ANALYSIS OF MARKOV RENEWAL SHOCK-MODELS

A trivariate stochastic process {X(n), Y-n, J(n)}(infinity)(n=0) is co nsidered, describing a sequence of random sheds {X(n)} at random inter vals {Y-n} with random system state {J(n)}. The triviariate stochastic process satisfies a Markov renewal property in that the magnitude of shocks and the shock intervals are correlated pairwise and the corresp onding joint distributions are affected by transitions of the system s tate which occur after each shock according to a Markov chain. Of inte rest is a system lifetime terminated whenever a shock magnitude exceed s a prespecified level z. The distribution of system lifetime, its mom ents and a related exponential limit theorem are derived explicitly. A similar transform analysis is conducted for a second type of system l ifetime with system failures caused by the cumulative magnitude of sho cks exceeding a fixed level z.