A simulation approach to multivariate quality control

The use of Multivariate Quality Control techniques is usually avoided by practitioners because of the complexity involved in the design, implementation, and maintenance of the control system. In this paper a new approach to multivariate control problems is proposed, the Simulated Minimax control chart. The new control chart consists of placing upper and lower control limits on the maximum and the minimum of the p correlated variables standardized sample means such that the chart has a fixed probability of Type I error. The position of the control limits is determined by simulating the samples taken from a multivariate normal population. A comparison of the performance of the Simulated Minimax control chart and the Chi-squared control chart in terms of the average run length (ARL) is provided for two scenarios (n=5, p=2, ϱ=0 and n=5, p=2, ϱ=0.5) under different shifts in the mean. The results show that the Simulated Minimax control chart has excellent ARL properties as compared to the Chi-squared control chart. Thus, the Simulated Minimax control chart provides practitioners the advantage of interpreting the signals right from the chart, plus the simplicity of its use, and an excellent ARL performance.