Reliability of fuzzy Cascade system (stress- strength) for Weibull distribution of the model (1+1) using simulation method

Abstract

This research included estimating the reliability of the fuzzy cascade system of  Weibull's distribution of one, two components and three components for each component of strength (x) and exposure to stress (y) through the presence of attenuation factor (k) which improves the path of the system, the Weibull distribution of the strength and stress variable with different shape parameters and different measurement parameters was used, the researcher also estimated the fuzzy marginal reliability per , as well as the study of the behavior of the reliability of the fuzzy cascade system and has used two methods to estimate the method of least squares the Shrinkage method, and to know the preference between them the researcher used the statistical criterion average squares of error (mse), The researcher concluded that the least squares method is the best when the sizes of the samples are small, while the preference of the shrinkage method when the sizes of the samples are medium and large, and the researcher also recommended paying attention to reliability and fog because they have an important role in practical life, as well as recommended choosing different distributions for both stress and strength.