Adaptive Process Monitoring Using Covariate Information

Statistical process control (SPC) charts provide a powerful tool for monitoring production lines in manufacturing industries. They are also used widely in other applications, such as sequential monitoring of internet traffic flows, disease incidences, health care systems, and more. In practice, quality/performance variables are often affected in a complex way by many covariates, such as material, labor, weather conditions, social/economic conditions, and so forth. Among all these covariates, some could be observed, some might be difficult to observe, and the others might even be difficult for us to notice their existence. Intuitively, an SPC chart could be improved by using helpful information in covariates. However, because of the complex relationship between the quality/performance variables and the covariates, shifts in the quality/performance variables could be due to certain covariates whose data cannot be collected. On the other hand, shifts in some observable covariates may not necessarily cause shifts in the quality/performance variables. Thus, it is challenging to properly use covariate information for process monitoring in a general setting. This article suggests a method to handle this problem. An effective exponentially weighted moving average chart is developed, in which its weighting parameter is chosen large if the related covariates included in the collected data tend to have a shift and small otherwise. Because the covariate information is used in the weighting parameter only, the chart is designed solely for detecting shifts in the quality/performance variables, but it can react to a future shift in the quality/performance variables quickly because the helpful covariate information has been used in its observation weighting mechanism. Extensive numerical studies show that this method is effective in many different cases.