MODEL OF NONHOMOGENEOUS ALTERNATING RENEWAL PROCESS

Abstract

In this article we propose a new mathematical model for calculating the system availability index that is at an arbitrary point of time in two possible states: an operable state and a failure state. In the construction of a mathematical model, the flows of failure and recovery were separated. New reliability characteristics of joint streams of events are introduced and defined. Some properties have been obtained, in particular, the connection of new reliability characteristics with the distributions of failure times and restores through the two-dimensional Volterra integral equations of the second kind is shown. A solution is obtained for the exponential distribution laws, which coincides with the classical one, obtained through the one-dimensional Volterra equation of the second kind. A new mathematical model allows to monotonely convert two independent recurrent flows of failure and recovery in an arbitrary way. Such opportunity allows, for example, to calculate the availability function of an aging system. In the final part of the article, an example of calculating the availability factor for a periodically non-uniform alternating process is considered. This situation takes place during work of supermarkets, seasonal sales, etc.