There are many applications of control charts in health-care monitoring and in public-health surveillance. We introduce these applications to industrial practitioners and discuss some of the ideas that arise that may be applicable in industrial monitoring. The advantages and disadvantages of the charting methods proposed in the health-care and public-health areas are considered. Some additional contributions in the industrial statistical process control literature relevant to this area are given. There are many application and research opportunities available in the use of control charts for health-related monitoring.

Control charts are powerful tools used to monitor the quality of processes. In practice, control chart limits are often calculated using parameter estimates from an in-control Phase I reference sample. In Phase II of the monitoring scheme, statistics based on new samples are compared with the estimated control limits to monitor for departures from the in-control state. Many studies that evaluate control chart performance in Phase II rely on the assumption that the in-control parameters are known. Although the additional variability introduced into the monitoring scheme through parameter estimation is known to affect the chart performance, many studies do not consider the effect of estimation on the performance of the chart. This paper contains a review of the literature that explicitly considers the effect of parameter estimation on control chart properties. Some recommendations are made and future research ideas in this area are provided.

In most statistical process control (SPC) applications, it is assumed that the quality of a process or product can be adequately represented by the distribution of a univariate quality characteristic or by the general multivariate distribution of a vector consisting of several correlated quality characteristics. In many practical situations, however, the quality of a process or product is better characterized and summarized by a relationship between a response variable and one or more explanatory variables. Thus, at each sampling stage, one observes a collection of data points that can be represented by a curve (or profile). In some calibration applications, the profile can be represented adequately by a simple straight-line model, while in other applications, more complicated models are needed. In this expository paper, we discuss some of the general issues involved in using control charts to monitor such process- and product-quality profiles and review the SPC literature on the topic. We relate this application to functional data analysis and review applications involving linear profiles, nonlinear profiles, and the use of splines and wavelets. We strongly encourage research in profile monitoring and provide some research ideas.

We propose control chart methods for process monitoring when the quality of a process or product is characterized by a linear function. In the historical analysis of Phase I data, we recommend methods including the use of a bivariate T² chart to check for stability of the regression coefficients in conjunction with a univariate Shewhart chart to check for stability of the variation about the regression line. We recommend the use of three univariate control charts in Phase II. These three charts are used to monitor the ????-intercept, the slope, and the variance of the deviations about the regression line, respectively. A simulation study shows that this type of Phase II method can detect sustained shifts in the parameters better than competing methods in terms of average run length performance. We also relate the monitoring of linear profiles to the control charting of regression-adjusted variables and other methods.

Statistical process control (SPC) methods are widely used to monitor and improve manufacturing processes and service operations. Disputes over the theory and application of these methods are frequent and often very intense. Some of the controversies and issues discussed are the relationship between hypothesis testing and control charting, the role of theory and the modeling of control chart performance, the relative merits of competing methods, the relevance of research on SPC and even the relevance of SPC itself. One purpose of the paper is to offer a resolution of some of these disagreements in order to improve the communication between practitioners and researchers.

The purpose of this paper is to provide an overview and our perspective of recent research and applications of statistical process monitoring. The focus is on work done over the past decade or so. We review briefly a number of important areas, including health-related monitoring, spatiotemporal surveillance, profile monitoring, use of autocorrelated data, the effect of estimation error, and high-dimensional monitoring, among others. We briefly discuss the choice of performance metrics. We provide references and offer some directions for further research.