Using the Weibull Distribution

Informationen zum Autor 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. Klappentext 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 WeibullThroughout 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(r), 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 Zusammenfassung 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 WeibullThroughout 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 anal...

Autorentext

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.

Klappentext

Understand and utilize the latest developments in Weibull inferential methods While 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, warranties and renewal theory Exact inference in Weibull regression Goodness of fit testing and distinguishing the Weibull from 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(r), 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

Inhalt

Preface xiii 1. Probability 1 1.1 Sample Spaces and Events, 2 1.2 Mutually Exclusive Events, 2 1.3 Venn Diagrams, 3 1.4 Unions of Events and Joint Probability, 4 1.5 Conditional Probability, 6 1.6 Independence, 8 1.7 Partitions and the Law of Total Probability, 9 1.8 Reliability, 12 1.9 Series Systems, 12 1.10 Parallel Systems, 13 1.11 Complex Systems, 15 1.12 Crosslinked Systems, 16 1.13 Reliability Importance, 19 References, 20 Exercises, 21 2. Discrete and Continuous Random Variables 23 2.1 Probability Distributions, 24 2.2 Functions of a Random Variable, 26 2.3 Jointly Distributed Discrete Random Variables, 28 2.4 Conditional Expectation, 32 2.5 The Binomial Distribution, 34 2.5.1 Confidence Limits for the Binomial Proportion p, 38 2.6 The Poisson Distribution, 39 2.7 The Geometric Distribution, 41 2.8 Continuous Random Variables, 42 2.8.1 The Hazard Function, 49 2.9 Jointly Distributed Continuous Random Variables, 51 2.10 Simulating Samples from Continuous Distributions, 52 2.11 The Normal Distribution, 54 2.12 Distribution of the Sample Mean, 60 2.12.1 P[X 2.13 The Lognormal Distribution, 66 2.14 Simple Linear Regression, 67 References, 69 Exercises, 69 3. Properties of the Weibull Distribution 73 3.1 The Weibull Cumulative Distribution Function (CDF), Percentiles, Moments, and Hazard Function, 73 3.1.1 Hazard Function, 75 3.1.2 The Mode, 77 3.1.3 Quantiles, 77 3.1.4 Moments, 78 3.2 The Minima of Weibull Samples, 82 3.3 Transformations, 83 3.3.1 The Power Transformation, 83 3.3.2 The Logarithmic Transforma…