Age replacement policy with lead-time for a system subject to non-homogeneous pure birth shocks

A system is subject to shocks that arrive according to a non-homogeneous pure birth process. Whenever a shock occurs, the system enters one of the two types of failure states. Type I failure (minor failure) is fixed by a minimal repair. Type II failure (catastrophic failure) is removed by a replacement. We consider an age replacement policy which replaces the system whenever its age reaches TT and a spare for replacement is available. The optimal cost minimization age T∗T∗ is derived under a cost structure. We demonstrate that this model includes more realistic factors and is a generalization of several previous models in the literature.