Detecting the process changes for multivariate nonlinear profile data

Abstract

In profile monitoring for a multivariate manufacturing process, the functional relationship of the multivariate profiles rarely occurs in linear form, and the real data usually do not follow a multivariate normal distribution. Thus, in this paper, the functional relationship of multivariate nonlinear profile data is described via a nonparametric regression model. We first fit the multivariate nonlinear profile data and obtain the reference profiles through support vector regression (SVR) model. The differences between the observed multivariate nonlinear profiles and the reference profiles are used to calculate the vector of metrics. Then, a nonparametric revised spatial rank exponential weighted moving average (RSREWMA) control chart is proposed in the phase II monitoring. Moreover, a simulation study is conducted to evaluate the detecting performance of our proposed nonparametric RSREWMA control chart under various process shifts using out-of-control average run length (ARL 1 ). The simulation results indicate that the SREWMA control chart coupled with the metric of mean absolute deviation (MAD) can be used to monitor the multivariate nonlinear profile data when a common fixed design (CFD) is not applicable in the phase II study. Finally, a realistic multivariate nonlinear profile example is used to demonstrate the usefulness of our proposed RSREWMA control chart and its monitoring schemes. KEYWORDS common fixed design (CFD), mean absolute deviation (MAD), multivariate nonlinear profile data, spatial rank exponential weighted moving average (SREWMA) control chart, support vector regression (SVR)

Kernel principal component analysis (PCA) control chart for monitoring mixed non-linear variable and attribute quality characteristics

“… Fan et al (2014) proposed a control chart based on filtering kernel independent component analysis–principal component analysis (FKICA–PCA) to monitor multivariate industrial processes. The nonparametric Revised Spatial Rank Exponential Weighted Moving Average (RSREWMA) control chart is developed to assess the multivariate nonlinear profile data ( Pan et al, 2019 ). Kernel PCA can be applied in monitoring such cases mentioned above by using the control chart approach.…”

Model robust profile monitoring for the generalized linear mixed model for Phase I analysis

“…Noorossana et al, 17 Eyvazian et al, 18 Soleimani et al, 19 Amiri et al, 20 Ayoubi et al, 21 Paynabar et al, 22 Bahrami et al 23 have studied multivariate profile monitoring. Methods for monitoring nonlinear profiles have been suggested by Vaghefi et al, 24 Williams et al, 25 Steiner et al, 26 Guevara and Vargas, 27 Chen et al, 28 Awad et al, 29 Pan et al, 30 Li et al 31 Jensen et al 32 proposed a method to monitor the profiles with autocorrelated data using the linear mixed model (LMM). Jensen and Birch 33 have proposed a method to monitor the nonlinear autocorrelated profile using the nonlinear mixed model.…”