Robust and Nonparametric Estimation of the Pareto Reliability Function

Abstract

The research addresses the topic of reliability, which is defined as the probability of any component of a system being completed within a specified period of time and under the same conditions. The reliability function and failure function of the Pareto distribution were studied. Several methods exist for estimating the reliability function, but the conditions for most of these methods are often missing in the data, such as abnormal, extreme, or unacceptable values. Two estimation methods (a robust method and a nonparametric method) were used: the MM-estimate and the nonparametric kernel estimation. After these two estimation formulas were derived to reach their capacity, a comparison was made between these estimates using simulation experiments with different sample sizes (10, 30 and 60). Each experiment was repeated 1,000 times to achieve the objective, and the results were compared using the mean square error (MSE) criterion. Through the results obtained, it was found that the best estimation method is the (MM-estimate) method, where it was estimated that the reliability function gradually decreases with time, which is consistent with the characteristics of this function.