Novel robust [formula omitted] and [formula omitted] charts using the generalized Kullback–Leibler divergence

Abstract

It is well known that the performance of g and h control charts heavily depends on how accurate the estimation of an unknown process parameter is. However, conventional methods, such as the method of moments and the maximum likelihood method, are easily influenced by data contamination. Thus, the performance of control charts with these estimators could deteriorate significantly when Phase-I data are contaminated by outliers. To overcome this issue, two robust methods using trimming and truncation were recently developed, whereas these methods suffer from loss of data information and lack of efficiency due to the data trimming and truncation for achieving robustness property. In this paper, we avoid the pitfall of existing methods using the asymptotically fully efficient statistical minimum distance method. We develop novel robust g and h control charts based on the generalized Kullback–Leibler divergence. Numerical results show that in terms of the average run length and the relative efficiency, the proposed method outperforms several existing ones, especially when the data contain outliers.