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Estimation of the Lifetime Distribution of the Parts from the Autopsy Statistics of the Machine

Isaac Meilijson
Journal of Applied Probability
Vol. 18, No. 4 (Dec., 1981), pp. 829-838
DOI: 10.2307/3213058
Stable URL: http://www.jstor.org/stable/3213058
Page Count: 10
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
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. We prove 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. We present a Newton-Kantorovič iterative method for the computation of those distributions. We deal informally with the relaxation of the assumptions and with the statistical problem where instead of the joint distribution of Z and I we have an empirical estimate of this joint distribution.

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