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 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. 
Mohammad Sepehrifar, Shantia Yarahmadian, and Richard Yamada
math.ST math.PR stat.TH