Joint monitoring of location and scale for modern univariate processes

Autocorrelated sequences of individual observations arise in many modern-day statistical process monitoring (SPM) applications. Often times, interest involves jointly monitoring both process location and scale. To jointly monitor autocorrelated individuals data, it is common to first fit a time series model to the in-control process and subsequently use this model to de-correlate the observations so that traditional individuals and moving-range (I-MR) charts can be applied. If the time series model is correctly specified such that the resulting residuals are normal and independently distributed, then applying I-MR control charts to the residual process should work well. However, if the residual process deviates from normality and/or, due to time series model misspecification, contains levels of autocorrelation, the false alarm rate of such a strategy can dramatically rise. In this paper we propose improvements to a recently published distribution-free joint monitoring strategy that permits tighter control of the in-control average run length when model misspecification is a concern. We evaluate its average run length performance and conclude that the improved joint monitoring strategy proposed in this work is a very useful tool for today's modern SPM practitioner. The proposed joint monitoring scheme is then applied to a real additive manufacturing process to illustrate its implementation in modern practice.