Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series A, Pt. 2, 233--243

IMPROVEMENT AND DETERIORATION OF A REPAIRABLE SYSTEM

By

NADER EBRAHIMI, *Indian Statistical Institute*

SUMMARY. Let [N(*t*); *t* ³
0] denote the number of failures in [0, *t*] of a repairable system. The conditional non-homogeneous Poisson process (often called a doubly stochastic Poisson process) appears reasonably consonant with situation where one has several measurements (characteristics) indicating condition of the system and can be used for modeling [N(*t*); *t* ³
0]. This paper presents several properties of this process. Given that the conditional NHHP is an appropriate model we also provide model-free definitions of system behaviour. Various properties of the definitions are studied.

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*AMS(1990) subject classification.* 60K10,62N05, 62B10, 60G15

*Key words and phrases*. conditional non-homogeneous poisson process, repairable system, non homogeneous Poisson process multiplicative intensity model