A parallel system of n identical components is subjected to shocks which occur randomly according to a nonhomogeneous Poisson process with intensity function λ(t). Failures of components are due to shocks and are classified into single and multiple failures according to the effect of such shock. Any shock which leads to single failure is said to have multiplicity 1. A multiple failure is the simultaneous failure of k (k≥2) components, and any shock which leads to such a failure is said to have multiplicity k. An optimal replacement period T* minimizing the long-run expected cost per unit time will be determined. A numerical example is presented at the end.
