Efficiency Evaluation of Weibull Distribution Parameter Estimators for Failure Data: A Comparative Study Using Simulation Experiments
DOI:
https://doi.org/10.17977/um067v6i62026p5Keywords:
Failure Times, Weibull Distribution, Maximum Likelihood Estimation Method, Shape Parameter, Scale Parameter, Method of Moments, Reliability Function, Least Squares MethodAbstract
The purpose of this study is to assess the efficiency of parameter estimation methods of Weibull distribution for the analysis of failure data and reliability data. This is done by comparing three approaches for estimation: Maximum Likelihood Estimation (MLE), Method of Moments (MoM) and Least Squares Method (LSM). The significance of this study lies in the fact that the Weibull distribution is widely used to model failure times because of its high flexibility and it can be used to model many failure rate patterns.
The method that is used as a simulation method is carried out by applying software called Stata 17 with the programming language Mata. The two-parameter Weibull distribution was used to generate data and had different values for the shape parameter (β) and sample sizes. The performance of the estimation methods was then assessed with the help of two statistical criteria: Mean Squared Error (MSE) and Bias.
The results indicate that the Mean Squared Error (MSE) and the Bias values of the Maximum Likelihood Estimation (MLE) method were smaller than the other methods in most of the cases. This means that it has a high efficiency for estimating the parameters of the Weibull distribution, especially with larger sample sizes. The results also showed that the Least Squares Method was good and close to the Maximum Likelihood Estimation method so that it can be used as an alternative method in some practical situations. The Method of Moments was found to be the least efficient method, particularly for high values of the shape parameter or for small sample sizes.
This study concludes that the choice of estimation method is mainly dependent on the sample size and failure data. It also suggests that in practical applications of reliability analysis and survival data the Maximum Likelihood Estimation method should be adopted as a standard method.
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