Preservation of the NBUCA Class of Life Distributions

Introduction As is well known, lifetime distributions can beclassified by stochastic ordering. Recently, Ahmad etal.1]defined a new aging class, namely, NBUCA(new better than used in increasing convex average),based upon the increasing convex average order. Inthe theory of economics, this order is known as weakthird-order stochastic dominance2]. Under the as-sumption that the elements are independent andidentically distributed (i.i.d.), the preservationproperties of this class under convo…

Preservation of the NBUCA Class of Life Distributions

The purpose of this paper is to discuss the closure properties of increasing convex average order and NBUCA life distributions. Under the assumption that the units are only independent, characterizations of NBUCA class of life distributions are given. It is shown that NBUCA class is closed under the random maxima and the formation of parallel systems of independent units. As an application of the main results, the behavior of this class is developed in terms of the monotonicity of the residual life of k-out-of n systems given the time at which the (n-k )-th failure has occurred.