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Mark Brown and Frank Proschan
Journal of Applied Probability
Vol. 20, No. 4 (Dec., 1983), pp. 851-859
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3213596
Page Count: 9
You can always find the topics here!Topics: Random variables, Mathematical monotonicity, Mathematical independent variables, Research grants, Mathematical theorems, Poisson process, Mathematical functions, Distributivity
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A device is repaired at failure. With probability p, it is returned to the 'good-as-new' state (perfect repair), with probability 1-p, it is returned to the functioning state, but it is only as good as a device of age equal to its age at failure (imperfect repair). Repair takes negligible time. We obtain the distribution Fp of the interval between successive good-as-new states in terms of the underlying life distribution F. We show that if F is in any of the life distribution classes IFR, DFR, IFRA, DFRA, NBU, NWU, DMRL, or IMRL, then Fp is in the same class. Finally, we obtain a number of monotonicity aroverties for various parameters and random variables of the stochastic process. The results obtained are of interest in the context of stochastic processes in general, as well as being useful in the particular imperfect repair model studied.
Journal of Applied Probability © 1983 Applied Probability Trust