Deviance residual‐based control charts for monitoring the beta‐distributed processes

Abstract

AbstractBeta‐distributed process outputs are common in manufacturing industry because they range from 0 to 1 based on inputs like yield. Under the normality assumption, Shewarts control charts and Hotelling's control charts based on the deviance residual have been applied to monitor the process mean of the beta‐distributed process outputs. The normality assumption can be violated according to the shape of the beta distribution. Therefore, without the normality assumption, we propose antirank control charts, exponentially weighted moving average (EWMA) control charts and cumulative sum (CUSUM) control charts. The proposed control charts outperform the existing control charts in the experimental results. The previous research has been focused on monitoring the process mean only. For the first time, in order to monitor the process variance of the beta‐distributed process outputs, we propose the multivariate exponentially weighted mean squared deviation (MEWMS) chart, the first norm distance of the MEWMS deviation from its expected value (MEWMSL1) chart, the chart based on MEWMS deviation with the approximated distribution of trace (MEWMSAT), the multivariate trace sum squared deviation (MTSSD) chart and the multivariate matrix sum squared deviation (MMSSD) chart based on the deviance residual. The proposed control charts are compared and recommended in terms of the experimental results. This research can be a guideline for practitioners who monitor the deviance residual.