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

Abstract

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(􀜡􀫙􁈻 increases Reliability increases. It is
also observed from the computations that deterministic model is more
reliable than Random model.