Nonparametric permutation and combination-based multivariate control charts with applications in microelectronics

In recent decades, multivariate statistical methods for monitoring and controlling of industrial processes have received increasing attention. Multivariate process control charts such as Hotelling's T2 and multivariate exponentially weighted moving average have gained acceptance as manufacturing process control tools especially for the semiconductor industry. We propose in this paper a novel multivariate nonparametric control chart based on the permutation and nonparametric combination (NPC) methodology. The proposed NPC chart is always an exact inferential procedure for every finite sample size and overcomes some limitations of traditional approaches such as the ability to include a large number of variables. Moreover, NPC chart offers several advantages because it is a robust solution with respect to the true underlying random error distribution, and it is not affected by the problem of the loss of degrees of freedom when keeping fixed the number of observations. Unlike traditional methods, when the number of informative variables increases its power monotonically increases as well (finite sample consistency property of NPC test). As confirmed by an extensive simulation study and by an application to some real case studies in the field of microelectronics, the NPC charts are certainly good alternatives with respect to the traditional multivariate control charts such as Hotelling's T2 especially in cases of asymmetric or heavy-tailed error distributions. Finally, NPC chart represents a suitable solution for monitoring a multivariate process when the number of observed process variables may be larger than the number of observations.