Method for improving the measurement system selection depending on part and process precisions

Abstract

This paper suggests a method for selecting the appropriate measurement system that at best fits to the precisions of part and process simultaneously. This method conducts a hypothesis test using the number of observations n, the probabilities of type I and type II errors, the required value of the capability index (Cp,Required) and the tolerance (Tol) of the evaluated specification to establish the corresponding critical values of the number of distinct categories (NDC∗) and the precision to tolerance ratio (PTR∗). Values of Cp,Required, NDC∗ and PTR∗ are then used to draw four quarters of plane. PTR∗ is plotted on the (Tol, σm) quarter of plane, NDC∗ is plotted on the (σm, σp) quarter of plane, Cp,Required is plotted on the (Tol, σp) quarter of plane and a 45° miter line is plotted on the (σm, σm) quarter of plane. The highest tolerable level of the measurement system variability (σm) is firstly assessed by means of PTR∗ in the quarter of plane (Tol, σm). Thereafter, the adequacy of this variability to the process precision is checked out by means of projections in the quarter of plane (σm, σm) using the miter line, thereafter in the quarter of plane (σm, σp) using NDC∗ and at last in the quarter of plane (Tol, σp) using Cp,Required. The application of the proposed method avoids both cases of over and lack of precisions of the selected measurement system regarding to the tolerance of the part and to the process variability.