Optimal Replacement Policies with Different Deviation Costs

This paper takes up the replacement problems for [Formula: see text]-out-of-[Formula: see text] system, where the deviation time and cost is provided. First, we consider the case when [Formula: see text]-out-of-[Formula: see text] system is replaced preventively at planned time or failure. The expected cost rate of the system with deviation cost is studied, and its optimal replacement policies are derived analytically. Next, the system is replaced preventively at period time or failure. Third, the optimal number of units is designed when the expected cost rate is minimized. And the numerical examples are given to illustrate the analytical discussions of the optimal replacement policies and optimal number of units for each model when the failure time of each unit has an exponential distribution. The findings of this paper extend the results in the literature from age replacement model to with deviation cost. Therefore, manager can use the results to formulate the optimal decision problem of their [Formula: see text]-out-of-[Formula: see text] systems with deviation cost.