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Statistical monitoring of multiple profiles simultaneously using Gaussian processes
Author(s) -
Jahani Salman,
Kontar Raed,
Veeramani Dharmaraj,
Zhou Shiyu
Publication year - 2018
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2326
Subject(s) - univariate , multivariate statistics , covariance , multivariate analysis , benchmark (surveying) , gaussian process , statistical process control , computer science , data mining , multivariate normal distribution , stability (learning theory) , gaussian , statistics , mathematics , process (computing) , machine learning , geography , operating system , physics , geodesy , quantum mechanics
Profile monitoring is the application of control charts to monitor the stability of a process over time when the process can be characterized by a functional relationship between a response variable and 1 or more explanatory variables. Most of the research in profile monitoring has been focused on monitoring univariate profiles, while multivariate profile data are widely observed in practice. In this paper, a monitoring approach based on a multivariate Gaussian process (MGP) model is proposed to monitor multivariate profiles simultaneously. In this regard, using a non‐separable covariance function, a MGP model is fitted to represent the baseline in‐control multivariate profile. Then, the stability of the process is tracked by monitoring a distance measure between the new observations of the multivariate profile and the baseline in‐control model. A key advantage of this method is that it considers correlations both within profiles and between profiles. We also introduce, as a benchmark, a univariate Gaussian process‐based profile monitoring scheme modified for multivariate profiles. The performance of the proposed approaches is investigated and compared through numerical studies and a real‐world case study. The analysis confirms the effectiveness of the MGP‐based monitoring scheme for multivariate profiles.