{"product_id":"using-the-weibull-distribution-reliability-modeling-and-inference-hardback-9781118217986","title":"Using the Weibull Distribution; Reliability, Modeling, and Inference (Hardback) 9781118217986","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eUsing the Weibull Distribution\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eReliability, Modeling, and Inference\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJohn I. McCool (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781118217986, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 28 September 2012\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e366 pages\u003cbr\u003e24.4 x 16.3 x 2.4 cm, 0.626 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003cb\u003eUnderstand and utilize the latest developments\u003c\/b\u003e \u003cb\u003ein Weibull inferential methods\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eWhile the Weibull distribution is widely used in science and engineering, most engineers do not have the necessary statistical training to implement the methodology effectively. \u003ci\u003eUsing the Weibull Distribution: Reliability, Modeling,\u003c\/i\u003e \u003ci\u003eand Inference\u003c\/i\u003e fills a gap in the current literature on the topic, introducing a self-contained presentation of the probabilistic basis for the methodology while providing powerful techniques for extracting information from data.\u003c\/p\u003e \u003cp\u003eThe author explains the use of the Weibull distribution and its statistical and probabilistic basis, providing a wealth of material that is not available in the current literature. The book begins by outlining the fundamental probability and statistical concepts that serve as a foundation for subsequent topics of coverage, including:\u003c\/p\u003e \u003cp\u003e• Optimum burn-in, age and block replacement, warranties\u003c\/p\u003e \u003cp\u003eand renewal theory\u003c\/p\u003e \u003cp\u003e• Exact inference in Weibull regression\u003c\/p\u003e \u003cp\u003e• Goodness of fit testing and distinguishing the Weibull\u003c\/p\u003e \u003cp\u003efrom the lognormal\u003c\/p\u003e \u003cp\u003e• Inference for the Three Parameter Weibull \u003c\/p\u003e \u003cp\u003eThroughout the book, a wealth of real-world examples showcases the discussed topics and each chapter concludes with a set of exercises, allowing readers to test their understanding of the presented material. In addition, a related website features the author's own software for implementing the discussed analyses along with a set of modules written in Mathcad®, and additional graphical interface software for performing simulations.\u003c\/p\u003e \u003cp\u003eWith its numerous hands-on examples, exercises, and software applications, \u003ci\u003eUsing the Weibull Distribution\u003c\/i\u003e is an excellent book for courses on quality control and reliability engineering at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for engineers, scientists, and business analysts who gather and interpret data that follows the Weibull distribution\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1. Probability 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Sample Spaces and Events 2\u003c\/p\u003e \u003cp\u003e1.2 Mutually Exclusive Events 2\u003c\/p\u003e \u003cp\u003e1.3 Venn Diagrams 3\u003c\/p\u003e \u003cp\u003e1.4 Unions of Events and Joint Probability 4\u003c\/p\u003e \u003cp\u003e1.5 Conditional Probability 6\u003c\/p\u003e \u003cp\u003e1.6 Independence 8\u003c\/p\u003e \u003cp\u003e1.7 Partitions and the Law of Total Probability 9\u003c\/p\u003e \u003cp\u003e1.8 Reliability 12\u003c\/p\u003e \u003cp\u003e1.9 Series Systems 12\u003c\/p\u003e \u003cp\u003e1.10 Parallel Systems 13\u003c\/p\u003e \u003cp\u003e1.11 Complex Systems 15\u003c\/p\u003e \u003cp\u003e1.12 Crosslinked Systems 16\u003c\/p\u003e \u003cp\u003e1.13 Reliability Importance 19\u003c\/p\u003e \u003cp\u003eReferences 20\u003c\/p\u003e \u003cp\u003eExercises 21\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2. Discrete and Continuous Random Variables 23\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Probability Distributions 24\u003c\/p\u003e \u003cp\u003e2.2 Functions of a Random Variable 26\u003c\/p\u003e \u003cp\u003e2.3 Jointly Distributed Discrete Random Variables 28\u003c\/p\u003e \u003cp\u003e2.4 Conditional Expectation 32\u003c\/p\u003e \u003cp\u003e2.5 The Binomial Distribution 34\u003c\/p\u003e \u003cp\u003e2.5.1 Confidence Limits for the Binomial Proportion p 38\u003c\/p\u003e \u003cp\u003e2.6 The Poisson Distribution 39\u003c\/p\u003e \u003cp\u003e2.7 The Geometric Distribution 41\u003c\/p\u003e \u003cp\u003e2.8 Continuous Random Variables 42\u003c\/p\u003e \u003cp\u003e2.8.1 The Hazard Function 49\u003c\/p\u003e \u003cp\u003e2.9 Jointly Distributed Continuous Random Variables 51\u003c\/p\u003e \u003cp\u003e2.10 Simulating Samples from Continuous Distributions 52\u003c\/p\u003e \u003cp\u003e2.11 The Normal Distribution 54\u003c\/p\u003e \u003cp\u003e2.12 Distribution of the Sample Mean 60\u003c\/p\u003e \u003cp\u003e2.12.1 P[X \u0026lt; Y] for Normal Variables 65\u003c\/p\u003e \u003cp\u003e2.13 The Lognormal Distribution 66\u003c\/p\u003e \u003cp\u003e2.14 Simple Linear Regression 67\u003c\/p\u003e \u003cp\u003eReferences 69\u003c\/p\u003e \u003cp\u003eExercises 69\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3. Properties of the Weibull Distribution 73\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The Weibull Cumulative Distribution Function (CDF) Percentiles Moments and Hazard Function 73\u003c\/p\u003e \u003cp\u003e3.1.1 Hazard Function 75\u003c\/p\u003e \u003cp\u003e3.1.2 The Mode 77\u003c\/p\u003e \u003cp\u003e3.1.3 Quantiles 77\u003c\/p\u003e \u003cp\u003e3.1.4 Moments 78\u003c\/p\u003e \u003cp\u003e3.2 The Minima of Weibull Samples 82\u003c\/p\u003e \u003cp\u003e3.3 Transformations 83\u003c\/p\u003e \u003cp\u003e3.3.1 The Power Transformation 83\u003c\/p\u003e \u003cp\u003e3.3.2 The Logarithmic Transformation 84\u003c\/p\u003e \u003cp\u003e3.4 The Conditional Weibull Distribution 86\u003c\/p\u003e \u003cp\u003e3.5 Quantiles for Order Statistics of a Weibull Sample 89\u003c\/p\u003e \u003cp\u003e3.5.1 The Weakest Link Phenomenon 92\u003c\/p\u003e \u003cp\u003e3.6 Simulating Weibull Samples 92\u003c\/p\u003e \u003cp\u003eReferences 94\u003c\/p\u003e \u003cp\u003eExercises 95\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4. Weibull Probability Models 97\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 System Reliability 97\u003c\/p\u003e \u003cp\u003e4.1.1 Series Systems 97\u003c\/p\u003e \u003cp\u003e4.1.2 Parallel Systems 99\u003c\/p\u003e \u003cp\u003e4.1.3 Standby Parallel 102\u003c\/p\u003e \u003cp\u003e4.2 Weibull Mixtures 103\u003c\/p\u003e \u003cp\u003e4.3 P(Y \u0026lt; X) 105\u003c\/p\u003e \u003cp\u003e4.4 Radial Error 108\u003c\/p\u003e \u003cp\u003e4.5 Pro Rata Warranty 110\u003c\/p\u003e \u003cp\u003e4.6 Optimum Age Replacement 112\u003c\/p\u003e \u003cp\u003e4.6.1 Age Replacement 115\u003c\/p\u003e \u003cp\u003e4.6.2 MTTF for a Maintained System 117\u003c\/p\u003e \u003cp\u003e4.7 Renewal Theory 119\u003c\/p\u003e \u003cp\u003e4.7.1 Block Replacement 121\u003c\/p\u003e \u003cp\u003e4.7.2 Free Replacement Warranty 122\u003c\/p\u003e \u003cp\u003e4.7.3 A Renewing Free Replacement Warranty 122\u003c\/p\u003e \u003cp\u003e4.8 Optimum Bidding 123\u003c\/p\u003e \u003cp\u003e4.9 Optimum Burn-In 124\u003c\/p\u003e \u003cp\u003e4.10 Spare Parts Provisioning 126\u003c\/p\u003e \u003cp\u003eReferences 127\u003c\/p\u003e \u003cp\u003eExercises 128\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5. Estimation in Single Samples 130\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Point