%0 Journal Article
%T Statistical Analysis of a Weibull Extension with Bathtub-Shaped Failure Rate Function
%A Ronghua Wang
%A Naijun Sha
%A Beiqing Gu
%A Xiaoling Xu
%J Advances in Statistics
%D 2014
%R 10.1155/2014/304724
%X We consider the parameter inference for a two-parameter life distribution with bathtub-shaped or increasing failure rate function. We present the point and interval estimations for the parameter of interest based on type-II censored samples. Through intensive Monte-Carlo simulations, we assess the performance of the proposed estimation methods by a comparison of precision. Example applications are demonstrated for the efficiency of the methods. 1. Introduction In reliability analysis, the failure rate function plays an essential role to characterize life phenomena. The failure pattern of many products/systems (as electronic and mechanical products, etc.) can be represented by a bathtub curve. It comprises three stages: initial stage (or burn-in) with a decreasing failure rate, middle stage with an approximately constant failure rate, and final stage with an increasing failure rate. Many probability distributions have been proposed to fit real life data with bathtub-shaped failure rates (e.g., [1¨C5]). Chen [6] proposed a two-parameter lifetime distribution (written as throughout this paper) with bathtub failure rate whose distribution function is where is the shape parameter and the scale parameter. Obviously, the transformed random variable follows the standard exponential distribution Exp (1). Also note that for small , and so the distribution , to some degree, can be treated as an extension of Weibull distribution. In reliability engineering, two common censoring mechanisms are widely applied in reliability testing for product life. For type-I censoring, the test is continued until a prespecified time is reached; whereas for type-II censoring, the test is carried out until a preset number of units failed. A significant amount of literature has emerged on various testing models with both data censoring schemes. Cha [7] considered a problem of determining optimal burn-in time in a bathtub-shaped failure model under both cases of type-I and type-II. Xiong [8] made a statistical inference on a step-stress model with type-II censored exponential data. Balakrishnan et al. [9] presented the order restricted MLE for multiple step-stress models with exponential lifetime under type-I and type-II censored sampling situations. A comparison of accelerated life testing for Weibull and lognormal distributions with type-II censoring was made by meeker [10], just to name a few. Particularly, for the distribution, there were some works done for parameter inference. Chen [6] presented the exact confidence intervals for the parameters based on type-II censored samples
%U http://www.hindawi.com/journals/as/2014/304724/