To read this content please select one of the options below:

Stochastic comparisons of series and parallel systems with independent heterogeneous Gumbel and truncated Gumbel components

Fatih Kızılaslan (Department of Statistics, Faculty of Arts and Sciences, Marmara University, Istanbul, Turkey)

International Journal of Quality & Reliability Management

ISSN: 0265-671X

Article publication date: 14 January 2021

Issue publication date: 30 July 2021

119

Abstract

Purpose

The purpose of this paper is to investigate the stochastic comparisons of the parallel system with independent heterogeneous Gumbel components and series and parallel systems with independent heterogeneous truncated Gumbel components in terms of various stochastic orderings.

Design/methodology/approach

The obtained results in this paper are obtained by using the vector majorization methods and results. First, the components of series and parallel systems are heterogeneous and having Gumbel or truncated Gumbel distributions. Second, multiple-outlier truncated Gumbel models are discussed for these systems. Then, the relationship between the systems having Gumbel components and Weibull components are considered. Finally, Monte Carlo simulations are performed to illustrate some obtained results.

Findings

The reversed hazard rate and likelihood ratio orderings are obtained for the parallel system of Gumbel components. Using these results, similar new results are derived for the series system of Weibull components. Stochastic comparisons for the series and parallel systems having truncated Gumbel components are established in terms of hazard rate, likelihood ratio and reversed hazard rate orderings. Some new results are also derived for the series and parallel systems of upper-truncated Weibull components.

Originality/value

To the best of our knowledge thus far, stochastic comparisons of series and parallel systems with Gumbel or truncated Gumble components have not been considered in the literature. Moreover, new results for Weibull and upper-truncated Weibull components are presented based on Gumbel case results.

Keywords

Acknowledgements

This work was supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under 2219 postdoctoral scholarship program.

Citation

Kızılaslan, F. (2021), "Stochastic comparisons of series and parallel systems with independent heterogeneous Gumbel and truncated Gumbel components", International Journal of Quality & Reliability Management, Vol. 38 No. 8, pp. 1771-1791. https://doi.org/10.1108/IJQRM-02-2020-0040

Publisher

:

Emerald Publishing Limited

Copyright © 2020, Emerald Publishing Limited

Related articles