Parameter estimation for Weibull distribution with right censored data using EM algorithm

The estimation process is supported by a number of statistical techniques, methods and procedures for analyzing the data on the variable of interest that may be the time that elapses from the welldefined initial instant, for example, installation of equipment, until the occurrence of a specific event, such as the failure of the equipment or component under consideration. The process aims to estimate the distribution parameters for modeling the system under review. The parameters are the distribution characteristics that show the behavior of a given population and therefore fixed for a specific system. Thus, the estimation of system parameters is obtained from the data collected from the population. System data analysis can be obtained from various possible sources, namely, laboratory tests or a recording of occurrences along its use (historical record). The parametric analysis assumes that the data fits a specific distribution, such as the Weibull distribution. The Weibull distribution has a wide application in various fields. These applications include its use to model the distribution phenomena of fatigue and the life of many devices, such as bearings, shaft and motor [1, 14, 20]. The popularity of the distribution of Weibull due to its great flexibility, i.e., as it can describe functions with failure intensity constant, increasing and decreasing, for different values of the shape parameter. Since the distribution of Weibull became widely recognized, various methods have been proposed to estimate its parameters [2,17,19]. However, the maximum-likelihood estimation method is currently one of the most used methods of estimation, for its versatility and provides reliable results [10]. The maximum-likelihood estimation method allows us to estimate the unknown parameters of a statistical model. These parameters are obtained by maximizing the likelihood function of the model in question [4].