The relevation can be considered as a replacement or repair policy in reliability, in which, when a unit fails, the unit is restored to a working condition just previous to the failure, in the sense that the age of the unit is not changed but the failure rate changes. It can be also considered as a generalization of the minimal repair policy and the load-sharing model. In this paper, we consider the problem of where to allocate a relevation in a system to increase the reliability of the system and the particular cases of load-sharing and minimal repair policies.

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The purpose of this paper is twofold. On the one hand, we provide sufficient conditions for the excess wealth order. These conditions are based on properties of the quantile functions which are useful when the dispersive order does not hold. On the other hand, we study sufficient conditions for the comparison in the increasing convex order of spacings of generalized order statistics. These results will be combined to show how we can provide comparisons of quantities of interest in reliability and insurance.