Reliability Function of the Special (3+1) Cascade Model

In this paper, a reliability function is found for the special case of cascade model where the model consists of (3 + 1) units and trace random variables that represent the strength and stress Rayleigh distribution, respectively. The mathematical formula of the reliability function was estimated by estimating the parameters of Rayleigh distribution in the five different estimation methods, Maximum likelihood method, Percentile method, Least Squares method, Weighted Least Squares method and Regression method. Using the MATLAB software, A Monte Carlo simulation is performed to compare the results of different estimation methods using the mean square error criterion. The simulation results showed that the best estimation methods for estimating the reliability model are ML estimator and Pr estimator.