Comparison of the Least Squares Method with the Weighted Least Squares Method in estimating the reliability function of the Half-normal distribution with a practical application

Abstract

The main objective in this research is to choose the best method for estimating the reliability function of the half-normal distribution as a failure model for two methods, the first is the Least Square Method (LS) and the second is the Least Square Weighted Method. The simulation method (Monte-Carlo) was used to compare the two methods and samples of different sizes n = 20, 50, 75, 250 were tested. The good conformity of the data representing the failure times of some of the machines of the General Company for Electrical Industries was tested, and the statistical criteria of the average square error (MSE) were used. And mean squares supplementary error (IMSE), and then reach the best method between the two methods used in estimating the reliability of the half-normal distribution (HN).