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

Document Type : Original Article

Authors

• Motahareh Parsa
• Hadi Jabbari
• Jafar Ahmadi

Ferdowsi University of Mashhad, Mashhad‎, ‎Iran

10.22067/smps.2024.45746

Abstract

‎This paper deals with a system's profit and efficiency functions consisting of a two-parallel components supported by (n-2) 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.

Keywords

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

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