Some results on residual life and inactivity time at random time

ABSTRACT

In this article, we enhance the study of residual life at random time (RLRT) and inactivity time at random time (ITRT). To this aim, first we provide some stochastic orderings results among ITRT in two-sample problems when they failed at two different random times. Then, we develop some sufficient conditions which lead to the stochastic comparisons of RLRT and ITRT based on variance residual life order. The results are expected to be useful in reliability theory, forensic science, queue theory, and actuarial science.

KEYWORDS:

• Ageing class
• Residual life (inactivity time) at random time
• Stochastic orders
• Totally positive of order 2 functions.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 60E15
• Secondary 62N05

Acknowledgments

We are thankful to the anonymous reviewer for his/her valuable comments and suggestions on the earlier version of the manuscript.

Funding

The financial support (Ref. No. SR/FTP/MS-016/2012) rendered by the Department of Science and Technology, Government of India is gratefully acknowledged.