Preventive Replacement Policy Research Articles

Optimal replacement policies for two-unit machines with increasing running costs 1

A machine consists of two stochastically failing units. Failure of either of the units causes a failure of the machine and the failed unit has to be replaced immediately. Associated with the units are running costs which increase with the age of the unit because of increasing maintenance costs, decreasing output, etc. A preventive replacement policy is proposed under which, at failure points, we also replace the second unit if its age exceeds a predetermined control limit. It is proved that, for two identical units with exponential life-time distributions and linear running costs, this policy is optimal and the optimal control limit is calculated. In an additional model we take into consideration the length of time it takes to replace one unit or both units. The method of solution is a variation of dynamic semi-Markov programming. Analytical results are obtained and the influence of the various parameters on them is investigated. Finally, we study the saving due to our policy in comparison with a policy in which only failed units are replaced.

Preventive Replacement of a 1-Unit System with a Wearout State

This paper is concerned with a 1-unit system with 3 types of states: usual, wearout, and failure; the hazard rate is constant in the usual state and is monotonically increasing and unbounded in the wearout state. In order to deal with this system in detail, we introduce two models: model 1 in which the period of normal operation is fixed and model 2 in which it is a random variable with a negative exponential distribution function. The models have different preventive replacement policies based on both age and state. Moreover we give the conditions under which these policies are effective.

Optimal Continuous Policies for Repair and Replacement

This paper investigates the problem of finding optimal replacement policies for equipment subject to failures with randomly distributed repair costs, the degree of reliability of the equipment being considered as a state of a Markov process. Algorithms have been devised to find optimal combined policies both for preventive replacement and for replacement in case of failure by using repair-limit strategies. First a simple procedure to obtain an optimal discrete policy is described. Then an algorithm is formulated in order to calculate an optimal continuous policy: it is shown how the optimal repair limit is the solution to an ordinary differential equation, and how the value of the repair limit determines the optimal preventive replacement policy.