Heteroscedastic latent variable modelling with applications to multivariate statistical process control

We present an approach for conducting multivariate statistical process control (MSPC) in noisy environments, i.e., when the signal to noise ratio is low, and, furthermore, noise standard deviation (uncertainty) affecting each collected value can vary over time, and is assumingly known. This approach is based upon a latent variable model structure, HLV (standing for heteroscedastic latent variable model), that explicitly integrates information regarding data uncertainty. Moderate amounts of missing data can also be handled in a coherent and fully integrated way through HLV. Several examples show the added value achieved under noisy conditions by adopting such an approach and a case study illustrates its application to a real industrial context of pulp and paper product quality data analysis.

[1]  S. Qin,et al.  Determining the number of principal components for best reconstruction , 2000 .

[2]  William H. Woodall,et al.  Controversies and Contradictions in Statistical Process Control , 2000 .

[3]  Douglas C. Montgomery,et al.  Introduction to Statistical Quality Control , 1986 .

[4]  Calyampudi R. Rao,et al.  Linear Statistical Inference and Its Applications. , 1975 .

[5]  Douglas C. Montgomery,et al.  Applied Statistics and Probability for Engineers, Third edition , 1994 .

[6]  E. V. Thomas,et al.  Non‐parametric statistical methods for multivariate calibration model selection and comparison , 2003 .

[7]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[8]  Frank Vogt,et al.  Dynamic determination of the dimension of PCA calibration models using F‐statistics , 2003 .

[9]  Nicolaas M. Faber,et al.  Comparison of two recently proposed expressions for partial least squares regression prediction error , 2000 .

[10]  Darren T. Andrews,et al.  Maximum Likelihood Multivariate Calibration , 2022 .

[11]  Rasmus Bro,et al.  Standard error of prediction for multiway PLS 1 : background and a simulation study , 2002 .

[12]  Desire L. Massart,et al.  Estimation of partial least squares regression prediction uncertainty when the reference values carry a sizeable measurement error , 2003 .

[13]  Karl S. Booksh,et al.  Selecting significant factors by the noise addition method in principal component analysis , 2001 .

[14]  Barry M. Wise,et al.  The process chemometrics approach to process monitoring and fault detection , 1995 .

[15]  F. Xavier Rius,et al.  Lack of fit in linear regression considering errors in both axes , 2000 .

[16]  Thomas E. Marlin,et al.  Multivariate statistical monitoring of process operating performance , 1991 .

[17]  Jordi Riu,et al.  Prediction intervals in linear regression taking into account errors on both axes , 2001 .

[18]  J. Riu,et al.  Assessing the accuracy of analytical methods using linear regression with errors in both axes. , 1996, Analytical chemistry.

[19]  Gene H. Golub,et al.  Matrix computations , 1983 .

[20]  Bruce R. Kowalski,et al.  Propagation of measurement errors for the validation of predictions obtained by principal component regression and partial least squares , 1997 .

[21]  Milan Meloun,et al.  Critical comparison of methods predicting the number of components in spectroscopic data , 2000 .

[22]  Darren T. Andrews,et al.  Maximum likelihood principal component analysis , 1997 .

[23]  Alexander Penlidis,et al.  An approach to interval estimation in partial least squares regression , 1993 .

[24]  Ignacio Lira,et al.  Evaluating the Measurement Uncertainty , 2002 .

[25]  N. Sidiropoulos,et al.  Maximum likelihood fitting using ordinary least squares algorithms , 2002 .

[26]  S. Qin,et al.  Selection of the Number of Principal Components: The Variance of the Reconstruction Error Criterion with a Comparison to Other Methods† , 1999 .

[27]  Alison J. Burnham,et al.  LATENT VARIABLE MULTIVARIATE REGRESSION MODELING , 1999 .

[28]  Theodora Kourti,et al.  Statistical Process Control of Multivariate Processes , 1994 .