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Comparing the expected system lifetimes of \(k\)-out-of-\(m\) systems using transmuted-G distributions. (English) Zbl 1463.62142
Summary: An open problem in reliability is comparison of expected system lifetimes. In this paper, using transmuted-G distributions [Z. M. Nofal et al., Commun. Stat., Theory Methods 46, No. 8, 4119–4136 (2017; Zbl 1368.62027)], we can represent large \(k\)-out-of-\(m\) and series-parallel/parallel-series systems. We study the asymptotic behavior of the order statistics of these type of systems, along with stochastic ordering, namely likelihood ratio order. An example is provided.
62G30 Order statistics; empirical distribution functions
62N05 Reliability and life testing
60E15 Inequalities; stochastic orderings