TY - JOUR

T1 - ESTIMATION OF THE LIFETIME DISTRIBUTION OF THE PARTS FROM THE AUTOPSY STATISTICS OF THE MACHINE.

AU - Meilijson, Isaac

PY - 1981

Y1 - 1981

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0019689587&partnerID=8YFLogxK

U2 - 10.1017/S0021900200034185

DO - 10.1017/S0021900200034185

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AN - SCOPUS:0019689587

SN - 0021-9002

VL - 18

SP - 829

EP - 838

JO - Journal of Applied Probability

JF - Journal of Applied Probability

IS - 4

ER -