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The goal of this article is to propose a criterion based on an adequate real distribution. In order to do this, the criterion must be able to integrate any type of distribution like unsymmetrical distributions, which are characteristic of the PDF shapes left by some manufacturing processes. To carry out this objective, two tasks should be realised. First, a criterion has to be constructed using the statistical approach. And next, the behaviour of the likelihood function against different kinds of PDF shape may be studied to define the most appropriate form of this function.

International standards provide, with the Geometrical Product Specification (GPS), tools for geometric specification and verification of mechanical parts based on tolerance zones (TZ). A TZ represents a domain space in which the real surface must be included. This space domain defines the set of geometries which are functionally equivalent. In a part design, numerous TZ are constraints related to a reference system. This last one is an ideal geometry, called datum, associated to real surfaces, called datum feature. A datum can be simple, if it is related to one datum feature, or forming a datum-system reference if it is related to two or three real surfaces. In this case, there is a hierarchy in the fitting process between the datum-system and the set of datum features. Hence, a primary, secondary and a tertiary datum should be considered. It is now commonly admitted that measurements are tainted with uncertainties. These uncertainties on datum feature estimations are propagated to the datum-system reference and then propagated to all TZ positions. Thus, considering the level arm effect between the datum and the TZ, uncertainties on TZ positions can become quickly of the same order of magnitude as the maximal admissible defect specified on product geometry. This paper presents a method permitting to estimate uncertainties on a datum-system reference.

This paper deals with the use of uncertainty propagation in a Design Of Experiments. The Guide to expression of Uncertainty in Measurement is applied to compute the Statistical Confidence Boundary of the response surface. Next, the uncertainties of the model are used to estimate the probability density function of the estimated optimal factors. After, the global optimum is searched to optimize the solution for a set of factors. This method finds the optimal solution using a D.O.E. response surface considering the uncertainty in experiments and models. This method maximizes the probability to find the overall optimum