Abstract
The two-parameter Weibull distribution is the predominant distribution in reliability and lifetime data analysis. The classical approach for estimating the scale (alpha ) and shape (beta ) parameters employs the maximum likelihood estimation (MLE) method. However, most MLE based-methods resort to numerical or graphical techniques due to the lack of closed-form expressions for the Weibull beta parameter. A Weibull beta parameter estimator based on perturbation theory is proposed in this work. An explicit expression for beta is obtained, making the estimation of both parameters straightforward. Several right-censored lifetime data sets with different sample sizes and censoring percentages were analyzed in order to assess the performance of the proposed estimator. Study case results show that our parameter estimator provides solutions of high accuracy, overpassing limitations of other parameter estimators.
Highlights
The two-parameter Weibull distribution is widely used in reliability engineering and lifetime data analysis because of its flexibility to properly model increasing and decreasing failure rates
Traditional parameter estimation methods call on probability plotting, least squares and maximum likelihood estimation (Lawless 1982)
One of the main findings of this work is that estimation of parameters is better performed using maximum likelihood estimation (MLE) and L-Moments Method (LM) estimators
Summary
The two-parameter Weibull distribution is widely used in reliability engineering and lifetime data analysis because of its flexibility to properly model increasing and decreasing failure rates It has gained the interest of researchers who have worked on its various aspects, such as inference, application and parameter estimation (see Nelson 1982; Cohen 1991; Johnson et al 1994; Meeker and Escobar 1998). Joarder et al (2011) consider statistical inferences of the unknown parameters of the Weibull distribution with rightcensored data samples, stating that the MLE cannot lead to explicit forms of the Weibull distribution They propose approximate maximum likelihood estimators (AMLE), which are obtained by expanding the MLE equations in Taylor series. MLE and Bayes estimators are applied to calculate the survival function and the failure rate of the Weibull distribution for censored data in Guure and Ibrahim (2012). These equations are explicitly solved one by one in order to obtain an increasingly accurate approximation to the true solution
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