Designs of Bayesian EWMA Variability Control Charts in the Presence of Measurement Error

Statistical process control may lead to false detection results in the presence of measurement error, so it is necessary to deal with the effect of measurement error. The Bayesian exponentially weighted moving average (EWMA) variability control chart, first proposed by Lin et al., is a distribution-free control chart, and it can effectively monitor process variance even if the process skewness varies with time. This paper investigates the influence of measurement error on the Bayesian EWMA variability control chart, and it proposes two designs for the Bayesian EWMA variability control chart in the presence of measurement error. One is to modify the control limits based on the biased error-prone monitoring statistics, called the error-embedded control chart. The other is to design the control limits based on the error-corrected monitoring statistics, called the error-corrected control chart. Simulation results prove that both of the proposed control charts are reliable and have good detection performance in the presence of measurement error. Moreover, the average run lengths of the proposed control charts are exactly the same, indicating that both of them are equivalent control charts. Comparison results show that the existing control chart in Lin et al. is not in-control robust and fails to detect a downward shift in process variance when measurement error is present. Thus, using the error-embedded control chart or the error-corrected control chart to monitor processes with measurement errors is reliable and effective. Moreover, the proposed control charts, where π11 = 1 and π10 = 0, can be applied to monitor processes without measurement errors since their detection performance is equal to that of the existing control chart in Lin et al. Finally, we demonstrate the application of the error-embedded control chart and the error-corrected control chart to analyze the data from the service time system of a bank branch and the data from a semiconductor manufacturing process, showing that the proposed control charts can indeed be applied to data with measurement errors.