Statistical Considerations on the Probing Error Test for Coordinate Measuring Machines

Coordinate Measuring Instruments (CMS) are complex. Differing from conventional measuring systems, which in most cases can perform only a single kind of measurement (e.g. a thermometer can measure temperature only, or a ruler can measure just lengths), CMS are usually very flexible. They can perform a vast variety of different measurement tasks, ranging from simple thickness or diameter measurement to geometric tolerance verification and even free-form surface scan. This has lead to need of the definition of a “task specific uncertainty”, i.e. the uncertainty a CMS can yield will depend strongly on the measurement task the CMS itself is performing. But if the uncertainty changes as the measurement task change, the uncertainty is not anymore adequate to state the performance of the CMS. The uncertainty is not anymore a parameter based on which a ranking of CMS can be proposed, nor it is possible to evaluate it once and for all by means of a calibration procedure. So it is often hard for the CMS buyer to identify the CMS fitting his requirements. Furthermore, it is difficult to check, by means of an uncertainty evaluation only, whether the CMS is performing as expected or not. Therefore, tests have been introduced for the ``acceptance and reverification'' of CMS, completely defined in national and international standards. Probably the most diffused standard of this kind is the ISO 10360, which at present consists of nine published parts and a few more under development. In this standard a series of tests has been developed which aims at verifying whether a CMS performs as stated by either the manufacturer (acceptance test) or the user (reverification test). These procedure act as a “go-no go” gauge: the test is passed or not passed, no intermediate possibility is considered. This limits the use of the test to understand what is going on with the machine, and where the machine itself can be improved. In this paper a statistical point of view on the tests proposed by the ISO 10360 standard is proposed. The aim is to evaluate the probability the tests state the CMS is behaving according the stated performance, which is usually defined the “operating characteristic” (OC) curve of the test. This helps understanding which is the test error probability, i.e. the probability of either stating the CMS is misbehaving when it is behaving correctly or vice versa. This is useful for both the CMS manufacturer, helping him to state correctly the performance of its machine (e.g. when declaring it in the system brochure) and the user when planning the testing of its machine. In particular, this preliminary work will focus on the performance of the classical “probing error” test, which is based on the sampling on 25 points on a reference sphere.