Robust Synthetic Control Charting

Abstract

The proposal of synthetic charting is based on the normality assumption. This assumption, however, is hard to attain in practice. Therefore, it is important to examine how the chart would response under some types of non-normal data. The focus of this article is to monitor location shifts using a synthetic chart and to validate its performance under the g-and-h distributions. This study shows that the effect of non-normality on the standard synthetic chart is not trivial, especially when the underlying distributions are heavy-tailed. With these types of distribution, Phase II monitoring of location using median-based estimators is advisable. In doing so, the synthetic chart is more robust to departure in the normality assumption with little effect on its out-of-control performance. This paper shows how the synthetic parameters should be attained to reflect the use of the modified one-step M-estimator (MOM) in its Winsorized version, and the median for Phase II. The assessment is based on the average run length and supported by the extra quadratic loss function. Finally, the practical application of the proposed synthetic charts is illustrated using real data.