A Random Field Model and Decision Support in Industrial Production
[Un modèle par champ aléatoire et un outil d’aide à la décision en production industrielle]
Journal de la société française de statistique, Tome 156 (2015) no. 3, pp. 1-26.

Nous proposons un nouvel outil d’aide à la décision pour l’étude d’un phénomène inconnu modélisé par un champ aléatoire représentant simultanément notre connaissance et notre manque d’information. Cet outil est la distribution d’une variable aléatoire appelée probabilité du risque de défaillance. Avant de préciser la définition de cet objet, nous décrivons un contexte industriel dans lequel un problème décisionnel apparaît et nous examinons des constructions bayésiennes de modèles par champs aléatoires.

We propose a new tool of decision support in front of a globally unknown phenomenon which is modeled by a random field representing simultaneously our knowledge and our lack of information. This tool is the distribution of a random variable called failure risk probability. Before giving the precise definition of this object, we describe an industrial context in which the decision problem occurs and we discuss Bayesian random field model constructions.

Keywords: kriging, Bayesian inference, Gaussian processes mixture prior, multivariate t-distribution, uncertainty analysis, manufacturing yield evaluation, decision support
Mot clés : krigeage, inférence bayésienne, mélange de processus gaussiens, distribution de Student multivariée, analyse d’incertitude, évaluation de rendement industriel, aide à la décision 
@article{JSFS_2015__156_3_1_0,
     author = {Oger, Julie and Lesigne, Emmanuel and Leduc, Philippe},
     title = {A {Random} {Field} {Model} and {Decision} {Support} in {Industrial} {Production}},
     journal = {Journal de la soci\'et\'e fran\c{c}aise de statistique},
     pages = {1--26},
     publisher = {Soci\'et\'e fran\c{c}aise de statistique},
     volume = {156},
     number = {3},
     year = {2015},
     zbl = {1381.62293},
     language = {en},
     url = {http://archive.numdam.org/item/JSFS_2015__156_3_1_0/}
}
TY  - JOUR
AU  - Oger, Julie
AU  - Lesigne, Emmanuel
AU  - Leduc, Philippe
TI  - A Random Field Model and Decision Support in Industrial Production
JO  - Journal de la société française de statistique
PY  - 2015
SP  - 1
EP  - 26
VL  - 156
IS  - 3
PB  - Société française de statistique
UR  - http://archive.numdam.org/item/JSFS_2015__156_3_1_0/
LA  - en
ID  - JSFS_2015__156_3_1_0
ER  - 
%0 Journal Article
%A Oger, Julie
%A Lesigne, Emmanuel
%A Leduc, Philippe
%T A Random Field Model and Decision Support in Industrial Production
%J Journal de la société française de statistique
%D 2015
%P 1-26
%V 156
%N 3
%I Société française de statistique
%U http://archive.numdam.org/item/JSFS_2015__156_3_1_0/
%G en
%F JSFS_2015__156_3_1_0
Oger, Julie; Lesigne, Emmanuel; Leduc, Philippe. A Random Field Model and Decision Support in Industrial Production. Journal de la société française de statistique, Tome 156 (2015) no. 3, pp. 1-26. http://archive.numdam.org/item/JSFS_2015__156_3_1_0/

[1] Auffray, Y.; Barbillon, P.; Marin, J.-M. Bounding rare event probabilities in computer experiments., Computational Statistics and Data Analysis, Volume 80(0) (2014), pp. 153-166 | Zbl

[2] Abrahamsen, P. A review of Gaussian random fields and correlation functions - 2nd edition, Norwegian Computing Center, 1997

[3] Berger, B.; De Oliviera, V.; Sansó, B. Objective Bayesian analysis of spatially correlated data, Journal of the American Statistical Association, Volume 96 (2000), pp. 1361-1374 | Zbl

[4] Caflish, R. Monte Carlo and quasi-Monte Carlo methods, Acta Numerica, Volume 7 (1998), pp. 1-49 | Zbl

[5] Currin, C.; Mitchell, T.; Morris, M.; Ylvisaker, D. A Bayesian approach to the design and analysis of computer experiments (1988) (Technical report)

[6] Cornford, D.; Nabney, I.; Williams, C. Modelling frontal discontinuities in wind fields, Journal of nonparametric statistics, Volume 14(1-2) (2002), pp. 43-58 | Zbl

[7] Cover, T.; Thomas, J. Elements of information theory, 2nd edition, Wiley-Interscience, 2006 | Zbl

[8] Emmerich, M.; Giannakoglou, K.; Naujoks, B. Single- and multiobjective evolutionary optimization assisted by Gaussian random field metamodels, IEEE Transactions on Evolutionary Computation, Volume 10 (2006), pp. 421-439

[9] Gelman, A. Prior distributions for variance parameters in hierarchical models, Bayesian Analysis, Volume 1 (2006), pp. 515-533 | Zbl

[10] Kato, K. Improved prediction for a multivariate normal distribution with unknown mean and variance, Annals of the Institute of Statistical Mathematics, Volume 61 (2009), pp. 531-542 | Zbl

[11] Kotz, S.; Nadarajah, S. Multivariate t-distributions and their applications, Cambridge University Press, 2004 | Zbl

[12] Matheron, G. Estimating and choosing. An essay on probability in practice. Translated from the French and with a preface by A. M. Hasofer., Springer-Verlag, 1989 | Zbl

[13] Oakley, J.; O’Hagan, A. Probabilistic sensitivity analysis of complex models: a Bayesian approach, Journal of the Royal Statistical Society, Volume 66 (2004), pp. 751-769 | Zbl

[14] Pearl, J. Do we need higher-order probabilities, and if so, what do they mean?, Conference on Uncertainty in Artificial Intelligence (1988)

[15] Pfingsten, T.; Herrmann, D.; Rasmussen, C. Model-based design analysis and yield optimization, IEEE Transactions on semiconductor manufacturing, Volume 19 (2006), pp. 475-486

[16] Robert, C. The Bayesian choice: from decision-theoretic foundations to computational implementation - 2nd edition, Springer-Verlag New York Inc., 2007, 602 pages | Zbl

[17] Rasmussen, C.; Williams, C. Gaussian processes for machine learning, The MIT Press, 2006 | Zbl

[18] Stein, M. Interpolation of spatial data: some theory for kriging, Springer, 1999 | Zbl

[19] Sacks, J.; Welch, W.; Mitchell, T.; Wynn, H. Design and analysis of computer experiments, Statistical Science, Volume 4 (1989), pp. 409-435 | Zbl

[20] Santner, T.; Williams, B.; Notz, W. The design and analysis of computer experiments, Springer, 2003 | Zbl

[21] Talbi, E. Metaheuristics: from design to implementation, 74, Wiley, 2009 | Zbl

[22] Zadeh, L. Fuzzy sets, Information and control, Volume 8 (1965), pp. 338-353 | Zbl