Orderings of component level versus system level at active redundancies for coherent systems with dependent components

Yan, Rongfang; Wang, Junrui; Lü, Bin

doi:10.1017/s0269964821000401

Cited by 2 publications

(1 citation statement)

References 57 publications

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“…Panja et al [29] investigated the usual stochastic and hazard rate orderings on series and parallel systems with dependent and heterogeneous components. For more relevant research the reliability of systems with dependent components, one can refer to the works in [30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Comparisons of Lifetimes of Series and Parallel Systems with Dependent Heterogeneous MOTL-G Components under Random Shocks

Jiao

Yan

2021

Symmetry

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To measure the magnitude among random variables, we can apply a partial order connection defined on a distribution class, which contains the symmetry. In this paper, based on majorization order and symmetry or asymmetry functions, we carry out stochastic comparisons of lifetimes of two series (parallel) systems with dependent or independent heterogeneous Marshall–Olkin Topp Leone G (MOTL-G) components under random shocks. Further, the effect of heterogeneity of the shape parameters of MOTL-G components and surviving probabilities from random shocks on the reliability of series and parallel systems in the sense of the usual stochastic and hazard rate orderings is investigated. First, we establish the usual stochastic and hazard rate orderings for the lifetimes of series and parallel systems when components are statistically dependent. Second, we also adopt the usual stochastic ordering to compare the lifetimes of the parallel systems under the assumption that components are statistically independent. The theoretical findings show that the weaker heterogeneity of shape parameters in terms of the weak majorization order results in the larger reliability of series and parallel systems and indicate that the more heterogeneity among the transformations of surviving probabilities from random shocks according to the weak majorization order leads to larger lifetimes of the parallel system. Finally, several numerical examples are provided to illustrate the main results, and the reliability of series system is analyzed by the real-data and proposed methods.

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