The reversed (backward) hazard rate ordering is an ordering for random variables which compares lifetimes with respect to their reversed hazard rate functions. In this paper, we have given some sufficient conditions under which the ordering between the components with respect to the reversed...

Recently, the concept of aging intensity (AI) function has been introduced in the literature for evaluating the aging property of a unit (that may be a system or a living organism) quantitatively. In this paper, we discuss the properties of AI function and study its nature for various...

We show that the order statistics, in a sample from a distribution that has a logconcave density function, are ordered in the up shifted likelihood ratio order. We also show that the order statistics from two different collections of random variables are ordered in the up shifted likelihood...

Di Crescenzo and Longobardi (2002) introduced a measure of uncertainty in past lifetime distributions and studied its relationship with residual entropy function. In the present paper, we introduce a quantile version of the entropy function in past lifetime and study its properties. Unlike the...

Any repairable system improves (deteriorates) with time if the interarrival times of failure tend to get larger (smaller) in some sense. In this paper we consider two such repairable systems, and their performance in terms of several partial orderings of their respective interarrival times of...

The characterization of distributions is well known in the field of Statistics and Reliability. This paper characterizes a few distributions with the help of failure rate, mean residual, log-odds rate, and aging intensity functions.

Ageing intensity (AI) function analyzes the ageing property of a system quantitatively. We study the behavior of a few generalized Weibull models and some system properties in terms of AI function. We establish that AI function provides a major and altogether a new role in studying system’s...

Recently, proportional mean remaining life (PMRL) model has been introduced in the literature for modelling and analysing failure time data. In this paper, some properties of PMRL model related to reliability analysis are investigated. Closure properties of a few aging classes and those of...