Reliability Analysis of Time-Dependent System when the Number of Cycles Follow Geometric Distribution and Stress-Strength Follow Exponential Distribution

Abstract

Failure of a system may occur due to certain type of stresses acting on them. If these stresses do not exceed a certain threshold value the system may work for a long period. On the other hand, if the stresses exceed the threshold they may fail within no time. There is uncertainty about stress and strength random variables at any instant of time and also about the behavior of the variables with respect to time and cycles. Time dependent stress- strength models are considered with repeated application of stress and also the change of the strength with time. Reliability of time dependent stress- strength system is carried out by considering each of stress and strength variables are random-fixed. In this paper to find the reliability, components are assumed to be identical and the number of cycles for any time period t is assumed to be random. Expression for system reliability have been attained when number of cycles can be follow Geometric distribution and stress and strength both follow exponential distribution & computations were also done.