A theoretical framework for multivariate quality control
Guerrero, Jose Luis
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https://hdl.handle.net/2142/19620
Description
Title
A theoretical framework for multivariate quality control
Author(s)
Guerrero, Jose Luis
Issue Date
1991
Doctoral Committee Chair(s)
Dessouky, Mohamed I.
Department of Study
Mechanical Science and Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Statistics
Engineering, Industrial
Language
eng
Abstract
A theoretical framework is proposed for multivariate quality control based on multivariate statistical analysis and information-theoretical measures. A flow chart is proposed to determine whether the process is in control taking into account the distribution of the vector of random variables X, and its correlation and variability structures.
Two system characteristics are used, namely the transinformation T(X) and the entropy H(X) of a system. These measures are used to determine changes in the correlation and variability structure of our process, respectively. Two multivariate distributions are investigated, namely the multivariate normal and the multivariate Poisson. The bivariate Poisson is analyzed in detail and the asymptotic properties for the bivariate binomial are examined.
Distributional studies for sample values of T(X) and H(X) are carried out under the assumptions of multivariate normality and bivariate Poisson. For the multivariate normal distribution we analyze the case of independent and dependent random variables. For the former case we obtain the moment generating function, cumulant function, mean and variance. For the dependent case we obtain asymptotic results for its moments and proposed dependence tests. The bivariate Poisson analysis is based on its expansion by Gram-Charlier polynomials. Diagnostic tests are outlined to determine which variables brought about the out-of-control state, when such a state has been indicated by the tests proposed above.
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