Philosophical and Statistical Foundation of Time and System Age Modelling

As Levich (1995) noted, “In today’s natural science time is an initial, un-definable concept. Nevertheless, the scientists’ intuitive idea of time essentially affects the experimental and theoretical results of scientific work.” Time as a concept has always been of vital importance in many fields of investigation. In most studies, time is an element that has a great bearing on the outcome, or on the interpretation of results. Instances of this may be, for example, when predictions of future changes are being made; in studies of system dynamics and evolution; the aging processes in complex systems; in the search for the underlying mechanism of dynamics. In reliability engineering, we use time and its extensions, for instance, random time, stopping time, censoring time, and fuzzy time, etc, in a seemingly natural and conventional way without any examination. The well-accepted notion of time is actually a concept of Newtonian mechanics and behaves like a geometric straight line. In this paper, we begin with an examination of the variability nature of time with a sequence examples in physics, biology, probability. The foundations of the concept of time both philosophically and mathematical are examined. Furthermore, the contradiction between engineering practices and reliability modeling exercises allows us to argue that the variable characteristic of time should be a basic component for defining both the system operating time and system age in reliability engineering modeling and maintenance policy decision-making. We also discuss the multivariate nature of system operating time and system age. Pre-time (event-ordering) and parametric time concepts are explored in the reliability engineering context and the application areas, including system substitutional time and system entropy time are discussed.