On Some Aspects of Strong Risk Class and Associated Ordering

Abstract

The paper opens up a new aging class and a new stochastic orders which is depend on risk class, that plays vital role in the reliability theory, finance topics, stochastic orders, and the economic theory. The article presents some new interesting implications and characterizations concerning this class. In addition, we list a series of inequalities that provide bounds for strong risk and some aging classes. Furthermore, a sufficient condition for a probability distribution to have a new class is provided. In addition, The paper demonstrates the preservation properties of a new stochastic order under some reliability operations such as mixture, and convolution. Moreover, some new reliability concepts based on discrete lifetime random variable are studied.