مقارنة بين تقدير MLE و Bootstrap باستخدام التوزيع الاسي لدالة المعولية Cascade (الاجهاد-المتانة)‎

Abstract EN

In this paper, the mathematical equation of the Cascade (1+1) equation derived Using the exponential distribution and Cascade (1+1) consisting of two Components, one is active, and the other is ready (reserve) called the system (stress - Strength) Cascade-back-up (stress - Strength) Cascade-back-up Cascade (1+1), As the failure of one of the components leads to the operation of the other Component.

Durability (?) and the system is subjected to a stress (u) and the Presence of the attenuation factor (K), which corrects the path of the system as it Improves the performance of the system through the stress imposed on the later Component that caused the failure of the previous problem.

In addition, two Methods used to estimate the reliability of the system Cascade (1+1) , which are the Method of greatest possibility (MLE) and the method of (Bootstrap), and then the Comparison between the two methods is based on the mean of error squares (MSE).

In this work, it can be concluded from the results of simulation experiments that the best estimation method between bootstrap (Bootstrap) and the method of greatest potential (MLE) using the comparison criterion (MSE), was the bootstrap method.