Optimal Number of Repairs Before Replacement for a System Subject to Shocks of a Non-Homogeneous Pure Birth Process
We consider a system subject to shocks that arrive according to a nonhomogeneous pure birth process (NHPBP). As a shock occurs, the system has two types of failures. Type-I failure (minor failure) is rectified by a general repair, whereas 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 policy with which the system is replaced at the nth type-I failure, or at any type-II failure. The aim of this paper is to determine the optimal policy n*, the number of minor failures up to replacement that minimizes the expected cost rate of the system subject to NHPBP shocks. The model is a generalization of the existing models, and is more applicable in practice. We present some numerical examples, and show that several classical models are the special cases of our model.
optimization repair replacement birth process maintenance shock model