## 1 Introduction
### Measurement Uncertainties Associated with Dimensional and Geometric Measurement Using CMM
Although no common understanding of software validation procedures currently exists, the reader is referred to [35], as well as to the European Metrology Research Project (EMRP) under the denomination 'Traceability for computationally-intensive metrology (TraCIM)' [36; 37; 38] for research performed on software validation in the field of metrology. In this paper, we aimed to analyze the measurement uncertainty from an empirical (experimental) perspective. From a review of the literature on the subject, the collective impact of the operator (training, skills, certification, GD&T decoding and interpretation, etc. ), the measurement strategy (amount of data, samples, number of measurements, etc. ), and the software employed (algorithms used, filtering or removal of outliers, optimization of the stability of the algorithm, layout handling, etc.) had been surprisingly overlooked. We proposed a new GD&T-based benchmark (test artifact) for evaluating (comparing) the performance of measurement systems in different measurement organizations (e.g., industry, schools, and metrology service companies) by considering the uncertainty that can be induced by the operator, the measurement strategy, and the software used. Under the conditions proposed by the equipment manufacturer, the current hardware is accurate enough to perform the \"good\" measurements to capture the actual position of a measuring point in the 3D space. In other words, the uncertainty induced by the measuring device is significantly less than that induced by the operator choices, the software options, and the measurement strategies. This means that the performance of a measurement system represents an estimation of the combined variation of the measurement errors (systematic and random errors), which include equipment (hardware) errors, algorithmic errors (software), and operator errors. In this paper, software and operator errors were combined into one, as they can be strongly correlated. According to the MSA approach, this was strictly a reproducibility study [11]. The basic concepts of metrology and related terms that conform to the International Vocabulary of Metrology (VIM) [39] were employed in the present work. According to VIM, reproducibility is the _'closeness of the agreement between the results of measurements of the same quantity, where the individual measurements are made: by different methods, with different measuring instruments, by different observers, in different laboratories, after intervals of time quite long compared with the duration of the single measurement, under different normal conditions of use of the instruments employed'_[39]. According to the Automotive Industry Action Group (AIAG) Measurement System Analysis (MSA) reference manual [11], reproducibility is traditionally referred to as the 'between appraisers' variability. Typically, the term is defined as the average of measurements made by different appraisers using the same measuring instrument when measuring the identical characteristic of the same part. For the remainder of this paper, MSA terminology will be used [11]. EV stands for Equipment Variation, which is the variation due to repeatability, and AV stands for Appraiser Variation, which is the variation due to reproducibility. To allow validation of this hypothesis, a GD&T-based artifact was designed using common geometric features (plane, cylinder, etc.) and free-form surfaces. A total of five parts were created, one without any intentional defect (part #1), and four others with a predefined number of intentional dimensional and geometrical defects (parts #2 to #5). The artifacts were intended for use in assessing the performance of many measurement institutes (interlaboratory comparison) in accordance with the dimensional and geometrical tolerance criteria. The remainder of this paper is structured as follows: In Section 2, we outline the proposed test artifact model, followed by an experimental procedure.