We provide an overview and perspective on the Phase I collection and analysis of data for use in process improvement and control charting. In Phase I, the focus is on understanding the process variability, assessing the stability of the process, investigating process-improvement ideas, selecting an appropriate in-control model, and providing estimates of the in-control model parameters. In our article, we review and synthesize many of the important developments that pertain to the analysis of process data in Phase I. We give our view of the major issues and developments in Phase I analysis. We identify the current best practices and some opportunities for future research in this area.

When in-control process parameters are estimated, Phase II control chart performance will vary among practitioners due to the use of different Phase I data sets. The typical measure of Phase II control chart performance, the average run length (ARL), becomes a random variable due to the selection of a Phase I data set for estimation. Aspects of the ARL distribution, such as the standard deviation of the average run length (SDARL), can be used to quantify the between-practitioner variability in control chart performance. In this article, we assess the in-control performance of the exponentially weighted moving average (EWMA) control chart in terms of the SDARL and percentiles of the ARL distribution when the process parameters are estimated. Our results show that the EWMA chart requires a much larger amount of Phase I data than previously recommended in the literature in order to sufficiently reduce the variation in the chart performance. We show that larger values of the EWMA smoothing constant result in higher levels of variability in the in-control ARL distribution; thus, more Phase I data are required for charts with larger smoothing constants. Because it could be extremely difficult to lower the variation in the in-control ARL values sufficiently due to practical limitations on the amount of the Phase I data, we recommend an alternative design criterion and a procedure based on the bootstrap approach.

The increasing availability of high-volume, high-velocity data sets, often containing variables of different data types, brings an increasing need for monitoring tools that are designed to handle these big data sets. While the research on multivariate statistical process monitoring tools is vast, the application of these tools for big data sets has received less attention. In this expository paper, we give an overview of the current state of data-driven multivariate statistical process monitoring methodology. We highlight some of the main directions involving statistical learning and dimension reduction techniques applied to control charts in research from supply chain, engineering, computer science, and statistics. The goal of this paper is to bring into better focus some of the monitoring and surveillance methodology informed by data mining techniques that show promise for monitoring large and diverse data sets. We introduce an example using Wikipedia search information and illustrate a few of the complexities of applying the available methods to a high-dimensional monitoring scenario. Throughout, we offer advice to practitioners and some suggestions for future research in this emerging area of research.

The goal of this case study is to answer four research questions related to fatigue through features derived from wearable sensors to measure patterns in steps: (1) How do important gait parameters change over time? (2) How do these sensor-based changes relate to the participant's subjective fatigue ratings over time? (3) Are there consistent patterns in performance across different individuals over time? and (4) Do these patterns vary systematically based on specific demographic characteristics? To answer these questions, we have combined multivariate changepoint methods with hierarchical time-series clustering and exploratory data analysis. The results improve our understanding of fatigue development.