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Preservation of mean inactivity time ordering for coherent systems

Part of: Survival analysis and censored data Distribution theory - Probability

Published online by Cambridge University Press:  05 October 2023

T. V. Rao  and
Sameen Naqvi
T. V. Rao*
Affiliation:
Indian Institute of Technology Hyderabad
Sameen Naqvi*
Affiliation:
Indian Institute of Technology Hyderabad
*
*Postal address: Indian Institute of Technology Hyderabad, Hyderabad 502285, India.
*Postal address: Indian Institute of Technology Hyderabad, Hyderabad 502285, India.
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Abstract

Preservation of stochastic orders through the system signature has captured the attention of researchers in recent years. Signature-based comparisons have been made for the usual stochastic order, hazard rate order, and likelihood ratio orders. However, for the mean residual life (MRL) order, it has recently been proved that the preservation result does not hold true in general, but rather holds for a particular class of distributions. In this paper, we study whether or not a similar preservation result holds for the mean inactivity time (MIT) order. We prove that the MIT order is not preserved from signatures to system lifetimes with independent and identically distributed (i.i.d.) components, but holds for special classes of distributions. The relationship between these classes and the order statistics is also highlighted. Furthermore, the distribution-free comparison of the performance of coherent systems with dependent and identically distributed (d.i.d.) components is studied under the MIT ordering, using diagonal-dependent copulas and distorted distributions.

Keywords

Coherent systemscopuladistorted distributionmean inactivity timestochastic orderssystem signature

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62N05: Reliability and life testing
Type
Original Article
Information
Advances in Applied Probability , First View , pp. 1 - 27
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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