pp 1–14 | Cite as

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

  • Arijit Patra
  • Chanchal KunduEmail author


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.


Generalized ageing classes Generalized stochastic orders Residual life (inactivity time) at random time Totally positive of order 2 functions 

Mathematics Subject Classification

Primary 60E15 Secondary 62N05, 60K10 



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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsRajiv Gandhi Institute of Petroleum TechnologyJaisIndia

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