Optimal Replacement Policy under Cumulative Damage Model with Strength Degradation
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A machine or production system is subject to random failure and it is replaced by a new one, and the process repeats. However, replacing the unit at failure may be expensive possibly producing hazardous effects. Hence, there is a need to replace it according to some replacement policy before the failure occurs (preventive replacement). The cost associated with each replacement due to failure (corrective replacement) is assumed to be higher than that with a preventive replacement. Thus, there is an incentive for attempting to replace before failure occurs. In this paper, we consider the problem of finding an optimal replacement strategy that balances the cost of replacement with the cost of failure and results in a minimum expected cost per unit time under cumulative damage model with strength degradation. The existing recommendations are applicable only under restricted distributional assumptions and/or with fixed strength. As theoretical evaluation of the expected cost per unit time turns out to be very complicated, a simulation-based algorithm is proposed to evaluate the expected cost rate and find the optimal replacement strategy. The proposed method is easy to implement having wider domain of application.
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