Reliability of the two-parameter exponential distribution for the serial and parallel systems Comparison of some methods of estimating a function

Abstract

 Some statistical methods have been used to estimate the shifting parameter and the scale parameter for the two-parameter exponential distribution and for the serial and parallel systems. Among these methods that were used for estimation and comparison are the Maximum likelihood (MEL) method and the Standard Bayes method. Where the comparison between these methods was done using the mean of error squares (MSE) statistical scale, and it was concluded through simulation experiments that the best way to estimate the parameters of the two-parameter exponential distribution and to estimate the reliability function and the reliability function of the sequential system and the reliability function of the parallel system is the method BES Standard (BMS).