Abstract
A non-repairable system is considered and the problem of finding its optimal preventive replacement time is revisited. In addition to minimizing the expected cost per unit time in a cycle, we also consider its variance as the measure of the risk of the optimal decision. A multi-objective optimization problem is then formulated where the two objective functions are the expectation and the variance. A sufficient condition is given for the existence of finite optimum in the case of the weighting method, where either the weight of the variance or the replacement costs are sufficiently small. In applying the e - constraint method there is always finite optimum if the upper bound for the expectation is close to its minimal value.
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