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, 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...

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...

Purpose: The purpose of this paper is to introduce a new probability density function having both unbounded and bounded support with a wider applicability. While the distribution with bounded support on [0, 1] has applications in insurance and inventory management with ability to fit risk...

In the present paper, we introduce a quantile based Rényi’s entropy function and its residual version. We study certain properties and applications of the measure. Unlike the residual Rényi’s entropy function, the quantile version uniquely determines the distribution.

A general method of introducing a parameter, called tilt parameter, has been discussed by Marshall and Olkin (1997) to give more flexibility in modelling. In this paper, we take the tilt parameter of the Marshall–Olkin extended family as a random variable. The closure of this model under...

The mean residual life function plays an important role in reliability theory and other branches of statistics. In this paper, we study some ageing properties of the residual life of , the nth upper k-records, given that , where n[greater-or-equal, slanted]m. Some stochastic comparison results...

Makino [Makino, T., 1984. Mean hazard rate and its applications to the normal approximation of the Weibull distribution. Naval Research Logistics Quarterly 31, 1-8] proves that, for any random variable X with finite mean [mu], E(1/r(X)][greater-or-equal, slanted]1/[mu], where r([dot operator])...

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...