin:0px;">What You Will Learn 301</p> <p style="margin:0px;">7.1 Introduction 301</p> <p style="margin:0px;">7.2 Modeling of Geometry 302</p> <p style="margin:0px;">7.2.1 Tolerances on Finished Metal Products 303</p> <p style="margin:0px;">7.2.2 Assembly of Components 303</p> <p style="margin:0px;">7.3 Modeling of Material Strength 308</p> <p style="margin:0px;">7.3.1 Statistics of Elastic Properties 308</p> <p style="margin:0px;">7.3.2 Statistical Models for Material Strength 309</p> <p style="margin:0px;">7.3.3 Model for Brittle Materials 309</p> <p style="margin:0px;">7.3.4 Model for Plastic Materials 311</p> <p style="margin:0px;">7.3.5 Model for Fiber Bundles 312</p> <p style="margin:0px;">7.4 Fatigue Strength 314</p> <p style="margin:0px;">7.4.1 Constant-Amplitude Fatigue Strength 314</p> <p style="margin:0px;">7.4.2 Variable-Amplitude Fatigue Strength 317</p> <p style="margin:0px;">7.5 Modeling of Loads 319</p> <p style="margin:0px;">7.5.1 Introduction 319</p> <p style="margin:0px;">7.5.2 Dead Loads 320</p> <p style="margin:0px;">7.5.3 Live Loads 320</p> <p style="margin:0px;">7.5.4 Wind Loads 321</p> <p style="margin:0px;">7.5.5 Earthquake Loads 326</p> <p style="margin:0px;">7.6 Numerical Solutions Using MATLAB and Excel 331</p> <p style="margin:0px;">References and Bibliography 333</p> <p style="margin:0px;">Review Questions 337</p> <p style="margin:0px;">Problems 339</p> <p style="margin:0px;">&nbsp;</p> <p style="margin:0px;">Chapter 8 Strength-Based Reliability 343</p> <p style="margin:0px;">What You Will Learn 343</p> <p style="margin:0px;">8.1 Introduction 343</p> <p style="margin:0px;">8.2 General Expression for Reliability 345</p> <p style="margin:0px;">8.3 Expression for Probability of Failure 348</p> <p style="margin:0px;">8.4 General Interpretation of Strength and Load 349</p> <p style="margin:0px;">8.5 Reliability for Known Probability Distributions of S and L 349</p> <p style="margin:0px;">8.5.1 Reliability When S and L Follow Normal Distribution 350</p> <p style="margin:0px;">8.5.2 Approximate Expressions of Reliability for Normal Distribution 352</p> <p style="margin:0px;">8.5.3 Reliability When S and L Follow Lognormal Distribution 356</p> <p style="margin:0px;">8.5.4 Reliability When S and L Follow Exponential Distribution 361</p> <p style="margin:0px;">8.5.5 Reliability When S and L Follow Extreme Value Distributions 363</p> <p style="margin:0px;">8.5.6 When S and L Follow Type-III Extremal Distributions 364</p> <p style="margin:0px;">8.5.7 Reliability in Terms of Experimentally Determined Distributions of S and L 365</p> <p style="margin:0px;">8.6 Factor of Safety Corresponding to a Given Reliability 369</p> <p style="margin:0px;">8.7 Reliability of Systems Involving More Than Two Random Parameters 373</p> <p style="margin:0px;">8.8 First-Order Second-Moment (FOSM) Method 380</p> <p style="margin:0px;">8.9 Hasofer-Lind Reliability Index with Two Normally Distributed Variables 383</p> <p style="margin:0px;">8.10 Hasofer-Lind Reliability Index with Several Normally Distributed Variables 385</p> <p style="margin:0px;">8.11 Reliability of Weakest-Link and Fail-Safe Systems 389</p> <p style="margin:0px;">8.11.1 Introduction 389</p> <p style="margin:0px;">8.11.2 Reliability of the Fundamental Problem 390</p> <p style="margin:0px;">8.11.3 Reliability of Weakest-Link (or Series) Systems 392</p> <p style="margin:0px;">8.11.4 Reliability Analysis of Fail-Safe (or Parallel) Systems 398</p> <p style="margin:0px;">8.12 Numerical Solutions Using MATLAB and Excel 400</p> <p style="margin:0px;">References and Bibliography 405</p> <p style="margin:0px;">Review Questions 407</p> <p style="margin:0px;">Problems 411</p> <p style="margin:0px;">&nbsp;</p> <p style="margin:0px;">Chapter 9 Design of Mechanical Components and Systems 425</p> <p style="margin:0px;">What You Will Learn 425</p> <p style="margin:0px;">9.1 Introduction 425</p> <p style="margin:0px;">9.2 Design of Mechanical Components 426</p> <p style="margin:0px;">9.3 