A Random Field Model and its Application in Industrial Production

Julie Oger (1) , Emmanuel Lesigne (1) , Philippe Leduc (2)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 ST-TOURS - STMicroelectronics [Tours]

In competitive industries, a reliable yield forecasting is a prime factor to accurately determine the production costs and therefore ensure profitability. Indeed, quantifying the risks long before the effective manufacturing process enables fact-based decision-making. From the development stage, improvement efforts can be early identified and prioritized. In order to measure the impact of industrial process fluctuations on the product performances, the construction of a failure risk probability estimator is presented in this article. The complex relationship between the process technology and the product design (non linearities, multi-modal features...) is handled via random process regression. A random field encodes, for each product configuration, the available information regarding the risk of non-compliance. After a brief presentation of the Gaussian model approach, we describe a Bayesian reasoning avoiding a priori choices of location and scale parameters. The Gaussian mixture prior, conditioned by measured (or calculated) data, yields a posterior characterized by a multivariate Student distribution. The probabilistic nature of the model is then operated to derive a failure risk probability, defined as a random variable. To do this, our approach is to consider as random all unknown, inaccessible or fluctuating data. In order to propagate uncertainties, a fuzzy set approach provides an appropriate framework for the implementation of a Bayesian model mimicking expert elicitation. The underlying leitmotiv is to insert minimal a priori information in the failure risk model. The relevancy of this concept is illustrated with theoretical examples.

Mots clés: Kriging; Bayesian inference; Gaussian processes mixture prior; multivariate t-distribution; uncertainty analysis; manufacturing yield evaluation

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Applications [stat.AP]

Julie Oger, Emmanuel Lesigne, Philippe Leduc. A Random Field Model and its Application in Industrial Production. 2013. ⟨hal-00914192v1⟩