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Title: Measurement Risk Analysis Definitions As Applied To Z540.3
Author: Del Caldwell, Dennis Jackson
Source: 2008 Measurement Science Conference
Year Published: 2008
Abstract: Measurement decision risk analysis provides a probability description of the possible results of a calibration scenario. Under a basic calibration testing scenario, the measurement from a Calibration Standard (CAL) is compared with the measurement from a Unit Under Test (UUT). If the difference between these measurements is greater than some required tolerance, the UUT is declared to be out of tolerance (OOT). The usual result of this OOT declaration is that the UUT is adjusted in some fashion so that the tested measurement is no longer OOT. Since the CAL makes measurements with some error, there is a probability that the decisions made through this testing process could be incorrect. The problem is trying to define the exact nature of these incorrect decisions in unmistakable terms. Typically, these incorrect decisions are described as false accept (incorrectly accepting an OOT UUT measurement) and false reject (incorrectly rejecting an in tolerance UUT measurement). This paper will focus on the false or incorrect acceptance decision aspect of measurement decision risk. This paper lays out the error mathematics describing representative measurement models applied to calibration scenarios. Using these error mathematics, the meaning of a false accept decision event is unambiguously described. Further, the probability of such events or probability of false accept decisions (PFA) can then be simply defined as the probability of such an event. The probability mathematics for calculating the PFA is shown. These probability equations do not require the assumption of specific probability distributions, such as the Normal (or Gaussian) distribution. However, as an example, this paper also provides the specific equations needed to calculate the PFA using the usual Normal distribution assumptions. Four methods for meeting PFA requirements are discussed. These methods are based on exact and conservative methods to estimate PFA for a calibration scenario, and exact and conservative methods to adjust the calibration scenario using guard bands.

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