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Sources of the Uncertainty for Infrared Tympanic Thermometer
According to the ISO GUM, the uncertainty of measurement is evaluated by “Type A” and “Type B” methods. The Type A evaluation of standard uncertainty is the evaluation method by statistical procedure. The Type B evaluation of standard uncertainty is the evaluation method by other information of the measurement and instrument. There are several items of uncertainty source for infrared tympanic thermometer.
1. The Standard Deviation
The standard uncertainty due to the estimate values of standard deviation of replicates ux is a Type A uncertainty. It was easy to calculate from the replicates of the measurement made using the IR thermometer at different conditions.
2. The Calibration Equation
The standard uncertainty due to the calibration of infrared thermometer is a Type A uncertainty. The uncertainty in a predicted value uy is calculated by follows:
uy=s1p+1n+(y−y¯¯¯)2∑(y2i)−(∑yi)2/n−−−−−−−−−−−−−−−−−−−−−√
(4)
where s is standard deviations of calibration equation, p is the number of replicates in the calibration; and n is the number of the sample data.
3. Uncertainty of the Reference Temperature
The uncertainty source of reference standard was provided by the manufacturer’s specifications. The distribution of uncertainty was assumed as normal distribution. The estimate of uncertainty for the standard temperature is:
uref=Uref2√
(5)
where Uref is the uncertainty source of TC-2000 temperature calibrator, and uref is the uncertainty due to the reference temperature.
4. Uncertainty Due to Nonlinearity and Repeatability
The source Unon due to nonlinearity and repeatability is specified by manufacturers. The variation response for this error source is assumed as a rectangular distribution. The uncertainty due to nonlinear and repeatability unon is calculated as:
unon=±Unon23√
(6)
where Unon is the uncertainty source due to the nonlinear and repeatability that represents a specification interval provided by the manufacturer; and unon is the uncertainty due to the nonlinear and repeatability made using the IR thermometer.
5. Uncertainty Due to Resolution
The uncertainty measurement due to resolution is assumed to be a rectangular distribution. It is considered as ±½ of the display scale value. The uncertainty value due to resolution ures is estimated as the follows:
ures=±Ures23√
(7)
where Ures is the uncertainty source due to the resolution effect, and ures is the uncertainty due to the resolution effect.
6. Uncertainty Due to Ambient Temperature Variation
The uncertainty source of ambient temperature was not mentioned by manufacturers. In this study, the effect of the ambient temperature on the variation of measurements made using the IR thermometer was evaluated by two-way ANOVA test. If the ambient temperature has significant effects on the variation of measurement, the uncertainty due to the ambient temperature can then be further estimated. The variation response from the temperature variation is assumed a rectangular distribution. The uncertainty due to temperature variation is:
utem=±Utem3√
(8)
where Utem is the uncertainty source due to the ambient temperature; and utem is the uncertainty due to the ambient temperature.
The uncertainty due to the reference temperature, nonlinearity and repeatability, resolution, and ambient temperature are classified as Type B uncertainty.
These uncertainty effects did not have significant correlations, and the combined standard uncertainty uc then be calculated as follows:
a. Uncertainty estimation of a fixed measuring point.
uc1=u2x+u2ref+u2non+u2res+u2tem−−−−−−−−−−−−−−−−−−−−−−−−−−√