Robust Monitoring of Contaminated Multivariate Data

Monitoring a process that suffers from data contamination using a traditional multivariate T2 chart can lead to an excessive number of false alarms. A diagnostic statistic can be used to distinguish between real control chart signals due to assignable causes and signals due to contamination from a single outlier. In phase II analysis, a traditional T2 control chart augmented by a diagnostic statistic improves the work stoppage rates for multivariate processes suffering from contaminated data and maintains the ability to detect process shifts. 1. Introduction Davis and Adams [1] consider the problem of dealing with contaminated data in univariate control charts. They consider monitoring a process for which measurement systems are problematic or unreliable, leading to occasional unusual measurements for key quality characteristics. These atypical measurements do not reflect the true state of the process and are referred to as outliers. A sample containing an outlier is said to be contaminated. Contaminated data can be troublesome for practitioners monitoring a process because a control chart signal could indicate a true process shift or could simply be the result of an outlier. Thus, Davis and Adams distinguish two types of signals: signals that indicate a process problem and signals that reflect a data problem. They propose use of a diagnostic statistic that allows the practitioner to distinguish between the two types of signals. When the control chart signals, a diagnostic statistic is calculated for that sample. If the value of the diagnostic statistic exceeds a threshold, then the signal could have been caused by contaminated data and further investigation is warranted before stopping the process. If the value of the diagnostic statistic does not exceed the threshold, then the signal is interpreted as a process problem and appropriate action is recommended. The benefit of such a scheme is clear-occurrence of unwarranted work stoppage is reduced and detrimental process adjustments are avoided. Davis and Adams restrict their analysis to the univariate case, but it is likely that many processes suffering from contamination issues are not characterized by a single quality characteristic, but by several correlated quality characteristics. A common tool for monitoring several quality characteristics simultaneously is the Hotelling T2 control chart. If the T2 chart is used to monitor a process that is known to occasionally generate contaminated samples and the chart signals, the analyst must determine if the process is out of control or if a contaminated