Methods for Estimating Parameters of Weibull Distribution

• Activity Number: 291
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Quality and Productivity Section
• Author(s): Nasser Fard*+ and Xuan Haung
• Companies: Northeastern University and Northeastern University
• Keywords: Weibull distribution ; parameter estimation ; accuracy ; simulation

Abstract

Due to the versatility of the Weibull distribution; this distribution is widely used in life/survival data analysis. The Weibull parameters can be estimated by either a graphical method or analytically, such as: the least squares method, the maximum likelihood method, or the method of moment. There are also other methods, such as, probability weighted moments, simple method of estimation, and the Monte Carlo simulation. Analytical methods usually involve a complicated calculation and accuracy of estimation depends on a specific application, type and size of data. Several factors, such as, the speed of data processing, the calculation complexity, and accuracy of results must be considered, prior to choosing a method for analyzing a given set of data and estimating the parameters of the Weibull distribution. Five distinct analytical methods are studied to determine the parameter estimation accuracy of these methods for various sample size and parameters. Total deviation and mean square error, are used as measurement tools, for the estimation accuracy. A simulation model is developed to estimate the Weibull parameters and to test the accuracy of the estimated parameters.