Title: Estimating parameters of the three-parameter Weibull distribution using a neural network

Authors: Babak Abbasi, Luis Rabelo, Mehdi Hosseinkouchack

Addresses: Department of Industrial Engineering, Sharif University of Technology, P.O. Box 11365–9414, Tehran, Iran. ' Department of Industrial Engineering and Management Systems, University of Central Florida, Orlando, Florida 32750, USA. ' Department of Business and Economics, Johann Wolfgang Goethe University, P.O. Box 055, Frankfurt am Main, Germany

Abstract: Weibull distributions play an important role in reliability studies and have many applications in engineering. It normally appears in the statistical scripts as having two parameters, making it easy to estimate its parameters. However, once you go beyond the two parameter distribution, things become complicated. For example, estimating the parameters of a three-parameter Weibull distribution has historically been a complicated and sometimes contentious line of research since classical estimation procedures such as Maximum Likelihood Estimation (MLE) have become almost too complicated to implement. In this paper, we will discuss an approach that takes advantage of Artificial Neural Networks (ANN), which allow us to propose a simple neural network that simultaneously estimates the three parameters. The ANN neural network exploits the concept of the moment method to estimate Weibull parameters using mean, standard deviation, median, skewness and kurtosis. To demonstrate the power of the proposed ANN-based method we conduct an extensive simulation study and compare the results of the proposed method with an MLE and two moment-based methods. [Submitted 23 September 2007; Revised 11 December 2007; Second revision 22 December 2007; Accepted 10 January 2008]

Keywords: three-parameter Weibull distribution; artificial neural networks; ANNs; moment method; parameter estimation; maximum likelihood estimation; MLE; simulation.

DOI: 10.1504/EJIE.2008.018438

European Journal of Industrial Engineering, 2008 Vol.2 No.4, pp.428 - 445

Available online: 22 May 2008

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