E-Book Overview
Textbook for a methods course or reference for an experimenter who is mainly interested in data analyses rather than in the mathematical development of the procedures. Provides the most useful statistical techniques, not only for the normal distribution, but for other important distributions
E-Book Content
STATISTICAL ANALYSIS OF RELIABILITY AND LIFE-TESTING MODELS STATISTICAL ANALYSIS OF RELIABILITY AND LIFE-TESTING MODELS Theory and Methods Second Edition LEE J. BAIN University of Missouri-Rolla Rolla, Missouri MAX ENGELHARDT University of Missouri-Rolla Rolla, Missouri and Idaho National Engineering laboratory EG&G Idaho, Inc. Idaho Falls, Idaho Marcel Dekker, Inc. New York • Basel • Hong Kong Library of Congress Cataloging-i~-Publication Data Bain, Lee J . Statistical analysis of reliability and life-testing models : theory and methods/Lee J . Bain, Max Engelhardt. - - 2nd ed. p. cm . - - (Statistics, textbooks and monographs; vol. 115) Includes bibliographical re f erences (p . ) and index . ISB 0-8247-8506-1 1. Reliability (Engineering)--Statistical methods . 2 . Accelerated life testing . 3. Distribution (Probability theory) 4. Mathematical statistics. I . Engelhardt, Max. II. Title. III . Series: Statistics, textbooks and monographs; v. 115 . TS1 73 . B34 1991 620' . 00452--dc20 91-7832 CIP This book is printed on acid-free paper. Copyright © 1991 by MARCEL DEKKER, I C. All Rights Reserved !ei ther this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical , including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in 1riting from the publishe1· . IARCEL DEKKER, I ·c . 270 Madison Avenue , New York, New York 10016 Current printing (last digit) : 10 9 8 7 6 5 4 3 2 l PRI 1TED 11 THE UNITED STATES OF AMERICA 1 Probabilistic Models 1. PROBABILITY 1.1. Introduction Suppose a certain physical phenomenon is of interest, and an experiment is conducted to obtain an observed value of this phenomenon. It may be possible to develop a mathematical model so that if the conditions of the experiment are known, then the outcome can he predetermined, at least to a sufficient degree of accuracy. example, Ohm's law, E = IR, For predicts the value of the electromotive force for a given level of current and resistance. example of a deterministic mathematical model. Ohm's law is an However, it may be that the outcome of the experiment cannot be determined on the ba-· sis of the available knowledge of the experiment. In this case a probabilistic mathematical model is necessary. 111ere are many different reasons why a probabilistic model may be required. In some cases the outcomes may truly occur by chance, such as when a die is rolled, any of the six possible faces may occur, on the other hand, it may be that some of the conditions of the experiment are simply unknown or cannot be controlled. For ex- ample, two light bulbs may be manufactured by the same process and used under the same general conditions but still fail at different times. Similarly, a deterministic model may exist but be too com- 1 Chapter 1 2 plex to develop, or some factor such as measurement error may nvcessitate the use of a probabilistic model. The purpose of this chapter is to set up the mathematical structure for describing a physical phenomenon in terms of a prob-ability model. Chapter 2 will review some of the general statis- tical procedures which are helpful in analyzing and selecting an appropriate probability distri