Stochastic comparisons of coherent systems with active redundancy at the component or system levels and component lifetimes following the accelerated life model

Abstract

An effective way to increase system reliability is to use redundancies (spares) into the systems either in component level or in system level. In this prospect, it is a significant issue that which set of available spares providing better system reliability in some stochastic sense. In this paper, we derive sufficient conditions under which a coherent system with a set of active redundancy at the component level or the system level provide better system reliability than that of the system with another set of redundancy, with respect some stochastic orders. We have derived the results for the component lifetimes following accelerated life (AL) model. The results obtained help us to design more reliable systems by allocating appropriate redundant components from the set of available options for the same. Various examples satisfying the sufficient conditions of the theoretical results are provided. Some results are illustrated with real‐world data.

Optimal redundancy allocations for series systems under hierarchical dependence structures

“…According to the recordings in Hand et al., 45 the tensile strengths of nine wires (cf., Table 2) were tested in a study involving a set of cables extracted from some high‐voltage electricity transmission network systems. This dataset has been widely used in many research papers on reliability optimization, to name but few, for example, You et al., 46 Zhang and Zhang, 33 and Panja et al 47 . Now, let us consider a cable composed of four wires connected in series, namely No.…”