Replacement policies of a shock model with imperfect preventive maintenance

This paper applies a sequential preventive maintenance (PM) policy to a cumulative damage shock model where each PM is imperfect. Shocks occur according to a Poisson process and the system fails with probability p(z) depending on the total damage z upon occurrence of shocks. If the system fails, it undergoes minimal repair. The PM is done at fixed intervals xk (k=1,2,...,N), and reduces the total damage according to its improvement factor bk. The expected cost rate until replacement is derived when p(z) is an exponential function and damages are independent and identically distributed. Optimal policies of interest minimizing the expected cost rate are discussed by assuming xk=x and bk=b. Namely, the authors obtain an optimal number N*(x) of replacement with x fixed, an optimal interval x*(N) of PMs with N fixed, and an optimal pair (N*,x*).