SHRINKAGE ESTIMATORS FOR CALCULATING RELIABILITY, WEIBULL CASE

摘要

The estimation of the reliability R= P(Y < X) , assuming X and Y to be independent and identically distributed random variables, has been extensively studied in the literature. Distribution functions such as Normal, Burr Type X, Exponential, Gamma, and Weibull have been considered. In this report, we consider the Weibull type of distributions. Utilizing the Maximum Likelihood Estimation (MLE), Uniformly Minimum Variance Unbiased Estimation (UMVUE), Shrinkage Estimation Procedures, Method of Moments, and other methods of estimation, using simulation, we will estimate the unknown parameters of the Weibull distribution. In particular, we will observe how well the shrinkage estimators will do compared with the MLE based on the mean squared error (MSE). Also, a comparison among the estimators found by the different methods will be done to choose the best results in calculating R. Those results will be made based on the ratio of the parameters and the sample sizes.