Orderings for series and parallel systems comprising heterogeneous new extended Weibull components

Abstract

This paper examines the problem of stochastic comparisons of series and parallel systems with independent heterogeneous new extended Weibull distributed components. For series systems, we obtain the usual stochastic order via the concepts of weak weighted and unordered majorization orders. Also, we strengthen this result to the hazard rate order under a restriction. For parallel systems, with the help of weak supermajorization and weak submajorization orders, we establish the usual stochastic order. The results of this paper can be used to find some bounds for the important aging characteristics of series and parallel systems consisting of independent heterogeneous new extended Weibull distributed components.

Keywords:

• Series systems
• parallel systems
• stochastic orders
• new extended Weibull distribution
• unordered majorization
• weighted majorization order

Acknowledgements

The authors express their sincere thanks to the Associate Editor and anonymous reviewer for providing many valuable comments and suggestions which resulted in an improvement in the presentation of this manuscript.

Additional information

Funding

This work has been conducted by University of Zabol (Grant Number UOZ-GR-3389).