Estimating Weibull Parameters Using Least Squares and Multilayer Perceptron vs. Bayes Estimation

Abstract

The Weibull distribution is regarded as among the finest in the family of failure distributions. One of the most commonly used parameters of the Weibull distribution (WD) is the ordinary least squares (OLS) technique, which is useful in reliability and lifetime modeling. In this study, we propose an approach based on the ordinary least squares and the multilayer perceptron (MLP) neural network called the OLSMLP that is based on the resilience of the OLS method. The MLP solves the problem of heteroscedasticity that distorts the estimation of the parameters of the WD due to the presence of outliers, and eases the difficulty of determining weights in case of the weighted least square (WLS). Another method is proposed by incorporating a weight into the general entropy (GE) loss function to estimate the parameters of the WD to obtain a modified loss function (WGE). Furthermore, a Monte Carlo simulation is performed to examine the performance of the proposed OLSMLP method in comparison with approximate Bayesian estimation (BLWGE) by using a weighted GE loss function. The results of the simulation showed that the two proposed methods produced good estimates even for small sample sizes. In addition, the techniques proposed here are typically the preferred options when estimating parameters compared with other available methods, in terms of the mean squared error and requirements related to time.