  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.
