No abstract

Using traditional control charts to monitor autocorrelated processes is not beneficial, because it will lead us to misleading detections in the processes. One of the methods used to deal with the control charts for autocorrelated process is the model-based approach. It uses an adequate time series model that fits the process and uses the residuals as monitoring statistics. For the said purpose, it is important to pick a suitable model that can adequately be used for different designs of control charts under specific time series model. This study intends to do the same for three popular types of charts namely Shewhart, exponentially weighted moving average, and cumulative sum. The models covered in this study include AR(1), MA (1), and ARMA(1,1) as the potential models to fit the process of interest. We have focused on two performance aspects namely efficiency and robustness. Average run length is used as a performance measure for different in-control and outof-control states of the autocorrelated processes under varying levels of autocorrelation. An application example based on a real data set is also included in the study to highlight the importance of the study proposals.

When using control charts to monitor manufacturing processes, the exponentially weighted moving average (EWMA) control chart is useful for detecting persistent shifts in the process parameter. This paper proposes enhancements to the applications of the EWMA control chart for those scenarios where the exact measurement of process units is difficult and expensive, but the visual ordering of the units can be done easily. The proposed charts use an auxiliary variable that is correlated with the process variable to provide efficient monitoring of shifts in the process mean and are formulated based on ranked set sampling (RSS) and median RSS schemes (MRSS). Simulation results showed that the proposed charting schemes are more efficient in detecting a shift in the process mean than the classical EWMA control chart and its modification. An example is provided to show the application of the proposed charts using a simulated benchmark process: the continuous stirred tank reactor (CSTR).

Control charts are mainly carried out in 2 interconnected phases: Phase I (retrospective phase) and Phase II (monitoring phase). Phase I uses a stable historical sample to establish control limits that will be used later in Phase II. The preciseness of the control limits obtained from Phase I can greatly affect the performance of control charts in Phase II. Monitoring the coefficient of variation (CV) is an effective approach when the process mean or standard deviation is not constant. Until now, little work has been dedicated on investigating the performance of CV control charts in Phase I. Viewed under this perspective, this study investigates the performance of CV control charts in Phase I in terms of probability to signal. A real‐life example is also provided to illustrate the working of CV charts in Phase I.