Hua Ke, Kai Yao

*Reliability Engineering and System Safety *148(2016)

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This paper studied the block replacement policy with uncertain lifetimes. By using the criterions of chance value, expected value and critical value, the block replacement problem was transformed into three different types of optimization problems. The optimal scheduled replacement time in each case was obtained, and its properties were investigated.

About the author

Hua Ke: School of Economics and Management,Tongji University. associate professor.

Kai Yao:School ofEconomicsandManagement,UniversityofChineseAcademyofSciences

Keywords

Block replacement policy, Maintenance, Renewal process, Uncertainty theory

Brief introduction

Preventive maintenance policies provide significant strategies of reducing the cost of a system which is caused by the failure and the replacement (or repair) of the units. However, it should not be carried out too frequently, otherwise the costs of preventive maintenance might outweigh the benefits. The objective of preventive maintenance is to minimize the average cost in the long run. In order to achieve this, an appropriate time for scheduled maintenance has been applied to the operations of the systems, such as the block replacement policy and the age replacement policy. This paper is dedicated to block replacement policy with uncertain lifetimes.

Block replacement, which means a unit is replaced at failure or at some scheduled time periodically, is usually used when there are a large number of similar units in a system. Block replacement policy aims at finding an optimal scheduled replacement time such that the average replacement cost is minimized. As we know, the lifetimes of the units in a system generally involve the human uncertainty. For example, a unit under the operations of a skilled operator generally has a longer lifetime than a unit under the operations of a fresh operator. Considering the human uncertainty in operating the system, this paper assumes that the lifetimes of the units are uncertain variables, and studies the uncertain block replacement policy. The paper first introduces the uncertain block replacement policy, and by using the criterion of chance value, it transforms the uncertain block replacement problem into an optimization problem. Then by using the criterion of expected value and critical value, the uncertain block replacement problem is transformed into another two different types of optimization problems. Finally, the difference between the three models, and the difference between the uncertain block replacement policy and stochastic block replacement policy was discussed.

The chance value model, the expected value model and the critical value model of the uncertain block replacement problem have their own scopes of applications. Sometimes, we have a budget for replacing the units which might be set by our leaders or our customers. In this case, we would like to please the leaders or the customers by minimizing the chance that the average replacement cost overruns the budget, then we will choose the chance value model. Sometimes, once we determine the scheduled replacement time, this strategy will be carried out many times. In this case, we would like to minimize the expected value of the average replacement cost, then we will choose the expected value model. Sometimes, we have to budget by ourselves for the average cost of replacing the units. In this case, we might want to minimize the budget subjected to the constraint that the average cost being less than the budget holds with a predetermined confidence level, then we will choose the critical value model.