Comparison between the two estimates of the possibility and bass function using the exponential distribution of the reliability function (Cascade, stress-strength)

Abstract

In this research, the mathematical equations for the reliability of the Cascade 1 + 1 system were derived for the (stress - toughness) variables that follow the exponential distribution, and the Cascade 1 + 1 system consists of two components, one of them is active and the other is ready (reserve) called the system (Stress - Durability (Cascade 1+1). As the failure of one of the components leads to the operation of the other spare component. Durability is represented by (v) and the system is subjected to stress represented by (u) in the presence of the attenuation factor (K), which corrects the path of the system as it improves the performance of the system by reducing the stress placed on the subsequent component that caused the failure of the previous component. In addition, two methods were used to estimate the reliability of the system (Cascade 1+1), which are the greatest possibility method (MLE) and Bayes method, and then the two methods were compared based on the mean squares error (MSE). The best method of estimation is the BES method.