A copula‐based approach on optimal allocation of hot standbys in series systems

In this paper, we propose a copula‐based approach to study the allocation problem of hot standbys in series systems composed of two heterogeneous and dependent components. By assuming that the lifetimes of components and spares are dependent and linked via a general survival copula, optimal allocation strategies are presented for the case of one and two redundancies at the component level. Further, redundancies allocation mechanisms are also compared between the allocations at the component level and the system level. For the case of one hot standby, we find that the performance of the redundant system at the component level is always worse than that at the system level. For the case of two hot standbys, the reversed allocation principle (i.e., Barlow–Proschan principle) is valid. Numerical examples and applications are also provided as illustrations. A real application on improving tensile strength of cables in high voltage electricity transmission network systems is presented for showing the applicability of our results.