Accession Number : ADA130163

Title :   Asymptotic Methods in Reliability Theory: A Review.

Descriptive Note : Technical rept.,

Corporate Author : DELAWARE UNIV NEWARK APPLIED MATHEMATICS INST

Personal Author(s) : Gertsbakh,Ilya B

PDF Url : ADA130163

Report Date : Sep 1982

Pagination or Media Count : 57

Abstract : Section 1 of this paper reviews some works related to reliability evaluation of nonrenewable systems. The assumption that element failure rates are low allows to obtain an expression for the main term in the asymptotic representation of system reliability function. Section 2 is devoted to renewable systems. The main index of interest in reliability is the time to the first system failure. A typical situation in reliability is that the repair time is much smaller than the element lifetime. This fast repair property leads to an interesting phenomenon that for many renewable systems the time to system failure converges in probability, under appropriate norming, to exponential distribution. Some basic theorems explaining this fact are presented and a series of typical examples is considered. Special attention is paid to reviewing the works describing the exponentiality phenomenon in the birth-and-death processes. Some important aspects of computing the normalizing constants are considered, among them, the role played by so-called main event. Section 2 contains also a review on various bounds on the deviation from exponentiality. Sections 3 , 4 describe some additional aspects of asymptotics in reliability. It is typical for the probabilistic models considered in these sections, that a small parameter is introduced in an explicit form into the characteristic of the random processes. A considerable part of this review is based on the sources which were originally published in Russian and are available in the English translation. (Author)

Descriptors :   *Mathematical models, *Numerical methods and procedures, *Asymptotic series, *Reliability, Theorems, Distribution functions, Exponential functions, Failure, Parameters, Approximation(Mathematics)

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE