Stochastic Comparisons of Series and Parallel Systems with Kumaraswamy-G Distributed Components

SYNOPTIC ABSTRACT

This article deals with stochastic comparisons of the series and parallel systems comprising Kumaraswamy generalized family of distributions. The results are established in two directions. We consider systems with different model parameters, and obtain some ordering results under the condition of multivariate chain majorization. Next, we use the notion of vector majorization and other related orders to establish various stochastic orders, such as the usual stochastic order, the likelihood ratio order, and the dispersive order. Further, results are obtained when components of two systems have independent and heterogeneous Kumaraswamy generalized family of distributions with different parent distribution functions. Numerical examples and counterexamples are provided to illustrate the established results.

KEY WORDS AND PHRASES:

• Order statistics
• majorization
• usual stochastic order
• likelihood ratio order
• dispersive order

Acknowledgements

The author sincerely wishes to thank an anonymous reviewer and the Editor for the suggestions which have considerably improved the content and the presentation of this article.