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      1. Naturvetenskap och teknik
      2. Matematik och naturvetenskap
      3. Matematik
      4. Matematisk statistik

      Using the Weibull Distribution

      Reliability, Modeling, and Inference

      AvJohn I. McCool

      Inbunden, Engelska, 2012

      Del 950 i serien Wiley Series in Probability and Statistics

      1 485 kr

      Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt över 249 kr.

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      E-bok

      1 735 kr

      E-bok

      1 708 kr

      Beskrivning

      Understand and utilize the latest developments in Weibull inferential methodsWhile the Weibull distribution is widely used in science and engineering, most engineers do not have the necessary statistical training to implement the methodology effectively. Using the Weibull Distribution: Reliability, Modeling, and Inference 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.The 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:• Optimum burn-in, age and block replacement, warrantiesand renewal theory• Exact inference in Weibull regression• Goodness of fit testing and distinguishing the Weibullfrom the lognormal• Inference for the Three Parameter Weibull Throughout 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.With its numerous hands-on examples, exercises, and software applications, Using the Weibull Distribution 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

      Produktinformation

      • Utgivningsdatum:2012-09-28
      • Mått:163 x 244 x 24 mm
      • Vikt:626 g
      • Format:Inbunden
      • Språk:Engelska
      • Serie:Wiley Series in Probability and Statistics
      • Antal sidor:366
      • Förlag:John Wiley & Sons Inc
      • ISBN:9781118217986

      Utforska kategorier

      • Matematisk statistik inom Naturvetenskap och teknik
      • Maskinteknik och material inom Naturvetenskap och teknik

      Mer om författaren

      JOHN I. McCOOL, PhD, is Professor of Systems Engineering at Penn State Great Valley School of Graduate Professional Studies. A Fellow of the American Society for Quality, Dr. McCool previously served as principal engineering scientist at SKF Industries Inc., where he conducted corporate as well as federally sponsored research projects with the Wright-Patterson Air Force Base, the Office of Naval Research, the Naval Air Propulsion Center, the Department of Energy, and the Air Force Office of Scientific Research.

