Usual stochastic ordering results for series and parallel systems with components having Exponentiated Chen distribution

In this paper, we have discussed the usual stochastic ordering relations between two systems. Each system consists of n mutually independent components. The components follow Exponentiated (Extended) Chen distribution with three parameters $α, β, λ$. Two popular systems are taken into consideration, one is the series system and another is the parallel system. The results in this paper are obtained by varying one parameter and the other parameters are kept constant. The hazard rate ordering or reversed hazard rate ordering relations that are not possible for series or parallel systems have been demonstrated with the help of counterexamples.

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