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Table 5.
The type B uncertainty analysis for OMRON MC-510 thermometer.
Table 6.
The type B uncertainty analysis for BRAUN IRT-3020 thermometer.
5. The Combined Standard Uncertainty
The uc values for two infrared tympanic thermometers at five observations are listed in Table 7.
Table 7.
The combined uncertainty for two IR thermometers.
According to Equation (9), the values of uc1 are calculated at 34.5, 36.0, 37.5, 39.0 and 40.5 °C of the standard temperature for MC-510 thermometer. The numeric values are 0.2519, 0.2499, 0.2316, 0.1851 and 0.2318 °C, respectively. For the polynomial form of calibration equation, the combining standard uncertainty calculated by Equation (10) to evaluate at these standard temperatures were 0.2685, 0.2324, 0.2321, 0.2246 and 0.2741, respectively. The result indicated that the polynomial calibration did not decrease the uncertainty for the MC-510 thermometer.
The values of uc are calculated at 34.5, 36.0, 37.5, 39.0 and 40.5 °C of the standard temperature for IRT-3020 thermometer. They are found to be 0.1491, 0.0873, 0.0872, 0.089 and 0.1324 by Equation (9), respectively. For the linear calibration equation, the combined standard uncertainty evaluated at these standard temperatures was 0.1395, 0.0965, 0.0965, 0.0967 and 0.1394 by Equation (10), respectively. This result indicated that the calibration equation did not improve the uncertainty of the IRT-3020 thermometer.
This study evaluated the accuracy and uncertainty for two types of infrared tympanic thermometers. If the reading values of both thermometers were recognized as the true values of tympanic temperature, the accuracy of these thermometers could meet the requirement of the ASTM standards in the temperature range below 37 °C. At the standard temperature of 37.5 °C, there was wide variation in measurement in both thermometers. The average value of several measurements could be used to improve the accuracy. That is, more data needs to be taken at this temperature point to ensure the accuracy. At the temperature range above 37.5 °C, the reading values of both types of infrared tympanic thermometer need to be transformed by calibration equation to improve their accuracy.
The errors of measurement could be classified as systematic and random errors. The systematic errors could be expressed as errors and improved by its calibration equation. These procedures have been studied. The random errors can only be improved by selecting of sensing elements or increasing sample numbers. The quantitative expression of this random error has been established in the international standards.
In the previous study, the uncertainty of measurement for thermometer, hygrometer and rough rice moisture meter could be improved by establishing the adequate calibration Equations. In this study, the measuring errors could be reduced by the calibration equations. That is the systematic errors could be decreased. However, the uncertainty of measurement for two infrared tympanic thermometers could not be improved by the calibration equations. The reason could be explained by the form of predictive uncertainty [Equation (4)]. The estimated values of standard deviations for calibration, Equations (11) and (12), were 0.1965 and 0.0696, respectively. These numeric values are all almost higher than the standard deviation of replicates for different standard temperature and ambient temperature. That is the reason that the predictive uncertainty calculated by Equation (4) is almost higher than that of standard deviations.
Many studies have been reported that compare the performance of the rectal thermometer and infrared tympanic thermometer. However, the performance of accuracy and uncertainty of the traditional mercury glass thermometer and the infrared tympanic thermometer were not mentioned by these researchers. That may be the reason for the inconsistency of their results.
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