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On stochastic comparisons of k-out-of-n systems with Weibull components

Part of: Distribution theory - Probability Operations research and management science

Published online by Cambridge University Press:  28 March 2018

Narayanaswamy Balakrishnan ,
Ghobad Barmalzan  and
Abedin Haidari
Narayanaswamy Balakrishnan*
Affiliation:
McMaster University
Ghobad Barmalzan*
Affiliation:
University of Zabol
Abedin Haidari*
Affiliation:
University of Zabol
*
* Postal address: Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, L85 4K1, Canada. Email address: [email protected]
** Postal address: Department of Statistics, University of Zabol, Sistan and Baluchestan, Iran.
** Postal address: Department of Statistics, University of Zabol, Sistan and Baluchestan, Iran.
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Abstract

In this paper we prove that a parallel system consisting of Weibull components with different scale parameters ages faster than a parallel system comprising Weibull components with equal scale parameters in the convex transform order when the lifetimes of components of both systems have different shape parameters satisfying some restriction. Moreover, while comparing these two systems, we show that the dispersive and the usual stochastic orders, and the right-spread order and the increasing convex order are equivalent. Further, some of the known results in the literature concerning comparisons of k-out-of-n systems in the exponential model are extended to the Weibull model. We also provide solutions to two open problems mentioned by Balakrishnan and Zhao (2013) and Zhao et al. (2016).

Keywords

Convex transform orderstar orderusual stochastic orderdispersive orderright-spread orderWeibull distributionk-out-of-n systemmultiple-outlier model

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 1 , March 2018 , pp. 216 - 232
Copyright
Copyright © Applied Probability Trust 2018 

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