A Decay Rate for Steady Guaranteed In‐Control Performance in Statistical Process Control Models With Cautious Parameter Learning

Abstract

Control charts with parameter estimates from small Phase I samples are at risk of providing inaccurate signals due to poor model fit. In turn, Guaranteed In‐Control Performance (GICP) approaches were introduced to account for the resulting variability in the conditional average run length. Combined GICP and Cautious Learning (GICP/CL) procedures were then proposed to mitigate the loss in sensitivity associated with GICP approaches. However, the performance of GICP/CL approaches is hitherto not fully explored. Previous research suggests that the convergence rate of the standard error, that is commonly used to adapt the control limits in GICP/CL frameworks, results in an unwanted gradual loss of detection power. This study explores the issue and shows that, when using the convergence rate of the standard error to adapt control limits, control charts calibrated for GICP have their sensitivity gradually decreased due to high variability in IC performance. Causes of high variability in the IC performance are small Phase I samples and low parameter updating frequencies. An alternative control limit adaption rate for steady GICP performance is proposed and recommendations for practical application are put forward.