Stochastic aspects of reversed aging intensity function of random quantiles

Abstract

Abstract This paper studies some stochastic properties of random quantiles according to the newly defined reliability measure called reversed aging intensity function. Preservation property of reversed aging intensity order under random quantile is obtained and using it, a lower bound and an upper bound for the reversed aging intensity function of a random quantile are derived. Preservation of two related monotonic reliability classes under random quantiles is also studied. We finally apply our results for reliability analysis of series systems with heterogeneous component lifetimes. Examples are included to examine and analyze the obtained results.

Keywords

• Reversed hazard rate
• Aging class
• Average intensity function
• Reversed aging intensity function
• Stochastic order
• T P 2 $TP_{2}$