EWMA control charts in statistical process monitoring

In today’s world, the amount of available data is steadily increasing, and it is often of interest to detect changes in the data. Statistical process monitoring (SPM) provides tools to monitor data streams and to signal changes in the data. One of these tools is the control chart. The topic of this dissertation is a special control chart: the exponentially weighted moving average (EWMA) chart. A control chart plots the data together with two control limits. A control chart signals a (possible) change when the plotted data exceeds the control limits. A control chart performs well if it signals changes in the data quickly, without triggering frequent false alarms. Before a control chart can be set up, estimates of the process parameters are needed. To this end an initial data set is collected. In practice this data set often contains outliers, recording errors, and other data quality issues. These so-called ‘contaminations’ are problematic as they influence the parameter estimates. We investigate robust estimation methods to ensure accurate estimation of the process parameters. We propose a new estimation method based on screening and show that this new method outperforms existing estimation methods, when the type of contaminations is unknown. In the second phase of this dissertation we study the effect of estimation on the performance of the EWMA chart and give recommendations regarding its design. We show that traditionally designed charts have very variable performance. We study an alternative design procedure based conditional performance which provides control over the variability in performance

A Head-to-Head Comparative Study of Control Charts based on Estimated Parameters

Implementation of the Shewhart, CUSUM, and EWMA charts requires estimates of the in-control process parameters. Many researchers have shown that estimation error strongly influences the performance of these charts. However, a given amount of estimation error may differ in effect across charts. Therefore, we perform a pairwise comparison of the effect of estimation error across these charts. We conclude that the Shewhart chart is more strongly affected by estimation error than the CUSUM and EWMA charts. Furthermore, we show that the general belief that the CUSUM and EWMA charts have similar performance no longer holds under estimated parameters

Robust Point Location Estimators for the EWMA Control Chart

In practice, the EWMA control chart for process monitoring is based on parameters estimated from a retrospective data set representing the process characteristic under study. This data set may contain contaminated observations, which in turn can affect the estimates and hence the control chart’s performance. We study the problem of estimating the location when the data set may or may not contain contaminated observations. We compare six point estimators proposed in the SPC literature. The quality of the estimators is evaluated in terms of estimation accuracy. Moreover, we study the impact of the estimators on the performance of the EWMA control chart based on the different location estimators

A robust estimator for location in Phase I based on an EWMA chart

In practice, a control chart for process monitoring (Phase II) is based on parameters estimated from data collected on the process characteristic under study (Phase I). The Phase I data could contain unacceptable data, which in turn could affect the monitoring. This article considers various estimation methods that are potentially relevant within the parameter estimation process. The quality of the Phase I study is evaluated in terms of the precision of the resulting estimates as well as the effectiveness of the exploratory data analysis, where effectiveness is measured by the proportion of observations that are correctly identified as unacceptable. Moreover, the impact of the Phase I estimation method on the performance of the EWMA control chart in Phase II is studied