Estimation of the Shape Parameter of Weibull Distribution based onType II Censored Data using EM Algorithm

Weibull distribution is a distribution that is often used in survival data analysis.The form of the Weibull distribution depends on the parameter values it has.One of the Weibull parameters is the shape parameter. The purpose of this research is to estimate the Weibull distribution form parameters using type II censored data with the Maximum Likelihood method, which ends with an iterative algorithm, the EM algorithm. The EM algorithm consists of two stages, those are Expectation and Maximization stages. In the Expectation stage, the conditional expectation of the ln likelihood function is calculated. The Maximization is the stage to maximize the conditional expectations of the ln likelihood function. In its implementation, the algorithm will be realized in a program with the help of Mathematica software.As an example illustration, an aircraft life component data case will be used.Many complete data (n) and observable data (r) are 13 and 10, respectively.Based on the calculation results, the estimated value of the form parameter (beta) is 1.60527.