Likelihood Ratio-Based Distribution-Free EWMA Control Charts

Nonparametric or distribution-free charts are useful in statistical process control when there is a lack of or limited knowledge about the underlying process distribution. Most existing approaches in the literature are for monitoring location parameters. They may not be effective with a change of distribution over time in many applications. This paper develops a new distribution-free control chart based on the integration of a powerful nonparametric goodness-of-fit test and the exponentially weighted moving-average (EWMA) control scheme. Benefiting from certain desirable properties of the test and the proposed charting statistic, our proposed control chart is computationally fast, convenient to use, and efficient in detecting potential shifts in location, scale, and shape. Thus, it offers robust protection against variation in various underlying distributions. Numerical studies and a real-data example show that the proposed approaches are quite effective in industrial applications, particularly in start-up and short-run situations.