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ESTIMATION OF SYSTEM RELIABILITY IN BROWNIAN

STRESS-STRENGTH MODELS BASED ON SAMPLE PATHS

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NADER EBRAHIMI AND T. RAMALLINGAM

*Division of Statistics and Statistical Consulting Laboratory, Northern Illinois University,*

DeKalb, IL 60115-2854, U.S.A.
(Received December 1, 1989; revised May 15, 1992)

**Abstract.**
Reliability of many stochastic systems depends on
uncertain
stress and strength patterns that are time dependent. In this paper, we consider
the problem of estimating the reliability of a system when both *X*(*t*) and
*Y*(*t*)
are assumed to be independent Brownian motion processes, where *X*(*t*) is the
system stress, and *Y*(*t*) is the system strength, at time *t*.

*Key words and phrases*:
Stress-strength model, stopped process,
maximum likelihood estimator, binary performance process, Brownian motion,
homogeneous Markov process, nonhomogeneous Markov process, first passage time,
inverse Gaussian distribution.

**Source**
( TeX ,
DVI ,
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