Reliability estimation of multi-component cascade system through Monte-Carlo simulation

Abstract

In the context of interference models of reliability theory, the cascade system is a particular type of standby system where the stress faced by the new component taking the place of a failed component is attenuated by a factor K, where K may be a constant, parameter or even a random variable; K is called an attenuation factor. To estimate reliability or its other characteristic of cascade system by analytical method is very difficult due complicated reliability expressions. Further, the real life data are hard to come. In this paper, an attempt has been made to estimate the reliability $\hat{R}$ of a cascade system when stress–strength (S–S) follow either exponential, normal or gamma distribution by using Monte-Carlo Simulation (MCS). We have checked normal approximation of estimated reliability samples ($\hat{R}$) by normal probability plot (NPP) and fitted normal distribution to those estimated reliability samples for which NPP shows good normal approximation. We have also performed Kolmogorov–Smirnov (K–S) one sample and $\chi^{2}$ -test for goodness of fit. For test of significance between estimated reliability $\hat{R}$ and true reliability R for some given values of parameters of distributions, t test and z-test are performed.