SOME STOCHASTIC MODELS FOR RELIABILITY OF SYSTEMS WITH CONTINUOUSLY DEPENDENT COMPONENT LIFE-TIMES (original) (raw)

Abstract. In two component parallel system, mutual continuous physical interactions create a specific sort of stochastic dependences between the times to failure of the components. In this paper an analysis of the component failure mechanism yields to stochastic description of the phenomena. Finally, an interesting stochastic model in the form of bivariate probability distribution is constructed. As a special case of the obtained general model the first Gumbel bivariate exponential probability distribution is obtained. This presentation may be considered as an extension of the conference paper from the same ‘ASMDA 2007’ conference, which is also uploaded in Academia. It additionally contains description of an idea of the component losing stochastic memory of a past stress. The corresponding “forgetting factors” are introduced and analyzed.