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

In this paper, we investigate the probabilistic characteristics of a unit driven by Dichotomous Markov Noise (DMN), as an external random life increasing and decreas-ing shocks. Using DMN, we will define two new aging classes of the overall increas-ing/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. General Theory The statistical theory of positive aging systems is an interdisciplinary domain of research, which is encountered in many physical, chemical, biological, and engi-neering safety systems. Here, we study the positive aging process driven by a Dichotomous Markov Noise (DMN). Describing the deterioration or positive aging of life in the engi-neering and biological systems, based on different aging criteria, has been the subject of investigation for several decades. For more technical details we refer the reader to Mar