Fatigue Design 431</p> <p style="margin:0px;">9.3.1 Deterministic Design Procedure 432</p> <p style="margin:0px;">9.3.2 Probabilistic Design Procedure 435</p> <p style="margin:0px;">9.4 Design of Mechanical Systems 439</p> <p style="margin:0px;">9.4.1 Reliability-Based Design of Gear Trains 439</p> <p style="margin:0px;">9.5 Reliability Analysis of Mechanical Systems 445</p> <p style="margin:0px;">9.5.1 Cam-Follower Systems 445</p> <p style="margin:0px;">9.5.2 Four-Bar Mechanisms 450</p> <p style="margin:0px;">9.6 Numerical Solutions Using MATLAB and Excel 457</p> <p style="margin:0px;">References and Bibliography 459</p> <p style="margin:0px;">Review Questions 459</p> <p style="margin:0px;">Problems 461</p> <p style="margin:0px;">&nbsp;</p> <p style="margin:0px;">Chapter 10 Monte Carlo Simulation 465</p> <p style="margin:0px;">What You Will Learn 465</p> <p style="margin:0px;">10.1 Introduction 465</p> <p style="margin:0px;">10.2 Generation of Random Numbers 466</p> <p style="margin:0px;">10.2.1 Generation of Random Numbers Following Standard Uniform Distribution 468</p> <p style="margin:0px;">10.2.2 Random Variables with Nonuniform Distribution 469</p> <p style="margin:0px;">10.2.3 Generation of Discrete Random Variables 472</p> <p style="margin:0px;">10.3 Generation of Jointly Distributed Random Numbers 475</p> <p style="margin:0px;">10.3.1 Independent Random Variables 475</p> <p style="margin:0px;">10.3.2 Dependent Random Variables 475</p> <p style="margin:0px;">10.3.3 Generation of Correlated Normal Random Variables 478</p> <p style="margin:0px;">10.4 Computation of Reliability 483</p> <p style="margin:0px;">10.4.1 Sample Size and Error in Simulation 483</p> <p style="margin:0px;">10.4.2 Example: Reliability Analysis of a Straight-Line Mechanism 485</p> <p style="margin:0px;">10.5 Numerical Solutions Using MATLAB and Excel 489</p> <p style="margin:0px;">References and Bibliography 491</p> <p style="margin:0px;">Review Questions 492</p> <p style="margin:0px;">Problems 494</p> <p style="margin:0px;">&nbsp;</p> <p style="margin:0px;">Chapter 11 Reliability-Based Optimum Design 504</p> <p style="margin:0px;">What You Will Learn 504</p> <p style="margin:0px;">11.1 Introduction 504</p> <p style="margin:0px;">11.2 Optimization Problem 505</p> <p style="margin:0px;">11.3 Formulation of Optimization Problems 507</p> <p style="margin:0px;">11.3.1 Reliability Allocation Problems 507</p> <p style="margin:0px;">11.3.2 Structural and Mechanical Design Problems 509</p> <p style="margin:0px;">11.4 Solution Techniques 516</p> <p style="margin:0px;">11.4.1 Graphical-Optimization Method 516</p> <p style="margin:0px;">11.4.2 Lagrange Multiplier Method 520</p> <p style="margin:0px;">11.4.3 Penalty Function Method (SUMT) 523</p> <p style="margin:0px;">11.4.4 Dynamic Programming 532</p> <p style="margin:0px;">11.5 Numerical Solutions Using MATLAB 538</p> <p style="margin:0px;">References and Bibliography 546</p> <p style="margin:0px;">Review Questions 546</p> <p style="margin:0px;">Problems 548</p> <p style="margin:0px;">&nbsp;</p> <p style="margin:0px;">Chapter 12 Failure Modes, Event-Tree, and Fault-Tree Analyses 554</p> <p style="margin:0px;">What You Will Learn 554</p> <p style="margin:0px;">12.1 Introduction 555</p> <p style="margin:0px;">12.2 System-Safety Analysis 555</p> <p style="margin:0px;">12.3 Failure Modes and Effects Analysis (FMEA) 557</p> <p style="margin:0px;">12.4 Event-Tree Analysis 558</p> <p style="margin:0px;">12.5 Fault-Tree Analysis (FTA) 564</p> <p style="margin:0px;">12.5.1 Concept 565</p> <p style="margin:0px;">12.5.2 Procedure 565</p> <p style="margin:0px;">12.6 Minimal Cut-Sets 572</p> <p style="margin:0px;">12.6.1 Probability of the TOP Event 574</p> <p style="margin:0px;">References and Bibliography 582</p> <p style="margin:0px;">Review Questions 583</p> <p style="margin:0px;">Problems 585</p> <p style="margin:0px;">&nbsp;</p> <p style="margin:0px;">Chapter 13 Reliability Testing 594</p> <p style="margin:0px;">What You