Multiple cumulative sum control charts for monitoring and diagnostics of correlated quality variables of different types with individual observations

Quality control applications in the modern era, especially for non-manufacturing processes, often involve having to monitor correlated variables of different types: continuous, count, and categorical. Most of the multivariate control charts in the existing literature implicitly assume that the correlated variables to be monitored are of the same type. Another equally challenging task in multivariate quality control that has received relatively little attention is identifying parameters that are actually out of control when an out-of-control signal is detected on a control chart. In this study, we propose utilizing multiple testing procedures to develop cumulative sum (CUSUM) charts for monitoring and diagnostics of correlated quality variables of different types for individual observations. The developed multiple testing procedure-based CUSUM (MTCUSUM) chart is shown to have similar overall performance with the multiple testing procedure-based exponentially weighted moving average (MTEWMA) chart in terms of detecting out-of-control processes. On the other hand, in terms of diagnostic capability, the proposed MTCUSUM charts have better overall performance. An example is used to demonstrate how the proposed charts can be applied in applications.