A distribution-free joint monitoring scheme for location and scale using individual observations

Recent advances in data acquisition and storage technologies have permitted the rapid collection of data over time at a relatively low cost. The implication of these advances to modern quality engineering is that many of today’s processes produce samples of individual observations that are grossly non-normal and, potentially, very highly autocorrelated. Consequently, the typical assumptions required by traditional control charting strategies for individual observations are not likely to be met by today’s more modern processes. This presents a significant challenge for today’s quality engineer practitioner, particularly when the false alarm rate of the monitoring strategy should be adequately controlled. In this effort, we propose a new joint monitoring scheme for location and scale using individual observations that relaxes some of the assumptions that limit the use of traditional control charts in today’s practice. In addition, the proposed method is extremely practitioner-friendly and easy to implement. We compare performances of our new scheme to the commonly-used individuals and moving range control charts. Results suggest the proposed scheme provides an effective and robust means to jointly monitor the kind of processes most prevalent in today’s modern industry. We demonstrate our method using open source data available from a selective laser melting (SLM) process, where the detection of hot spots at a given location on a manufactured part was of interest.