Will Learn 594</p> <p style="margin:0px;">13.1 Introduction 595</p> <p style="margin:0px;">13.1.1 Objectives of Reliability Tests 595</p> <p style="margin:0px;">13.1.2 Details of a Reliability Test 596</p> <p style="margin:0px;">13.2 Analysis of Failure Time 596</p> <p style="margin:0px;">13.2.1 Analysis of Individual Failure Data 596</p> <p style="margin:0px;">13.2.2 Analysis of Grouped Failure Data 599</p> <p style="margin:0px;">13.3 Accelerated Life Testing 601</p> <p style="margin:0px;">13.3.1 Testing Until Partial Failure 601</p> <p style="margin:0px;">13.3.2 Magnified Loading 602</p> <p style="margin:0px;">13.3.3 Sudden-death Testing 605</p> <p style="margin:0px;">13.4 Sequential Life Testing 608</p> <p style="margin:0px;">13.5 Statistical Inference and Parameter Estimation 610</p> <p style="margin:0px;">13.5.1 Maximum-likelihood Method 611</p> <p style="margin:0px;">13.6 Confidence Intervals 613</p> <p style="margin:0px;">13.6.1 Confidence Interval on the Mean of a Normal Random Variable of Known Standard Deviation 615</p> <p style="margin:0px;">13.6.2 Confidence Interval on the Mean of a Normal Random Variable of Unknown Standard Deviation 616</p> <p style="margin:0px;">13.6.3 Confidence Interval on the Standard Deviation of a Normal Random Variable with Unknown Mean 618</p> <p style="margin:0px;">13.7 Plotting of Reliability Data 620</p> <p style="margin:0px;">13.7.1 Least-Squares Technique 620</p> <p style="margin:0px;">13.7.2 Linear Rectification 621</p> <p style="margin:0px;">13.7.3 Plotting Positions 621</p> <p style="margin:0px;">13.7.4 Exponential Distribution 621</p> <p style="margin:0px;">13.7.5 Normal Distribution 623</p> <p style="margin:0px;">13.7.6 Lognormal Distribution 626</p> <p style="margin:0px;">13.7.7 Weibull Distribution 626</p> <p style="margin:0px;">13.8 Numerical Solutions Using MATLAB 630</p> <p style="margin:0px;">13.8.1 Parameter Estimation and Confidence Intervals 630</p> <p style="margin:0px;">13.8.2 Plotting of Data 632</p> <p style="margin:0px;">References and Bibliography 634</p> <p style="margin:0px;">Review Questions 635</p> <p style="margin:0px;">Problems 638</p> <p style="margin:0px;">&nbsp;</p> <p style="margin:0px;">Chapter 14 Quality Control and Reliability 642</p> <p style="margin:0px;">What You Will Learn 642</p> <p style="margin:0px;">14.1 Introduction 642</p> <p style="margin:0px;">14.2 Importance of Controlling Dimensions of Products 644</p> <p style="margin:0px;">14.3 Important Discrete Probability Distributions 647</p> <p style="margin:0px;">14.3.1 Binomial Distribution 647</p> <p style="margin:0px;">14.3.2 Hypergeometric Distribution 648</p> <p style="margin:0px;">14.3.3 Poisson Distribution 649</p> <p style="margin:0px;">14.3.4 Relationship Between Poisson and Exponential Distributions 650</p> <p style="margin:0px;">14.4 Six Sigma Approach and Reliability 650</p> <p style="margin:0px;">14.4.1 Implementation of the Six Sigma Approach 657</p> <p style="margin:0px;">14.5 Acceptance Sampling 658</p> <p style="margin:0px;">14.5.1 Characteristics of Sampling Plans 659</p> <p style="margin:0px;">14.6 Process Capability 659</p> <p style="margin:0px;">14.7 Quality Control Charts 664</p> <p style="margin:0px;">14.7.1 The p-Chart 665</p> <p style="margin:0px;">14.7.2 The X-Chart 667</p> <p style="margin:0px;">14.7.3 The R-Chart 670</p> <p style="margin:0px;">14.7.4 The c-Chart 672</p> <p style="margin:0px;">14.8 Risks 673</p> <p style="margin:0px;">14.9 Operating Characteristic (OC) Curve 674</p> <p style="margin:0px;">14.9.1 OC Curve 675</p> <p style="margin:0px;">14.9.2 Construction of OC Curve 675</p> <p style="margin:0px;">14.9.3 Designing a Single Sampling Plan with a Specified OC Curve 677</p> <p style="margin:0px;">14.10 T aguchi Method 678</p> <p style="margin:0px;">14.10.1 Basic Concept 678</p> <p style="margin:0px;">14.10.2 Loss Function 679</p> <p style="margin:0px;">14.10.3 Noise Factors 681</p> <p style="margin:0px;">14.10.4 On-Line Versus Off-Line Quality Control 682</p> <p