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(12)
The predicted errors of Equation (12) are shown in Figure 6. All the predicted errors were located within the requirement range of the ASTM standards except for the standard temperature of 37.5 °C. However, the mean value of several replicates at this temperature could reduce the predictive errors.
Figure 6.
The predicted errors of calibration equation of BRAUN IRT-3020 thermometer.
3. The Replicate of the Infrared Tympanic Thermometer
The standard deviation of five measurements of MC-510 thermometer at different standard temperatures and three levels of ambient temperatures are shown in Figure 7.
Figure 7.
The standard deviation of five measurements of OMRON MC-510 thermometer at different standard temperatures and three leaves of ambient temperatures.
At the standard temperature of 36 °C, the standard deviations for three ambient temperatures were higher than that of other standard temperatures. To evaluate the factors affecting the standard deviations of MC-510 thermometer, two-way ANOVA table was established and the significant tests were executed by F test with a 95% confidence level. The result is listed in Table 2.
Table 2.
Analysis of variance ANOVA table for the effect of standard temperature and ambient temperature on the measurement of OMRON MC-510 thermometer.
In comparison with the variations of measurements, the standard temperature has significantly affected the variations of standard deviations. However, the ambient temperature showed no significant effects on the variation of measurements (P = 0.1305>0.05). The ambient temperature did not influence the variation of standard deviation of each measurement. The uncertainty source of ambient temperature was not considered for the evaluation of uncertainty of the MC-510 thermometer. The distribution of standard deviation of the Braun IRT-3020 measurement is presented in Figure 8. The ambient temperature did not have the significant effect on the standard deviations. At the standard temperature of 39 °C, the standard deviations were closed at 39 °C.
Figure 8.
The standard deviation of five measurements of BRAUN IRT-3020 thermometer at different standard temperatures and three leaves of ambient temperatures.
The two-way ANOVA table for the evaluation of the factors affecting the standard deviations of the IRT-3020 thermometer is listed in Table 3. The results indicated that the standard temperatures (P = 0.9355 > 0.05) and the ambient temperatures (P = 0.2274 > 0.05) did not have the significant effects on the standard deviation of IRT-3020 measurements. The effect of ambient temperature on the uncertainty of IRT-3020 was not considered in further analysis.
Table 3.
Analysis of variance ANOVA table for the effect of standard temperature and ambient temperature on the measurement of BRAUN IRT-3020 thermometer.
4. Calculation of the Uncertainty of Infrared Tympanic Thermometer
The adequate calibration equation for OMRON MC-510 thermometer is the polynomial equation and the best calibration equation for BRAUN IRT-3020 is a linear form. The uncertainty due to the replications of measurement is the standard deviation of each measurement. However, the uncertainty derived from the calibration equation is calculated by Equation (4). The type A uncertainty of several observations for two-types of infrared tympanic thermometers are listed in Table 4. For the OMRON MC-510 thermometer, the uncertainty of calibration equation did not reduce as compared to the uncertainty calculated from standard deviations of each observation. The same results could be found for the BRAUN IRT-3020 thermometers.
Table 4.
The type A uncertainty of several observations for two infrared tympanic thermometers.
The type B uncertainty analysis for the two infrared tympanic thermometers was calculated byEquation (5), (6) and (7). This result is listed in Tables 5–6. Comparing these sources of uncertainty for two-type infrared tympanic thermometers, the main source of the uncertainty included the specification of nonlinear and repeatability (type B) and the standard deviations (type A).