Multivariate Statistical Process Control Charts: An Overview

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.quality control, process control, multivariate statistical process control, Hotelling's T-square, CUSUM, EWMA, PCA, PLS

Viral Evolution and Adaptation as a Multivariate Branching Process

In the present work we analyze the problem of adaptation and evolution of RNA virus populations, by defining the basic stochastic model as a multivariate branching process in close relation with the branching process advanced by Demetrius, Schuster and Sigmund ("Polynucleotide evolution and branching processes", Bull. Math. Biol. 46 (1985) 239-262), in their study of polynucleotide evolution. We show that in the absence of beneficial forces the model is exactly solvable. As a result it is possible to prove several key results directly related to known typical properties of these systems like (i) proof, in the context of the theory of branching processes, of the lethal mutagenesis criterion proposed by Bull, Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", J. Virology 18 (2007) 2930-2939); (ii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation and (iii) the quantitative description of the evolution of the expected values in four distinct regimes: transient, "stationary" equilibrium, extinction threshold and lethal mutagenesis. Moreover, new insights on the dynamics of evolving virus populations can be foreseen.Comment: 39 pages, 3 figures. International Symposium on Mathematical and Computational Biology, Tempe, Arizona, USA, 6 - 10 November 2012. Fernando Antoneli, Francisco Bosco, Diogo Castro, And Luiz Mario Janini (2013) Viral Evolution and Adaptation as a Multivariate Branching Process. Biomat 2012: pp. 217-243. Ed.: R. P. Mondaini. World Scientific, Singapor

Infinite Mixtures of Multivariate Gaussian Processes

This paper presents a new model called infinite mixtures of multivariate Gaussian processes, which can be used to learn vector-valued functions and applied to multitask learning. As an extension of the single multivariate Gaussian process, the mixture model has the advantages of modeling multimodal data and alleviating the computationally cubic complexity of the multivariate Gaussian process. A Dirichlet process prior is adopted to allow the (possibly infinite) number of mixture components to be automatically inferred from training data, and Markov chain Monte Carlo sampling techniques are used for parameter and latent variable inference. Preliminary experimental results on multivariate regression show the feasibility of the proposed model.Comment: Proceedings of the International Conference on Machine Learning and Cybernetics, 2013, pages 1011-101

Spectral tail processes and max-stable approximations of multivariate regularly varying time series

A regularly varying time series as introduced in Basrak and Segers (2009) is a (multivariate) time series such that all finite dimensional distributions are multivariate regularly varying. The extremal behavior of such a process can then be described by the index of regular variation and the so-called spectral tail process, which is the limiting distribution of the rescaled process, given an extreme event at time 0. As shown in Basrak and Segers (2009), the stationarity of the underlying time series implies a certain structure of the spectral tail process, informally known as the "time change formula". In this article, we show that on the other hand, every process which satisfies this property is in fact the spectral tail process of an underlying stationary max-stable process. The spectral tail process and the corresponding max-stable process then provide two complementary views on the extremal behavior of a multivariate regularly varying stationary time series

Multivariate Krawtchouk polynomials and composition birth and death processes

This paper defines the multivariate Krawtchouk polynomials, orthogonal on the multinomial distribution, and summarizes their properties as a review. The multivariate Krawtchouk polynomials are symmetric functions of orthogonal sets of functions defined on each of N multinomial trials. The dual multivariate Krawtchouk polynomials, which also have a polynomial structure, are seen to occur naturally as spectral orthogonal polynomials in a Karlin and McGregor spectral representation of transition functions in a composition birth and death process. In this Markov composition process in continuous time there are N independent and identically distributed birth and death processes each with support 0,1, .... The state space in the composition process is the number of processes in the different states 0,1,... Dealing with the spectral representation requires new extensions of the multivariate Krawtchouk polynomials to orthogonal polynomials on a multinomial distribution with a countable infinity of states

Multivariate statistical process monitoring

U industrijskoj proizvodnji prisutan je stalni rast zahtjeva, u prvom redu, u pogledu ekonomičnosti proizvodnje, kvalitete proizvoda, stupnja sigurnosti i zaštite okoliša. Put ka ispunjenju ovih zahtjeva vodi kroz uvođenje sve složenijih sustava automatskog upravljanja, što ima za posljedicu mjerenje sve većeg broja procesnih veličina i sve složenije mjerne sustave. Osnova za kvalitetno vođenje procesa je kvalitetno i pouzdano mjerenje procesnih veličina. Kvar na procesnoj opremi može značajno narušiti proizvodni proces, pa čak prouzrokovati ispad proizvodnje što rezultira visokim dodatnim troškovima. U ovom radu se analizira način automatskog otkrivanja kvara i identifikacije mjesta kvara u procesnoj mjernoj opremi, tj. senzorima. U ovom smislu mogu poslužiti različite statističke metode kojima se analiziraju podaci koji pristižu iz mjernog sustava. U radu se PCA i ICA metode koriste za modeliranje odnosa među procesnim veličinama, dok se za otkrivanje nastanka kvara koriste Hotellingova (T**2), I**2 i Q (SPE) statistike jer omogućuju otkrivanje neobičnih varijabilnosti unutar i izvan normalnog radnog područja procesa. Za identifikaciju mjesta (uzroka) kvara koriste se dijagrami doprinosa. Izvedeni algoritmi statističkog nadzora procesa temeljeni na PCA metodi i ICA metodi primijenjeni su na dva procesa različite složenosti te je uspoređena njihova sposobnost otkrivanja kvara.Demands regarding production efficiency, product quality, safety levels and environment protection are continuously increasing in the process industry. The way to accomplish these demands is to introduce ever more complex automatic control systems which require more process variables to be measured and more advanced measurement systems. Quality and reliable measurements of process variables are the basis for the quality process control. Process equipment failures can significantly deteriorate production process and even cause production outage, resulting in high additional costs. This paper analyzes automatic fault detection and identification of process measurement equipment, i.e. sensors. Different statistical methods can be used for this purpose in a way that continuously acquired measurements are analyzed by these methods. In this paper, PCA and ICA methods are used for relationship modelling which exists between process variables while Hotelling\u27s (T**2), I**2 and Q (SPE) statistics are used for fault detection because they provide an indication of unusual variability within and outside normal process workspace. Contribution plots are used for fault identification. The algorithms for the statistical process monitoring based on PCA and ICA methods are derived and applied to the two processes of different complexity. Apart from that, their fault detection ability is mutually compared