style="margin:0px;">14.10.5 Three-Step Design Approach 683</p> <p style="margin:0px;">14.10.6 Experimental Design 683</p> <p style="margin:0px;">14.10.7 Signal-To-Noise Ratio 687</p> <p style="margin:0px;">14.10.8 Experimental Design in the Presence of Noise Factors 689</p> <p style="margin:0px;">14.11 Numerical Solutions Using MATLAB 697</p> <p style="margin:0px;">References and Bibliography 698</p> <p style="margin:0px;">Review Questions 699</p> <p style="margin:0px;">Problems 701</p> <p style="margin:0px;">&nbsp;</p> <p style="margin:0px;">Chapter 15 Maintainability and Availability 706</p> <p style="margin:0px;">What You Will Learn 706</p> <p style="margin:0px;">15.1 Introduction 706</p> <p style="margin:0px;">15.2 Maintainability 707</p> <p style="margin:0px;">15.2.1 Overview 707</p> <p style="margin:0px;">15.2.2 Preventive Maintenance 708</p> <p style="margin:0px;">15.2.3 Imperfect Maintenance 712</p> <p style="margin:0px;">15.2.4 Repair-time Distributions 713</p> <p style="margin:0px;">15.2.5 Unrepaired Failures 716</p> <p style="margin:0px;">15.2.6 Optimal Replacement Strategy 717</p> <p style="margin:0px;">15.2.7 Spare Parts Requirement 719</p> <p style="margin:0px;">15.3 Availability 720</p> <p style="margin:0px;">15.3.1 Definitions [15.1, 15.3] 720</p> <p style="margin:0px;">15.3.2 Availability Analysis 721</p> <p style="margin:0px;">15.3.3 Development of the Model 722</p> <p style="margin:0px;">15.3.4 Systems with a Single Component 723</p> <p style="margin:0px;">15.3.5 Series Systems 726</p> <p style="margin:0px;">15.3.6 Parallel Systems 729</p> <p style="margin:0px;">15.4 Optimization Approaches 730</p> <p style="margin:0px;">15.5 Numerical Solutions Using MATLAB and Excel 731</p> <p style="margin:0px;">References and Bibliography 733</p> <p style="margin:0px;">Review Questions 734</p> <p style="margin:0px;">Problems 736</p> <p style="margin:0px;">&nbsp;</p> <p style="margin:0px;">Chapter 16 Warranties 739</p> <p style="margin:0px;">What You Will Learn 739</p> <p style="margin:0px;">16.1 Introduction 740</p> <p style="margin:0px;">16.2 T ypes of Warranties 742</p> <p style="margin:0px;">16.3 Warranty Cost Based on a Single Failure During the Warranty Period 742</p> <p style="margin:0px;">16.3.1 Free Replacement Warranty 742</p> <p style="margin:0px;">16.3.2 Pro-rata Warranty 744</p> <p style="margin:0px;">16.3.3 Combined Free Replacement Warranty and Pro-rata Warranty (FRW/PRW) Policy 747</p> <p style="margin:0px;">16.3.4 FRW Policy Equivalent to a FRW/PRW Policy 749</p> <p style="margin:0px;">16.3.5 Lump-sum Payment Type of Warranty 750</p> <p style="margin:0px;">16.4 Warranty Costs Considering the Time Value of Money 752</p> <p style="margin:0px;">16.4.1 FRW Policy 752</p> <p style="margin:0px;">16.4.2 PRW Policy 753</p> <p style="margin:0px;">16.5 Warranty Reserve Fund Considering the Time Value of Money and Future Changes in the Price of the Product 754</p> <p style="margin:0px;">16.6 Warranty Analysis Considering Multiple Failures During the Warranty Period 757</p> <p style="margin:0px;">16.6.1 Renewal Process 758</p> <p style="margin:0px;">16.6.2 Computation and Use of Renewal Functions 759</p> <p style="margin:0px;">16.7 Optimum Warranty Period 764</p> <p style="margin:0px;">16.8 Two-dimensional Warranties 768</p> <p style="margin:0px;">16.9 Numerical Solutions Using MATLAB 770</p> <p style="margin:0px;">References and Bibliography 772</p> <p style="margin:0px;">Review Questions 773</p> <p style="margin:0px;">Problems 775</p> <p style="margin:0px;">&nbsp;</p> <p style="margin:0px;">Appendix A Standard Normal Distribution Function 779</p> <p style="margin:0px;">Appendix B Values of ta, n for Specific Values of a and n of t Distribution 782</p> <p style="margin:0px;">Appendix C Values of x2n, a Corresponding to Specific Values of a and n of x2-Distribution 784</p> <p style="margin:0px;">Appendix D Product Liability 787</p> <p style="margin:0px;">Answers to Selected Problems 791</p> <p style="margin:0px;">Index 795</p>