Standby redundancy allocation for series and parallel systems

The allocation of redundant components to a system is an efficient technique to improve its lifetime. In this article, we study the problem of two standby redundancy allocations for series and parallel systems, consisting of n-component (n≥2), in the sense of various stochastic orderings. It is assumed that components and redundancies follow a general lifetime distribution. For the case of allocating two redundancies to a series (parallel) system, we show that allocating the relatively stronger redundancy to the weaker component and the weaker redundancy to the stronger components can result in a system lifetime that is longer (shorter) in terms of the usual stochastic order. Moreover, various results associated with the hazard rate and reversed hazard rate orders are established. The outcomes of various papers are strengthened and generalized through our results. In addition, some applications are provided to illustrate our findings.