Determination of parameters of the Weibull distribution by applying the method of least squares

Abstract

Weibull distribution is one of the most frequently used theoretical models for approximation of empirical distributions of random variables with continuous variation. Procedures for graphical, grapho-analytical and analytical determination of Weibull distribution parameters are described in detail in this paper. Based on the graphical method for determining the position parameters of three-parameter Weibull distribution, the analytical procedure is developed, which is based on the application of the method of least squares. The set of points is approximating with the square parabola, and based on the sign of the second derivative, the information for further proceedings is obtained. For the defined procedure, an algorithm of the computer program for determination of the Weibull distribution parameters is presented in paper. By using the program, based on data from the exploitation related to the operation time until failure, the reliability modelling of wheel’s drum in braking system of light commercial vehicles was performed. The graphical and non-parametric tests were used to test the theoretical model of distribution.