Characterization Problems Associated with the Exponential Distribution

Azlarov, T. A.; Olkin, I.; Stein, M.; Volodin, N. A.

Problems of calculating the reliability of instruments and systems and the development of measures to increase efficiency and reduce operational costs confronted physicists and mathe­ maticians at the end of the '40's and the beginning of the '50's in connection with the unrelia­ bility of electro-vacuum instruments used in aviation. Since then steadily increasing demands for the accuracy, reliability and complexity required in electronic equipment have served as a stimulus in the development of the theory of reliability. From 1950 to 1955 Epstein and Sobel [67,68] and Davis [62], in an analysis of statistical data of the operating time of an instrument up to failure, showed that the distribution is exponential in many cases. Consequently, the ex­ ponential distribution became basic to research associated with experiments on life expectancy. Further research has shown that there are a whole series of problems in reliability theory for which the exponential distribution is inapplicable. However, it can practically always be used as a first approximation. The ease of computational work due to the nice properties of the exponential distribution (for example, the lack of memory property, see Section 1) is also a reason for its frequent use. AB a rule, data on the behavior of the failure rate function are used to test the hypothesis that a given distribution belongs to the class of exponential distributions, and order statistics are used to estimate the parameter of the exponential distribution.

Details

Published by: Springer

Publication Date: 2011-10-01

Format: Paperback

ISBN-13: 9781461293743

DOI: 10.1007/978-1-4612-4956-6

Dimensions: 235cm x155cm

Pages: 137