SIMULATION ANALYSIS OF SYSTEM LIFE WHEN COMPONENT LIVES ARE DETERMINED BY A MARKED POINT PROCESS.

We consider an r component system having an arbitrary binary monotone structure function. We suppose that shocks occur according to apoint process and that, independent of what has already occurred, each new shock is one of r different types, with respective probabilities p₁, ..., p_r. We further suppose that there are given integers n₁, ...,n_r such that component i fails (and remains failed) when there have been a total of n_i type-i shocks. Letting L be the time at which the system fails, we are interested in using simulation to estimate 피 [L], 피 [L²], and 핃 (L > t). We show how to efficiently accomplish this when the point process is (i) a Poisson, (ii) a renewal, and (iii) a Hawkes process. [ABSTRACT FROM AUTHOR]