      Innehållsförteckning

      • Preface xiii1. Probability 11.1 Sample Spaces and Events 21.2 Mutually Exclusive Events 21.3 Venn Diagrams 31.4 Unions of Events and Joint Probability 41.5 Conditional Probability 61.6 Independence 81.7 Partitions and the Law of Total Probability 91.8 Reliability 121.9 Series Systems 121.10 Parallel Systems 131.11 Complex Systems 151.12 Crosslinked Systems 161.13 Reliability Importance 19References 20Exercises 212. Discrete and Continuous Random Variables 232.1 Probability Distributions 242.2 Functions of a Random Variable 262.3 Jointly Distributed Discrete Random Variables 282.4 Conditional Expectation 322.5 The Binomial Distribution 342.5.1 Confidence Limits for the Binomial Proportion p 382.6 The Poisson Distribution 392.7 The Geometric Distribution 412.8 Continuous Random Variables 422.8.1 The Hazard Function 492.9 Jointly Distributed Continuous Random Variables 512.10 Simulating Samples from Continuous Distributions 522.11 The Normal Distribution 542.12 Distribution of the Sample Mean 602.12.1 P[X < Y] for Normal Variables 652.13 The Lognormal Distribution 662.14 Simple Linear Regression 67References 69Exercises 693. Properties of the Weibull Distribution 733.1 The Weibull Cumulative Distribution Function (CDF) Percentiles Moments and Hazard Function 733.1.1 Hazard Function 753.1.2 The Mode 773.1.3 Quantiles 773.1.4 Moments 783.2 The Minima of Weibull Samples 823.3 Transformations 833.3.1 The Power Transformation 833.3.2 The Logarithmic Transformation 843.4 The Conditional Weibull Distribution 863.5 Quantiles for Order Statistics of a Weibull Sample 893.5.1 The Weakest Link Phenomenon 923.6 Simulating Weibull Samples 92References 94Exercises 954. Weibull Probability Models 974.1 System Reliability 974.1.1 Series Systems 974.1.2 Parallel Systems 994.1.3 Standby Parallel 1024.2 Weibull Mixtures 1034.3 P(Y < X) 1054.4 Radial Error 1084.5 Pro Rata Warranty 1104.6 Optimum Age Replacement 1124.6.1 Age Replacement 1154.6.2 MTTF for a Maintained System 1174.7 Renewal Theory 1194.7.1 Block Replacement 1214.7.2 Free Replacement Warranty 1224.7.3 A Renewing Free Replacement Warranty 1224.8 Optimum Bidding 1234.9 Optimum Burn-In 1244.10 Spare Parts Provisioning 126References 127Exercises 1285. Estimation in Single Samples 1305.1 Point and Interval Estimation 1305.2 Censoring 1305.3 Estimation Methods 1325.3.1 Menon’s Method 1325.3.2 An Order Statistic Estimate of x0.10 1345.4 Graphical Estimation of Weibull Parameters 1365.4.1 Complete Samples 1365.4.2 Graphical Estimation in Censored Samples 1405.5 Maximum Likelihood Estimation 1455.5.1 The Exponential Distribution 1475.5.2 Confidence Intervals for the Exponential Distribution—Type II Censoring 1475.5.3 Estimation for the Exponential Distribution—Interval Censoring 1505.5.4 Estimation for the Exponential Distribution—Type I Censoring 1515.5.5 Estimation for the Exponential Distribution—The Zero Failures Case 1535.6 ML Estimation for the Weibull Distribution 1545.6.1 Shape Parameter Known 1545.6.2 Confidence Interval for the Weibull Scale Parameter—Shape Parameter Known Type II Censoring 1555.6.3 ML Estimation for the Weibull Distribution—Shape Parameter Unknown 1575.6.4 Confidence Intervals for Weibull Parameters—Complete and Type II Censored Samples 1625.6.5 Interval Censoring with the Weibull 1675.6.6 Confidence Limits for Weibull Parameters—Type I Censoring 167References 177Exercises 1796. Sample Size Selection Hypothesis Testing and Goodness of Fit 1806.1 Precision Measure for Maximum Likelihood (ML) Estimates 1806.2 Interval Estimates from Menon’s Method of Estimation 1826.3 Hypothesis Testing—Single Samples 1846.4 Operating Characteristic (OC) Curves for One-Sided Tests of the Weibull Shape Parameter 1886.5 OC Curves for One-Sided Tests on a Weibull Percentile 1916.6 Goodness of Fit 1956.6.1 Completely Specified Distribution 1956.6.2 Distribution Parameters Not Specified 1986.6.3 Censored Samples 2016.6.4 The Program ADStat 2016.7 Lognormal versus Weibull 204References 210Exercises 2127. The Program Pivotal.exe 2137.1 Relationship among Quantiles 2167.2 Series Systems 2177.3 Confidence Limits on Reliability 2187.4 Using Pivotal.exe for OC Curve Calculations 2217.5 Prediction Intervals 2247.6 Sudden Death Tests 2267.7 Design of Optimal Sudden Death Tests 230References 233Exercises 2348. Inference from Multiple Samples 2358.1 Multiple Weibull Samples 2358.2 Testing the Homogeneity of Shape Parameters 2368.3 Estimating the Common Shape Parameter 2388.3.1 Interval Estimation of the Common Shape Parameter 2398.4 Interval Estimation of a Percentile 2448.5 Testing Whether the Scale Parameters Are Equal 2498.5.1 The SPR Test 2508.5.2 Likelihood Ratio Test 2528.6 Multiple Comparison Tests for Differences in Scale Parameters 2578.7 An Alternative Multiple Comparison Test for Percentiles 2598.8 The Program Multi-Weibull.exe 2618.9 Inference on P (Y < X) 2668.9.1 ML Estimation 2678.9.2 Normal Approximation 2698.9.3 An Exact Simulation Solution 2718.9.4 Confi dence Intervals 273References 274Exercises 2749. Weibull Regression 2769.1 The Power Law Model 2769.2 ML Estimation 2789.3 Example 2799.4 Pivotal Functions 2809.5 Confidence Intervals 2819.6 Testing the Power Law Model 2819.7 Monte Carlo Results 2829.8 Example Concluded 2859.9 Approximating u* at Other Stress Levels 2879.10 Precision 2899.11 Stress Levels in Different Proportions Than Tabulated 2899.12 Discussion 2919.13 The Disk Operating System (DOS) Program REGEST 291References 296Exercises 29610. The Three-Parameter Weibull Distribution 29810.1 The Model 29810.2 Estimation and Inference for the Weibull Location Parameter 30010.3 Testing the Two- versus Three-Parameter Weibull Distribution 30110.4 Power of the Test 30210.5 Interval Estimation 30210.6 Input and Output Screens of LOCEST.exe 30710.7 The Program LocationPivotal.exe 30910.8 Simulated Example 311References 311Exercises 31211 Factorial Experiments with Weibull Response 31311.1 Introduction 31311.2 The Multiplicative Model 31411.3 Data 31711.4 Estimation 31711.5 Test for the Appropriate Model 31911.6 Monte Carlo Results 32011.7 The DOS Program TWOWAY 32011.8 Illustration of the Influence of Factor Effects on the Shape Parameter Estimates 32011.9 Numerical Examples 327References 331Exercises 332Index 333
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