The Frechet Reliability for (2+2) Cascade Model

Abstract

In this paper, a reliability function for one of the cascade models was found; the model consists of two basic components (B_1 and B_2 ) and two spare components (B_3 and B_4 ), and it is sufficient for the model to be in a working state with the presence of two active components and, in case of failure of one of the two basic components, it is compensated with one of the two standby components to keep the model running. It was assumed that the strength-stress factors traced the Frechet, the parameters of the Frechet were estimated by three different estimation methods (Moments, Least Squares and Weighted Least Square,), after which the reliability of the model was estimated. Monte Carlo simulations were also conducted to compare the results and find out which estimation methods are the best to estimate the reliability of the model using two statistical criteria: MSE and MAPE, where it was presented that least square estimation is the preferred for estimating the function of reliability.