and Interval Estimation 130\u003c\/p\u003e \u003cp\u003e5.2 Censoring 130\u003c\/p\u003e \u003cp\u003e5.3 Estimation Methods 132\u003c\/p\u003e \u003cp\u003e5.3.1 Menon’s Method 132\u003c\/p\u003e \u003cp\u003e5.3.2 An Order Statistic Estimate of x0.10 134\u003c\/p\u003e \u003cp\u003e5.4 Graphical Estimation of Weibull Parameters 136\u003c\/p\u003e \u003cp\u003e5.4.1 Complete Samples 136\u003c\/p\u003e \u003cp\u003e5.4.2 Graphical Estimation in Censored Samples 140\u003c\/p\u003e \u003cp\u003e5.5 Maximum Likelihood Estimation 145\u003c\/p\u003e \u003cp\u003e5.5.1 The Exponential Distribution 147\u003c\/p\u003e \u003cp\u003e5.5.2 Confidence Intervals for the Exponential Distribution—Type II Censoring 147\u003c\/p\u003e \u003cp\u003e5.5.3 Estimation for the Exponential Distribution—Interval Censoring 150\u003c\/p\u003e \u003cp\u003e5.5.4 Estimation for the Exponential Distribution—Type I Censoring 151\u003c\/p\u003e \u003cp\u003e5.5.5 Estimation for the Exponential Distribution—The Zero Failures Case 153\u003c\/p\u003e \u003cp\u003e5.6 ML Estimation for the Weibull Distribution 154\u003c\/p\u003e \u003cp\u003e5.6.1 Shape Parameter Known 154\u003c\/p\u003e \u003cp\u003e5.6.2 Confidence Interval for the Weibull Scale Parameter—Shape Parameter Known Type II Censoring 155\u003c\/p\u003e \u003cp\u003e5.6.3 ML Estimation for the Weibull Distribution—Shape Parameter Unknown 157\u003c\/p\u003e \u003cp\u003e5.6.4 Confidence Intervals for Weibull Parameters—Complete and Type II Censored Samples 162\u003c\/p\u003e \u003cp\u003e5.6.5 Interval Censoring with the Weibull 167\u003c\/p\u003e \u003cp\u003e5.6.6 Confidence Limits for Weibull Parameters—Type I Censoring 167\u003c\/p\u003e \u003cp\u003eReferences 177\u003c\/p\u003e \u003cp\u003eExercises 179\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6. Sample Size Selection Hypothesis Testing and Goodness of Fit 180\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Precision Measure for Maximum Likelihood (ML) Estimates 180\u003c\/p\u003e \u003cp\u003e6.2 Interval Estimates from Menon’s Method of Estimation 182\u003c\/p\u003e \u003cp\u003e6.3 Hypothesis Testing—Single Samples 184\u003c\/p\u003e \u003cp\u003e6.4 Operating Characteristic (OC) Curves for One-Sided Tests of the Weibull Shape Parameter 188\u003c\/p\u003e \u003cp\u003e6.5 OC Curves for One-Sided Tests on a Weibull Percentile 191\u003c\/p\u003e \u003cp\u003e6.6 Goodness of Fit 195\u003c\/p\u003e \u003cp\u003e6.6.1 Completely Specified Distribution 195\u003c\/p\u003e \u003cp\u003e6.6.2 Distribution Parameters Not Specified 198\u003c\/p\u003e \u003cp\u003e6.6.3 Censored Samples 201\u003c\/p\u003e \u003cp\u003e6.6.4 The Program ADStat 201\u003c\/p\u003e \u003cp\u003e6.7 Lognormal versus Weibull 204\u003c\/p\u003e \u003cp\u003eReferences 210\u003c\/p\u003e \u003cp\u003eExercises 212\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7. The Program Pivotal.exe 213\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Relationship among Quantiles 216\u003c\/p\u003e \u003cp\u003e7.2 Series Systems 217\u003c\/p\u003e \u003cp\u003e7.3 Confidence Limits on Reliability 218\u003c\/p\u003e \u003cp\u003e7.4 Using Pivotal.exe for OC Curve Calculations 221\u003c\/p\u003e \u003cp\u003e7.5 Prediction Intervals 224\u003c\/p\u003e \u003cp\u003e7.6 Sudden Death Tests 226\u003c\/p\u003e \u003cp\u003e7.7 Design of Optimal Sudden Death Tests 230\u003c\/p\u003e \u003cp\u003eReferences 233\u003c\/p\u003e \u003cp\u003eExercises 234\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8. Inference from Multiple Samples 235\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Multiple Weibull Samples 235\u003c\/p\u003e \u003cp\u003e8.2 Testing the Homogeneity of Shape Parameters 236\u003c\/p\u003e \u003cp\u003e8.3 Estimating the Common Shape Parameter 238\u003c\/p\u003e \u003cp\u003e8.3.1 Interval