On classes of life distributions: Dichotomous Markov Noise Shock Model With Hypothesis Testing Applications

TL;DR

This paper explores the probabilistic behavior of systems influenced by Dichotomous Markov Noise, introduces new aging classes, and develops a nonparametric test for exponentiality within these classes.

Contribution

It defines new aging classes based on long-term behavior under DMN and proposes a novel nonparametric test for exponentiality against decreasing life distributions.

Findings

Introduction of two new aging classes (OIL/ODL) based on long-term behavior.

Derivation of a moment inequality for ODL class systems.

Development of a nonparametric test for exponentiality against decreasing life distributions.

Abstract

In this paper, we investigate the probabilistic characteristics of a unit driven by Dichotomous Markov Noise (DMN), as an external random life increasing and decreasing shocks. Using DMN, we will define two new aging classes of the overall increasing/decreasing (OIL/ODL) nature in the long time behavior, which are separated by an exponential steady state regime. In addition, a moment inequality is derived for the system whose life distribution is in an overall life decreasing (ODL) class. We use this inequality to devise a nonparametric testing procedure for exponentiality against an alternative overall decreasing life distribution.