On the identification of the probability density function of a dimension from data with measurement errors

Abstract

Metrology tools are applicable to check whether dimensions lay within their tolerance intervals. However, measurement errors cannot be avoided. This paper develops a method to partially correct the effect of such errors in case their probability density function is known. We assume that the probability density function associated with the measured dimension is available, for instance identified after multiple parts are manufactured and their dimension is measured. In this context, the probability density function of the measured value is the convolution product between the probability density functions of the measurement error and of the true value, respectively. Therefore, characterizing the true value is a challenging task, as this involves a deconvolution. We propose a procedure based on: (i) the transformation of the integral involved in the convolution product into a sum using numerical integration; (ii) the definition of a set of non-linear equalities solved using Newton-Raphson's procedure. An application example is used to discuss the relevance of the proposed method and the influence of various parameters on the results.