Estimation of the Common Shape Parameter 239\u003c\/p\u003e \u003cp\u003e8.4 Interval Estimation of a Percentile 244\u003c\/p\u003e \u003cp\u003e8.5 Testing Whether the Scale Parameters Are Equal 249\u003c\/p\u003e \u003cp\u003e8.5.1 The SPR Test 250\u003c\/p\u003e \u003cp\u003e8.5.2 Likelihood Ratio Test 252\u003c\/p\u003e \u003cp\u003e8.6 Multiple Comparison Tests for Differences in Scale Parameters 257\u003c\/p\u003e \u003cp\u003e8.7 An Alternative Multiple Comparison Test for Percentiles 259\u003c\/p\u003e \u003cp\u003e8.8 The Program Multi-Weibull.exe 261\u003c\/p\u003e \u003cp\u003e8.9 Inference on P (Y \u0026lt; X) 266\u003c\/p\u003e \u003cp\u003e8.9.1 ML Estimation 267\u003c\/p\u003e \u003cp\u003e8.9.2 Normal Approximation 269\u003c\/p\u003e \u003cp\u003e8.9.3 An Exact Simulation Solution 271\u003c\/p\u003e \u003cp\u003e8.9.4 Confi dence Intervals 273\u003c\/p\u003e \u003cp\u003eReferences 274\u003c\/p\u003e \u003cp\u003eExercises 274\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9. Weibull Regression 276\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 The Power Law Model 276\u003c\/p\u003e \u003cp\u003e9.2 ML Estimation 278\u003c\/p\u003e \u003cp\u003e9.3 Example 279\u003c\/p\u003e \u003cp\u003e9.4 Pivotal Functions 280\u003c\/p\u003e \u003cp\u003e9.5 Confidence Intervals 281\u003c\/p\u003e \u003cp\u003e9.6 Testing the Power Law Model 281\u003c\/p\u003e \u003cp\u003e9.7 Monte Carlo Results 282\u003c\/p\u003e \u003cp\u003e9.8 Example Concluded 285\u003c\/p\u003e \u003cp\u003e9.9 Approximating u* at Other Stress Levels 287\u003c\/p\u003e \u003cp\u003e9.10 Precision 289\u003c\/p\u003e \u003cp\u003e9.11 Stress Levels in Different Proportions Than Tabulated 289\u003c\/p\u003e \u003cp\u003e9.12 Discussion 291\u003c\/p\u003e \u003cp\u003e9.13 The Disk Operating System (DOS) Program REGEST 291\u003c\/p\u003e \u003cp\u003eReferences 296\u003c\/p\u003e \u003cp\u003eExercises 296\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10. The Three-Parameter Weibull Distribution 298\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 The Model 298\u003c\/p\u003e \u003cp\u003e10.2 Estimation and Inference for the Weibull Location Parameter 300\u003c\/p\u003e \u003cp\u003e10.3 Testing the Two- versus Three-Parameter Weibull Distribution 301\u003c\/p\u003e \u003cp\u003e10.4 Power of the Test 302\u003c\/p\u003e \u003cp\u003e10.5 Interval Estimation 302\u003c\/p\u003e \u003cp\u003e10.6 Input and Output Screens of LOCEST.exe 307\u003c\/p\u003e \u003cp\u003e10.7 The Program LocationPivotal.exe 309\u003c\/p\u003e \u003cp\u003e10.8 Simulated Example 311\u003c\/p\u003e \u003cp\u003eReferences 311\u003c\/p\u003e \u003cp\u003eExercises 312\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Factorial Experiments with Weibull Response 313\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 313\u003c\/p\u003e \u003cp\u003e11.2 The Multiplicative Model 314\u003c\/p\u003e \u003cp\u003e11.3 Data 317\u003c\/p\u003e \u003cp\u003e11.4 Estimation 317\u003c\/p\u003e \u003cp\u003e11.5 Test for the Appropriate Model 319\u003c\/p\u003e \u003cp\u003e11.6 Monte Carlo Results 320\u003c\/p\u003e \u003cp\u003e11.7 The DOS Program TWOWAY 320\u003c\/p\u003e \u003cp\u003e11.8 Illustration of the Influence of Factor Effects on the Shape Parameter Estimates 320\u003c\/p\u003e \u003cp\u003e11.9 Numerical Examples 327\u003c\/p\u003e \u003cp\u003eReferences 331\u003c\/p\u003e \u003cp\u003eExercises 332\u003c\/p\u003e \u003cp\u003eIndex 333\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52417758593304,"sku":"9781118217986","price":85.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781118217986.jpg?v=1784507129","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/using-the-weibull-distribution-reliability-modeling-and-inference-hardback-9781118217986","provider":"Freshly Printed Books","version":"1.0","type":"link"}