Extended optimal replacement policy for a system subject to non‐homogeneous pure birth shocks

This article studies the optimal replacement policy with general repairs for an operating system subject to shocks occurring to a non‐homogeneous pure birth process (NHPBP). A shock causes that the system experiences one of two types of failures: type‐I failure (minor failure) is rectified by a general repair, or type‐II failure (catastrophic failure) is removed by an unplanned replacement. The probabilities of these two types of failures depend on the number of shocks since the last replacement. We consider a bivariate replacement policy (n, T) under which the system is replaced at planned life age T, or at the nth type‐I failure, or at any type‐II failure, whichever occurs first. The optimal replacement schedule which minimizes the expected cost rate model is derived analytically and discussed numerically.