Lindley Approximate Bayes Estimation of Reliability Function in Weibull Model with Precautionary Loss

Abstract

The two parameter Weibull distribution is a continuous distribution widely used in the study of reliability and life data. In this paper, we focus on different estimation approaches of two-parameter Weibull distribution based censored samples of lifetime data with type II censoring including, maximum likelihood (ML) and Bayesian estimation methodology of its Reliability Function. The ML estimation of the parameters and reliability function of Two parameter Weibull distribution is provided using the Newton–Raphson (NR) iterative method. The Bayesian estimates are provided via Lindley approximation. In the Bayesian estimation approach, for the shape and scale parameters, the Gamma prior is considered with Precautionary Loss Function. Finally, a simulated data set is analyzed for illustrative purposes to show the applicability of the proposed estimation methods. The performances of the ML and Bayesian estimates of reliability function are compared based mean squared errors (MSE) criteria.