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[This paper is intended primarily for the benefit of those in the audience who have concerns relating to the risks associated with decisions based on coordinate metrology data, and attendant economic consequences. Relevant methodologies will be reviewed and illustrated with a case study.] ___________________________________________________________________________________________ The past two decades have witnessed dramatic advances in the treatment of measurement uncertainty and, in particular, its relationship to conformance testing and measurement traceability. This is reflected, in part, in the large number of research publications and conference papers appearing on the topic and, perhaps most notably, in the proliferation of new and revised, national and international standards addressing the subject. [1-6]. Treatments of measurement decision risk and the economics of metrology have been on the rise in the technical literature and in recent standards as well [cf.7,8]. Measurement uncertainty evaluation in three-dimensional coordinate metrology has been a challenging problem due to the widely varying measurands and conditions of measurement encountered. Nevertheless, viable methods have been recognized in the standards community [9-12]. A typical workpiece evaluation in coordinate metrology will entail multiple measurands, each assessed according to a specific protocol and each having an associated tolerance. Thus measurement uncertainty for the workpiece as a whole is really a set of task-specific uncertainties, one for each measurand. The determination of measurement decision risks (false accept/false reject) will reflect that complexity. In relating each measurement uncertainty to its corresponding tolerance, it is necessary to treat each according to its appropriate type (two-sided vs. single-sided-upper vs. single-sided lower tolerances). Then overall decision risks can be evaluated by appropriately aggregating the results of risks associated with the individual measurands. A case study will be presented. Cost-of-ownership models applied to metrology equipment have largely dealt with single-measurand conditions and been focused on applications in the semiconductor industry [cf.13]. The extension to multiple measurands has recently been presented in the literature [14]. Consideration will be given to the application of this model to coordinate metrology as a logical extension of the evaluation of multiple-measurand decision risks. __________________________________________________________________________ References [1] Guide to the Expression of Uncertainty in Measurement (GUM) ISO Guide 98, BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML, International Organization for Standardization,Geneva, 1995. [2] General Requirements for the Competence of Testing and Calibration Laboratories, ISO 17025, International Organization for Standardization, Geneva, 1999. [3] American National Standard for Calibration - Requirements for the Calibration of Measuring and Test Equipment, (ANSI/NCSL) Z540.3-2006, American National Standards Institute/National Conference of Standards Laboratories, Boulder, CO, 2006. [4] Metrological Traceability of Dimensional Measurements to the SI Unit of Length,” ASME B89.7.5-2006, The American Society of Mechanical Engineers, New York, 2006. [5] Geometrical Product Specifications (GPS) -- Inspection by measurement of workpieces and measuring equipment -- Part 1: Decision rules for proving conformance or non-conformance with specifications, ISO 14253-1, International Organization for Standardization, Geneva, 1998. [6] Guidelines for Decision Rules: Considering Measurement Uncertainty in Determining Conformance to Specifications, ASME B89.7.3.1-2001, The American Society of Mechanical Engineers, New York, 2001. [7] Measurement Uncertainty and Conformance Testing: Risk Analysis, ASME B89.7.4.1-2005, The American Society of Mechanical Engineers, New York, 2005. [8] Castrup, H., Risk Analysis Methods for Complying with Z540.3, NCSL International Workshop and Symposium, St. Paul, MN, June 29-July 2, 2007. [9] Geometrical Product Specifications (GPS) -- Coordinate measuring machines (CMM): Technique for determining the uncertainty of measurement -- Part 2: Use of multiple measurements strategies in calibration artefacts, ISO/CD TS 15530-2, International Organization for Standardization, Geneva. [10] Geometrical Product Specifications (GPS) -- Coordinate measuring machines (CMM): Technique for determining the uncertainty of measurement -- Part 3: Use of calibrated workpieces or standards, ISO/TS 15530-3, International Organization for Standardization, Geneva, 2004. [11] Geometrical Product Specifications (GPS) -- Coordinate measuring machines (CMM): Technique for determining the uncertainty of measurement -- Technique for determining the uncertainty of measurement -- Part 4: Evaluating task-specific measurement uncertainty using simulation, ISO/PRF TS 15530-4, International Organization for Standardization, Geneva. [12] Evaluation of measurement data – Supplement 1 to the “Guide to the Expression of Uncertainty in Measurement” - Propagation of Distributions using a Monte Carlo Method, (final draft), JCGM, BIPM, Paris, 2006. [13] Dance D, Estimating the Cost of Ownership for Test and Metrology, SEMI Manufacturing Test Conference, July 1993. [14] Sohn, S.Y.and Moon, H.U., Cost of Ownership Model for Inspection of Multiple Quantity Attributes, IEEE Transactions on Semiconductor Manufacturing, 16, 565-571, (2003). |
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