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 -