ENBIS: European Network for Business and Industrial Statistics

Comparison between two methods of metamodel building (spline and kriging) for the efficiency calculation of a micro electronic component.

23 September 2008, 15:00 – 15:20

Abstract

Submitted by

Nicolas Durrande

Authors

Durrande De Crecy

Abstract

Production hazards usually lead to a difference between the theoretical dimension of an electronic component and the actual dimension observed after production. In most cases these differences aren’t problematic since all components produced comply with standards. However, in some cases, a percentage of the production doesn’t comply with a particular criterion and has to be disposed of. This allows us to define the efficiency of the production as the percentage of valid components at the end of the production process.

In our study, we know the probability law of the thickness of the different coats making up the component. Furthermore we have a numerical simulator that gives certain characteristics of the spectral response of a filter according to the thickness of 10 coats. Unfortunately the evaluation of the response by the simulator is costly and the efficiency of the production process can’t be calculated with the simulator by a Monte-Carlo method. The solution is to build a metamodel based on a limited number of evaluations by the simulator.

There are many ways to choose the points to be calculated by the simulator and lots of ways to build the metamodel. We study three kinds of space filling designs (Halton sequence, LHS with the criteria maximin and a classic design with arbitrarily chosen points) and three kinds of metamodels (spline type thin plate, ordinary kriging and universal kriging). Eventually the models are compared and two methods for the efficiency’s calculation are studied, one of these using the kriging variance.

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