Stochastic comparisons of series and parallel systems with independent heterogeneous Gumbel and truncated Gumbel components
International Journal of Quality & Reliability Management
ISSN: 0265-671X
Article publication date: 14 January 2021
Issue publication date: 30 July 2021
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
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