A NOVEL MEANS OF ESTIMATING QUANTILES FOR 2-PARAMETER WEIBULL DISTRIBUTION UNDER THE RIGHT RANDOM CENSORING MODEL

Kuo-Ching Chiou (Taiwan) and Lee-Ing Tong (Taiwan)

Abstract

Censoring models are frequently used in reliability analysis to reduce experimental time. Three types of censoring models are type-I, type-II and random censoring. In this study, we focus on the right random censoring model. In this model, if the failure time exceeds its associated censoring time, then the failure time becomes a censored observation. In this case, many authors (see Lawless [Statistical Models and Methods for Lifetime Data, John Wiley, New York, 1982], Lee [Statistical Methods for Survival Data Analysis, 2nd ed., Wiley, New York, 1992], Miller [Survival Analysis, John Wiley, New York, 1981], among others) considered using the observed censoring time to impute the censored observation which, however, underestimates the true failure time. Herein, two methods to impute the censored observations are proposed in a right random censoring model for a 2-parameter Weibull distribution. By a Monte Carlo simulation, the quantile estimates are calculated to assess the performance of the proposed imputation methods with respect to their relative mean square error. Simulation results indicate that the two imputation methods proposed herein are superior to the available methods in [Statistical Models and Methods for Lifetime Data, John Wiley, New York, 1982, Statistical Methods for Survival Data Analysis, 2nd ed., Wiley, New York, 1992, Survival Analysis, John Wiley, New York, 1981] if the shape parameter of Weibull distribution exceeds 1, except for the lower quantiles.

Keywords and phrases: random censoring model, failure time, censoring time, imputation, quantile, relative mean square error.