ESTIMATION OF THE LIFETIME DISTRIBUTION OF THE PARTS FROM THE AUTOPSY STATISTICS OF THE MACHINE.

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Abstract

Given a coherent reliability system, let Z be the age of the machine at breakdown, and I the set of parts dead by time Z. It is proved that if all lifetime distributions are non-atomic and share the same essential extrema, and if the incidence matrix of the minimal cut sets has rank equal to the number of parts, then the joint distribution of Z and I determines uniquely the lifetime distribution of each part. A Newton-Kantorovic iterative method is presented for the computation of those distributions. The relaxation of the assumptions and the statistical problem, where instead of the joint distribution of Z and I one has an empirical estimate of this joint distribution are dealt with informally.

Original languageEnglish
Pages (from-to)829-838
Number of pages10
JournalJournal of Applied Probability
Volume18
Issue number4
DOIs
StatePublished - 1981

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