Weibull Estimates in Reliability: An Order Statistics Approach

摘要

The Exponential and Weibull distributions are well-known failure time distributions in reliability theory and survival analysis. Order statistics occur naturally in life testing and in survival analysis. The properties of order statistics and the results of order statistics are used to estimate the three-parameter Weibull distributions. This study ranges from order statistics to distribution theory and then to survival analysis. To know the survival distribution function S(t), many distributional forms have been used. Moments of order statistics help us to estimate the one-parameter and two-parameter forms, but to estimate the three-parameter Weibull distribution is a challenging one. Hence we make this study as a twofold study: firstly, to study the order statistics for Weibull distributions and their moments, and secondly, apply the computed moments of order statistics to estimate the location and scale parameters (with the shape parameter being fixed) based on complete as well as type II right-censored samples. To achieve the goal, data have been simulated for the failure time and their moments estimated based on the order statistics, and we explained how the conventional estimators play their role in reliability in order to verify the accuracy of the numerical computations.