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On generalized orderings and ageing classes for residual life and inactivity time at random time

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Abstract

In this paper, we enhance the study of ageing classes and stochastic comparisons of residual life at random time (RLRT) and inactivity time at random time (ITRT). We provide some new preservation properties of generalized ageing classes (viz. s-IFR, s-DFR) and generalized stochastic ordering (s-FR) for RLRT and ITRT, where s is a non-negative integer. An application in reliability theory is also investigated. The results strengthen some results available in the literature and are expected to be useful in reliability theory, forensic science, econometrics, queueing theory and actuarial science.

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Acknowledgements

We would like to thank the anonymous reviewers and the editor for their constructive suggestions/comments that substantially improve the quality of the manuscript. The financial support (Ref. No. SR/FTP/MS-016/2012) rendered by the Department of Science and Technology, Government of India is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mathematics, Rajiv Gandhi Institute of Petroleum Technology, Jais, UP, 229 304, India

    Arijit Patra & Chanchal Kundu

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  1. Arijit Patra
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  2. Chanchal Kundu
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Correspondence to Chanchal Kundu.

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Patra, A., Kundu, C. On generalized orderings and ageing classes for residual life and inactivity time at random time. Metrika 82, 691–704 (2019). https://doi.org/10.1007/s00184-018-0701-0

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