The two-parameter Weibull distribution is one of the most widely applied probability distributions, particularly in reliability and lifetime modelings. Correct estimation of the shape parameter of the Weibull distribution plays a central role in these areas of statistical analysis. Many different methods can be used to estimate this parameter, most of which utilize regression methods. In this paper, we presented various regression methods for estimating the Weibull shape parameter and an experimental study using classical regression methods to compare the results of the methods. A complete list of the parameter estimators considered in this study is as follows: ordinary least squares (OLS), weighted least squares (WLS, Bergman, F&T, Lu), non-parametric robust Theil's (Theil) and weighted Theil's (WeTheil), robust Winsorized least squares (WinLS), and M-estimators (Huber, Andrew, Tukey, Cauchy, Welsch, Hampel and Logistic). Estimator performances were compared based on bias and mean square error criteria using Monte-Carlo simulations. The simulation results demonstrated that for small, complete, and non-outlier data sets, the Bergman, F&T, and Lu estimators are more efficient than the others. When the data set contains one or two outliers in the X direction, Theil is the most efficient estimator.where b is the scale parameter and c is the shape parameter. When c = 1, the Weibull distribution reduces to the exponential distribution, and when c = 2, the Weibull distribution is Rayleigh. When c = 3.48, the distribution is close to Normal.The Weibull shape parameter (c) is very important because it determines the behavior of the failure rate of the product or system, 1 and has been used as a measure of reliability. It can be estimated from a sample using either linear regression, maximum likelihood, or the method of moments. The problem of estimating the Weibull shape parameter is not new; it has been studied for more than 30 years. However, some open issues still remain, especially for the linear regression methods. 2 Regression analysis is a simple method for investigating and modeling the functional relationship between variables. The simplest case is the so-called simple linear regression model, which contains only one independent variable and, can be written asThe WLS method was suggested based on the fact that some observation values used in regression analysis are quite different from others. This method aims to eliminate the adverse effects of contradictory values on the model by placing a different weight on each A. A. YAVUZ
