Run-length performance of regression control charts with estimated parameters

The regression control chart is an effective statistical process control (SPC) tool in situations where the output characteristic of interest is affected by an external covariate. It has many applications, including monitoring and diagnosing multistage processes. Its basic purpose is to remove the influence of the covariate using regression adjustment and then apply a regular control scheme to the regression residual. In practice, the regression model relating the output and the covariate is rarely known and needs to be estimated. Little is known about the performance of the regression control chart when the true parameters are replaced with their estimates. In this paper, the run length performance of regression control charts with estimated parameters is studied. Two types of regression control charts are considered: a Shewhart control for regression residuals, and an exponentially weighted moving average (EWMA) control for regression residuals.