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Estimation of the Lifetime Distribution of the Parts from the Autopsy Statistics of the Machine
Journal of Applied Probability
Vol. 18, No. 4 (Dec., 1981), pp. 829-838
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3213058
Page Count: 10
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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.
Journal of Applied Probability © 1981 Applied Probability Trust