Optimum design and replacement policies for k-out-of-n systems with deviation time and cost

In this paper, a new repairable k-out-of-n system model is proposed, in which the deviation cost of the system is taken into account. Firstly, the standard k-out-of-n system is replaced at planned time or at the failure time. Next, replacement policies are studied at planned time or periodic time when k is a constant. Thirdly, replacement policies are studied at planned time or periodic time when k is a random number, respectively. Finally, replacement policies are planned at the completion of random working time. The expected cost rate functions and its optimum replacement policies are derived analytically for each model. Meanwhile, optimum number of units is designed. The analytical solution of replacement policies for each model is discussed. Numerical examples are given to demonstrate our results.

Automated summary

A new repairable k-out-of-n system model is proposed in this paper, taking into account the deviation cost of the system and studying different replacement policies and optimum number of units. Numerical examples demonstrate the effectiveness of the model.