Estimation for Weibull Distribution with Type II Highly Censored Data

Due to cost and time consideration, it is difficult to observe all of the product's lifetime within a reasonable time period. Hence, censored lifetime data is usually collected in real applications. Even when accelerated life tests (ALT) are used, censoring is usually inevitable. Especially for highly reliable products nowadays, the censoring proportions are more likely greater than 0.5. Such data is called highly censored data. In such cases, it is not easy to obtain a precise estimation of reliability information that is of interest, even though the maximum likelihood (ML) method is utilized. With respect to the scenario that highly censored data occurs due to time restriction (i.e., cost is not of main concern), a remedy could be to put a great number of devices into testing. This is sometimes called quantity acceleration. The main purpose of the paper is to address this issue. For the whole censored data (including failure times and the running times of unfailed items), traditional methods (including the ML method) have been used to estimate the reliability information of interest. This paper provides an alternative approach based on the observed lifetime data. Specifically, with respect to a type II highly censored data from a Weibull distribution, we treat the failure data as the smallest extreme distribution and then model that extreme using the Peaks-over-Threshold (POT) model to estimate the lifetime quantile of interest. A comparison with the ML method is made to evaluate the effectiveness of the proposed method.