Design of control charts for statistical process monitoring

Statistical Process Monitoring (SPM) provides statistical tools and techniques to understand process variation. Process variation is divided into common cause and special cause variation. A process operating under common cause variation is said to be in-control, while a process operating under both common cause and special cause variation is said to be out-of-control. An in-control process is stable and can be improved, while an out-of-control process is unstable and should be brought in-control. Control charts are used to determine whether a process is in-control or out-of-control. The performance of control charts can be evaluated by the so-called average runlength (ARL). The in-control ARL is the average number of samples that must be taken before a control chart gives an out-of-control signal when the process is in-control. When process parameters are estimated, the in-control ARL is a random variable with high variability. In this context, the expected value of the in-control ARL has been used to evaluate and design Phase II control charts. However, this ignores the individual chart performance. Hence, control charts are now evaluated and designed to provide a minimum in-control ARL performance with a specified probability. In this thesis I propose better methods of evaluating the in-control ARL and deriving sample size requirements and charting constants to design control charts

A head-to-head comparison of the out-of-control performance of control charts adjusted for parameter estimation

When in-control process parameters are estimated, this can have a substantial effect on the control chart performance. In particular, it may lead to high false alarm rates for a large number of practitioners. In recent literature, control limit adjustments have been proposed for Shewhart, CUSUM and EWMA control charts in order to provide a specified in-control performance with a specified high probability. In this paper, we compare the out-of-control performance of these adjusted Shewhart, CUSUM and EWMA control charts for sustained shifts in the process mean. We find that the CUSUM control chart has faster detection of sustained shifts compared to both the EWMA and Shewhart control charts. This finding generalizes to almost all shift sizes and estimation errors considered in this paper. The performance of the EWMA is not far worse than that of the CUSUM, but the Shewhart control chart is much slower in detecting sustained shifts in the mean compared to these other two charts

An alternative design of the two-sided CUSUM chart for monitoring the mean when parameters are estimated

In recent literature on control charts, the exceedance probability criterion has been introduced to provide a minimum in-control performance with a specified probability. In this paper we evaluate the two-sided Phase II CUSUM charts and its in-control conditional average run length (CARLIN) distribution with respect to the exceedance probability criterion. Traditionally, the CARLIN distribution and its parameters has been calculated by Markov Chains and simulations. We present in this paper a generalization of the Siegmund formula to calculate the CARLIN distribution and its parameters. This closed form formula is easy and faster to apply compared to Markov Chains. Consequently, we use it to make sample size recommendations and to adjust the charting constants via the exceedance probability criterion. The adjustments are done without bootstrapping. Results show that, in order to prevent low CARLIN values, more Phase I data are required than has been recommended in the literature. Tables of the adjusted charting constants are provided to facilitate chart implementation. The adjusted constants significantly improve the in-control performance, at the marginal cost of a lower out-of-control performance. Balancing the trade-off between the in-control and out-of-control performance is illustrated with real data and tables of charting constants.</p

A head-to-head comparison of the out-of-control performance of control charts adjusted for parameter estimation

When in-control process parameters are estimated, this can have a substantial effect on the control chart performance. In particular, it may lead to high false alarm rates for a large number of practitioners. In recent literature, control limit adjustments have been proposed for Shewhart, CUSUM and EWMA control charts in order to provide a specified in-control performance with a specified high probability. In this paper, we compare the out-of-control performance of these adjusted Shewhart, CUSUM and EWMA control charts for sustained shifts in the process mean. We find that the CUSUM control chart has faster detection of sustained shifts compared to both the EWMA and Shewhart control charts. This finding generalizes to almost all shift sizes and estimation errors considered in this paper. The performance of the EWMA is not far worse than that of the CUSUM, but the Shewhart control chart is much slower in detecting sustained shifts in the mean compared to these other two charts

