Some copula-based results on optimal number of cold standby components in parallel systems

‎This paper deals with a system's profit and efficiency functions consisting of a two-parallel components supported by (n-۲) cold standby redundancy‎. ‎It is supposed that the components are not repairable and the failed component is immediately replaced with one of the cold standby components‎. ‎Because the lifetimes of active components are dependent‎, ‎their dependency is modelled by Farlie-Gumbel-Morgenstern (FGM) copula function‎. ‎Finding the optimal n according to the highest profit function of the system and efficiency values is studied while the effect of the dependence parameter is considered‎. ‎It is concluded that though increasing n grants higher system reliability it is not always wise as long as the redundancy maintenance costs‎. ‎Due to the complexity of the formulas‎, ‎for the large values of n‎, ‎the results are analyzed numerically and graphically‎. ‎Finally‎, ‎some examples are given to illustrate the results‎.

کلیدواژه ها:

‎Cold standby redundancy ، ‎ ‎Copula function ، Profit function ، ‎ ‎Reliability ، ‎System efficiency