Optimal replacement policy with replacement last under cumulative damage models

In this study, we discuss a preventive replacement policy under cumulative damage models that include the concept of replacement last. The system is subject to two types of shocks (represented by type 1 shock and type 2 shock) whose probabilities depend on age. Each type 1 shock leads to an amount of additive damage to the system and also causes a minor failure of the system, which can be rectified by a minimal repair. The system will have a catastrophic failure as long as the accumulated damage exceeds a failure level threshold L. Meanwhile, type 2 shock will cause catastrophic failure of the system. The system is replaced preventively at age tau or the n-th type 1 shock or the time instant when the accumulated damage exceeds a pre-specified level k (but less than L), whichever occurs last, and is replaced correctively at the first type 2 shock or the time which the accumulated damage exceeds L, whichever occurs first. The average cost rate is developed and the optimal replacement policy is discussed analytically and computed numerically.

Automated summary

This study examines a preventive replacement policy under cumulative damage models that involve the concept of replacement last, analyzing the system's response to two types of shocks and its optimal replacement strategies. The average cost rate is developed and the optimal replacement policy is discussed through analytical and numerical methods.