Guaranteed in‐control performance of the EWMA chart for monitoring the mean

Research on the performance evaluation and the design of the Phase II EWMA control chart for monitoring the mean, when parameters are estimated, have mainly focused on the marginal in-control average run-length (ARLIN). Recent research has highlighted the high variability in the in-control performance of these charts. This has led to the recommendation of studying of the conditional in-control average run-length (CARLIN) distribution. We study the performance and the design of the Phase II EWMA chart for the mean, using the CARLIN distribution and the exceedance probability criterion (EPC). The CARLIN distribution is approximated by the Markov Chain method and Monte Carlo simulations. Our results show that in-order to design charts that guarantee a specified EPC, more Phase I data are needed than previously recommended in the literature. A method for adjusting the Phase II EWMA control chart limits, to achieve a specified EPC, for the available amount of data at hand, is presented. This method does not involve bootstrapping and produces results that are about the same as some existing results. Tables and Graphs of the adjusted constants are provided. An in-control and out-of-control performance evaluation of the adjusted limits EWMA chart is presented. Results show that, for moderate to large shifts, the performance of the adjusted limits EWMA chart is quite satisfactory. For small shifts, an in-control and out-of-control performance tradeoff can be made to improve performance

Guaranteed in-control performance of the EWMA chart for monitoring the mean

Research on the performance evaluation and the design of the Phase II EWMA control chart for monitoring the mean, when parameters are estimated, have mainly focused on the marginal in-control average run-length (ARLIN). Recent research has highlighted the high variability in the in-control performance of these charts. This has led to the recommendation of studying of the conditional in-control average run-length (CARLIN) distribution. We study the performance and the design of the Phase II EWMA chart for the mean, using the CARLIN distribution and the exceedance probability criterion (EPC). The CARLIN distribution is approximated by the Markov Chain method and Monte Carlo simulations. Our results show that in-order to design charts that guarantee a specified EPC, more Phase I data are needed than previously recommended in the literature. A method for adjusting the Phase II EWMA control chart limits, to achieve a specified EPC, for the available amount of data at hand, is presented. This method does not involve bootstrapping and produces results that are about the same as some existing results. Tables and Graphs of the adjusted constants are provided. An in-control and out-of-control performance evaluation of the adjusted limits EWMA chart is presented. Results show that, for moderate to large shifts, the performance of the adjusted limits EWMA chart is quite satisfactory. For small shifts, an in-control and out-of-control performance tradeoff can be made to improve performance

Guaranteed in-control performance of the EWMA chart for monitoring the mean

Research on the performance evaluation and the design of the Phase II EWMA control chart for monitoring the mean, when parameters are estimated, have mainly focused on the marginal in-control average run-length (ARLIN). Recent research has highlighted the high variability in the in-control performance of these charts. This has led to the recommendation of studying of the conditional in-control average run-length (CARLIN) distribution. We study the performance and the design of the Phase II EWMA chart for the mean, using the CARLIN distribution and the exceedance probability criterion (EPC). The CARLIN distribution is approximated by the Markov Chain method and Monte Carlo simulations. Our results show that in-order to design charts that guarantee a specified EPC, more Phase I data are needed than previously recommended in the literature. A method for adjusting the Phase II EWMA control chart limits, to achieve a specified EPC, for the available amount of data at hand, is presented. This method does not involve bootstrapping and produces results that are about the same as some existing results. Tables and Graphs of the adjusted constants are provided. An in-control and out-of-control performance evaluation of the adjusted limits EWMA chart is presented. Results show that, for moderate to large shifts, the performance of the adjusted limits EWMA chart is quite satisfactory. For small shifts, an in-control and out-of-control performance tradeoff can be made to improve performance

A head-to-head comparison of the out-of-control performance of control charts adjusted for parameter estimation

When in-control process parameters are estimated, this can have a substantial effect on the control chart performance. In particular, it may lead to high false alarm rates for a large number of practitioners. In recent literature, control limit adjustments have been proposed for Shewhart, CUSUM and EWMA control charts in order to provide a specified in-control performance with a specified high probability. In this paper, we compare the out-of-control performance of these adjusted Shewhart, CUSUM and EWMA control charts for sustained shifts in the process mean. We find that the CUSUM control chart has faster detection of sustained shifts compared to both the EWMA and Shewhart control charts. This finding generalizes to almost all shift sizes and estimation errors considered in this paper. The performance of the EWMA is not far worse than that of the CUSUM, but the Shewhart control chart is much slower in detecting sustained shifts in the mean compared to these other two charts