Accession Number : AD0627434

Title :   SOME INEQUALITIES FOR RELIABILITY FUNCTIONS,

Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB

Personal Author(s) : Birnbaum,Z. W. ; Esary,J. D.

Report Date : OCT 1965

Pagination or Media Count : 27

Abstract : For the class of coherent binary systems the inequality h'(p) > or = h(p)(1 - h(p))/(p(1-p)) has been previously proven, where p = component reliability, h(p) = system reliability; hence h'(p) = rate of change of system reliability as a function of component reliability. In the present study essential improvements of this inequality are obtained under the assumption that n = number of components, and one or both of the following parameters are known: the 'length' of the system, i.e. the smallest number of components such that their functioning assures the functioning of the system, and the 'width' of the system, i.e. the smallest number of components such that if they fail the system must fail. The usefulness of these results is due to the fact that in practice n, length, and width are often known although the system is so complex that a study of some of its details for reliability purposes may be prohibitive. An immediate application of such inequalities is that when it is known that for component reliability P0 the system has attained reliability h(P sub 0) = P sub 0, then a lower bound can be given for the system reliability h(p) for all P > or = P sub 0. (Author)

Descriptors :   (*RELIABILITY, PROBABILITY), (*INEQUALITIES, PROBABILITY), FUNCTIONS(MATHEMATICS), FAILURE(MECHANICS), MAINTENANCE, PERFORMANCE(ENGINEERING)

Subject Categories : Operations Research
      Mfg & Industrial Eng & Control of Product Sys

Distribution Statement : APPROVED FOR PUBLIC RELEASE