E-Book Overview
Engineers face numerous uncertainties in the design and development of products and processes. To deal with the uncertainties inherent in measured information, they make use of a variety of statistical techniques. This outstanding text presents single-variable statistical distributions that are useful in engineering design and analysis. It lists significant properties of these distributions and describes methods for estimating parameters and their standard errors, constructing confidence intervals, testing hypotheses, and plotting data. Each distribution is worked through typical applications. Figures are used extensively to clarify concepts. Methods are illustrated by numerous fully worked examples in the form of Mathcad documents that readers can use as templates for their own data, eliminating the need for programming. Intended as both a text and reference, the book assumes an elementary knowledge of calculus and probability. Graduate and advanced undergraduate students, as well as practicing engineers and scientists, will be able to use this book to solve practical problems connected with the uncertainty assessment in a wide range of engineering contexts.
E-Book Content
Statistical Distributions in Engineering KARL BURY Contents Preface page ix PART ONE: STATISTICAL BACKGROUND 1 Introduction Uncertainty in the Engineering Context Data Models Decisions Example 2 Statistics Sampling Distributions Summation Statistics Order Statistics Simulation Example 3 Inference Information Point Estimators Confidence Intervals Tests Probability Plot Example PART TWO: DISCRETE DISTRIBUTIONS 4 Introduction to Discrete Distributions Examples 5 Hypergeometric Distributions Introduction Properties Inferences Applications Examples 6 Binomial Distributions Introduction Properties CONTENTS Inferences Applications Examples 7 Negative Binomial Distributions Introduction Properties Inferences Applications Examples 8 Poisson Distributions Introduction Properties Inferences Applications Examples PART THREE: CONTINUOUS DISTRIBUTIONS 9 10 Introduction to Continuous Distributions Normal Distributions Introduction Properties Sampling Distributions Probability Plot Point Estimates Interval Estimates and Tests: Complete Samples Interval Estimates: Censored Samples Applications Examples 11 Log-Normal Distributions Introduction Properties: Two-Parameter Model Properties: Three-Parameter Model Probability Plot Point Estimates: Two-Parameter Model Interval Estimates: Two-Parameter Model Estimates: Three-Parameter Model Applications Examples 12 Exponential Distributions Introduction Censoring Properties Probability Plot CONTENTS Point Estimates: One-Parameter Model Interval Estimates: One-Parameter Model Point Estimates: Two-Parameter Model Interval Estimates: Two-Parameter Model Applications Life Testing Examples 13 Gamma Distributions Introduction Properties: Two-Parameter Model Properties: Three-Parameter Model Special Cases: Chi-Squared, Erlang, and Exponential Models Probability Plot Point Estimates: Two-Parameter Model Interval Estimates: Two-Parameter Model Point Estimates: Three-Parameter Model Applications Life Testing Examples 14 Beta Distributions Introduction Properties: Two-Parameter Model Properties: Four-Parameter Model Special Case: Uniform Distributions Probability Plot Point Estimates: Two-Parameter Model Interval Estimates: Two-Parameter Model Point Estimates: Four-Parameter Model Applications Examples 15 Gumbel Distributions Introduction Properties Probability Plot Point Estimates Interval Estimates and Tests Applicatio