On‐line Identification and Quantification of Mean Shifts in Bivariate Processes using a Neural Network‐based Approach

Many statistical process control (SPC) problems are multivariate in nature because the quality of a given process or product is determined by several interrelated variables. Various multivariate control charts (e.g. Hotelling's T² , multivariate cumulative sum and multivariate exponentially weighted moving average charts) have been designed for detecting mean shifts. However, the main shortcoming of such charts is that they can detect an unusual event but do not directly provide the information required by a practitioner to determine which variable or group of variables has caused the out‐of‐control signal. In addition, these charts cannot provide more detailed shift information, for example the shift magnitude, which would be very useful for quality practitioners to search the assignable causes that give rise to the out‐of‐control situation. This work proposes a neural network‐based model that can identify and quantify the mean shifts in bivariate processes on‐line. The performance evaluation performed by the simulation demonstrates that the proposed model outperforms the conventional multivariate control schemes in terms of average run length, and can accurately estimate the magnitude of the shift of each of the shifted variables in a real‐time mode. Extensive simulation is also carried out to examine the effects of correlation on the performance of the proposed model. A numerical example is presented to illustrate the usage of the proposed model. Although a mean shift identification and quantification tool for bivariate SPC is the particular application presented here, the proposed neural network‐based methodology can be applied to multivariate SPC in general.