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Some new results on stochastic comparisons of coherent systems using signatures

Part of: Sampling theory, sample surveys Survival analysis and censored data Distribution theory - Probability Nonparametric inference

Published online by Cambridge University Press:  04 May 2020

Ebrahim Amini-Seresht ,
Baha-Eldin Khaledi  and
Subhash Kochar
Ebrahim Amini-Seresht*
Affiliation:
Bu-Ali Sina University
Baha-Eldin Khaledi*
Affiliation:
Florida International University
Subhash Kochar*
Affiliation:
Portland State University
*
*Postal address: Department of Statistics, Bu-Ali Sina University, Hamedan, Iran. Email address: e.amini64@yahoo.com
**Postal address: Department of Mathematics and Statistics, Florida International University, Miami, USA. Email address: bkhaledi@fiu.edu
***Postal address: Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, USA. Email address: kochar@pdx.edu
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Abstract

We consider coherent systems with independent and identically distributed components. While it is clear that the system’s life will be stochastically larger when the components are replaced with stochastically better components, we show that, in general, similar results may not hold for hazard rate, reverse hazard rate, and likelihood ratio orderings. We find sufficient conditions on the signature vector for these results to hold. These results are combined with other well-known results in the literature to get more general results for comparing two systems of the same size with different signature vectors and possibly with different independent and identically distributed component lifetimes. Some numerical examples are also provided to illustrate the theoretical results.

Keywords

Likelihood ratio orderhazard rate orderreversed hazard rate ordercoherent systems

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62N05: Reliability and life testing 62G30: Order statistics; empirical distribution functions 62D05: Sampling theory, sample surveys
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 1 , March 2020 , pp. 156 - 173
Copyright
© Applied Probability Trust 2020

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