이상치에 대한 와이블 분포의 로버스트 추정법 개발

Abstract

Purpose: This study investigates the development of novel robust estimation techniques for the Weibull distribution model with contaminated data. Therefore, we propose the application of simple but robust estimators and furthermore, compare our methods with existing methods so as to evaluate performance.BRMethods: We define five simple but robust estimators namely – the ‘e’ estimator with percentile; the ‘W.med’ estimator with weighted median; the ‘med1’ estimator which estimates the slope of the Weibull plot using the Hodges-Lehmann-type approach; and finally, the ‘med2’ and ‘med3’ estimators which use median and slope linear regression. Furthermore, using Monte Carlo simulations, we show that our proposed estimators are inlier-resistant as well as outlier-resistant under contamination.BRResults: We evaluated the performance of our proposed methods using the generalized mean square error and relative efficiency parameters. The results reveal that when data is contaminated, our methods outperform other existing methods.BRConclusion: The Hodges-Lehmann-type ‘med1’ approach is preferred when there is mild data contamination. Otherwise, we recommend adopting the median-type ‘med3’ approach in the situation of serious data contamination. More so, real applications (Weibull analysis, t chart) are also illustrated.