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Ordering and ageing properties of developed sequential order statistics governed by the Archimedean copula

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

Published online by Cambridge University Press:  26 June 2023

Tanmay Sahoo  and
Nil Kamal Hazra
Tanmay Sahoo*
Affiliation:
Indian Institute of Technology Jodhpur
Nil Kamal Hazra*
Affiliation:
Indian Institute of Technology Jodhpur
*
*Postal address: Department of Mathematics, Indian Institute of Technology Jodhpur, Karwar 342037, India.
*Postal address: Department of Mathematics, Indian Institute of Technology Jodhpur, Karwar 342037, India.
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Abstract

Developed sequential order statistics (DSOS) are very useful in modeling the lifetimes of systems with dependent components, where the failure of one component affects the performance of remaining surviving components. We study some stochastic comparison results for DSOS in both one-sample and two-sample scenarios. Furthermore, we study various ageing properties of DSOS. We state many useful results for generalized order statistics as well as ordinary order statistics with dependent random variables. At the end, some numerical examples are given to illustrate the proposed results.

Keywords

k-out-of-n systemsstochastic ageingsstochastic orders

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60E15: Inequalities; stochastic orderings 60K10: Applications (reliability, demand theory, etc.)
Type
Original Article
Information
Advances in Applied Probability , Volume 56 , Issue 2 , June 2024 , pp. 464 - 494
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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