ESTIMATION OF SYSTEM RELIABILITY IN BROWNIAN STRESS-STRENGTH MODELS BASED ON SAMPLE PATHS

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.