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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.
##### MSC:
 62G30 Order statistics; empirical distribution functions 62N05 Reliability and life testing 60E15 Inequalities; stochastic orderings