More predictable, less predictable and stable counting processes

Abstract

In a counting process considered at time t the focus is often on the length of the current interarrival time, whereas points in the past may be said to constitute information about the process. The paper introduces new concepts on how to quantify predictability of the future behavior of counting processes based on the past information and considers then situations in which the future points become more (or less) predictable. Various properties of our proposed concepts are studied and applications relevant to the reliability of repairable systems are given.