Reliability of Time Dependent Stress-Strength Model for Deterministic and Random Cycles

In certain situations and with certain types of equipments time-to-failure may not be quantity of interest. The systems may work practically for an infinite period of time if all the factors are within the prescribed tolerances. Their failure occurs due to certain types of stresses acting on them. If these stresses do not exceed a certain threshold value, they may work for a very long period; If the stresses exceed the threshold, they fail in no time, these models are stress dependent models. Stress and strength are time varying in many real-life systems. In this article reliability analysis of time dependent stress strength system is carried out by considering each of stress variables are deterministic and strength variables are random independent and vice versa for deterministic and random cycles. In case1 if stress and strength follow Exponential and Rayleigh distributions, it is observed that, for deterministic cycles, strength parameter(μ) and number of cycles(n) increases, reliability value decreases and for random cycles parameter value(α) and time(t) increases reliability decreases and in case2 stress strength follow Exponential and Rayleigh distributions, no. of cycles(n) and parameter value(α) increases, Reliability decreases and stress parameter(λ) and strength (y₀) increases Reliability increases. It is also observed from the computations that deterministic model is more reliable than Random model.