Control Charts for Correlated Process Parameters

Abstract

An urgent practical task is to ensure the serviceability and safety of complex technical and information systems by monitoring their current states. Additionally, an important task is to use control charts to automatically detect the moment when certain limit states are exceeded by the characteristic features (parameters) of the technological process. In practice, it is quite common for characteristic features to be correlated. The presence of correlation affects the effectiveness of control charts in determining the moment of process disruption. The study objective is to compare the effectiveness of using different control chart types to control a correlated parameter process. The following control charts were studied: Shewhart, Hotelling, and modified Shewhart charts − principal component charts. Numerical modeling of a two-parameter process was conducted with the introduction of a non-random change in one of them at two control points, i.e., the process disorder was modeled at the appropriate time points. Subsequently, statistical studies of the modeled process were conducted using three types of control charts. The results revealed that the Shewhart charts did not reveal any process disruption, which is explained by the correlation of the parameters. Hotelling charts revealed a processing disorder at two points, but they do not indicate the cause of the disorder. The calculated partial Hotelling criterion did not indicate the cause of the disorder. The principal component charts revealed both the presence of a process disorder in two points and identified which parameter caused the disorder. This result demonstrates the effectiveness of principal component charts in detecting process disorder with correlated parameters, as well as their superiority over other charts that were studied. In addition, with an increase in the number of parameters, this method becomes even more effective, as it allows to reduce the number of parameters studied while maintaining their statistical significance. Keywords: effectiveness of control charts, Shewhart charts, Hotelling charts, principal components, statistical quality control, correlation of parameters.