A generalized age-dependent minimal repair with random working times

Two extended preventive replacement models for systems that execute projects at random times are discussed in this paper. The system is subject to shocks at which the system experiences one of two kinds of failures whose probabilities depend on age. A type I failure will cause a minor failure of the system and is fixed by a minimal repair. A type II failure will lead to a catastrophic failure of the system, and a corrective replacement is required at such failure. First, we investigate a preventive replacement policy where the system is replaced at the m-th type I failure, or at the time instant when the n-th working project is completed, or at age tau, or at the first type II failure, whichever occurs first. In addition, we also investigate another preventive replacement model where the system is replaced preventively at the time instant when the n-th working project is completed, or at the m-th type I failure, or at age tau, whichever occurs last, and is replaced correctively at the first type II failure. We formulate the long-run expected cost rate for each replacement policy, and determine analytically the optimum preventive replacement policy. We also show that several previous replacement models in the literature are special cases of our models. Finally, a procedure for finding the optimum preventive replacement schedule is presented and some numerical examples are given illustrating the present policies.

Automated summary

This paper discusses two extended preventive replacement models for systems that execute projects at random times. The system is subject to shocks and experiences two types of failures with probabilities depending on age. The long-run expected cost rate for each replacement policy is analyzed, and the optimum preventive replacement policy is determined analytically. The paper also shows that several previous replacement models in the literature are special cases of these two models.