Extended optimal replacement model with random minimal repair costs

This paper proposes a generalized replacement policy where a system has two types of failures and is replaced at the n-th type I failure (minor failure) or first type II failure (catastrophic failure) or at age T, whichever occurs first. Type I and type II failures are age-dependent. Type I failures are removed by minimal repairs. The cost of the minimal repair of the system at age z depends on the random part C(z) and the deterministic part c(z). The expected cost rate is obtained. The optimal n* and optimal T* which would minimize the cost rate are discussed. Various special cases are considered. Finally, a numerical example is given.