^{*}

This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (

Infrared tympanic thermometers (ITTs) are easy to use and have a quick response time. They are widely used for temperature measurement of the human body. The accuracy and uncertainty of measurement is the importance performance indicator for these meters. The performance of two infrared tympanic thermometers, Braun THT-3020 and OMRON MC-510, were evaluated in this study. The cell of a temperature calibrator was modified to serve as the standard temperature of the blackbody. The errors of measurement for the two meters were reduced by the calibration equation. The predictive values could meet the requirements of the ASTM standard. The sources of uncertainty include the standard deviations of replication at fixed temperature or the predicted values of calibration equation, reference standard values and resolution. The uncertainty analysis shows that the uncertainty of calibration equation is the main source for combined uncertainty. Ambient temperature did not have the significant effects on the measured performance. The calibration equations could improve the accuracy of ITTs. However, these equations did not improve the uncertainty of ITTs.

Body temperature is an indication to express the health condition or pathological state. Measurement of body temperature has become an essentially diagnostic method for medical treatment. There are two traditional methods to measure the body temperature. The first type is the glass mercury thermometer. This thermometer is inexpensive and easy to use. However, the response time is from 3 to 5 minutes. The glass material is extremely fragile and can be dangerous to the human body. The second type is the electronic digital thermometer. Its sensing element is made of a thermistor or resistance detector. This meter can measure the temperature within several seconds. However, the electronic device is affected by aging problems. The sensing elements of digital thermometer still need to have contact with the human body. Several problems exist in the clinical operation. The patient reaction, such as children or infant, could affect the measurement of these contact thermometers.

The best method is to measure the core body temperature, such as the temperature of coronary arteries. However, this is impossible except by using invasive surgical procedures. Recently, many literatures reported that the core temperature can be measured by detecting the positions near the membrane of the ear canal [

The reliability and accuracy of infrared tympanic thermometer have been discussed by many researchers. Their results are inconsistent. Dodd

The inconsistency of the measurement may be explained by the performance, confidence level, and uncertainty of the infrared thermometer. The factors affecting the performance of infrared tympanic thermometer were discussed by Heusch

The calibration of the infrared thermometer is very important to ensure its performance. Because the emissivity of canal is very close to unity, the temperature of a black body cavity is usually served as the standard temperature for calibration. Cascetta [

Pusnik

Recently, uncertainty evaluation had been widely applied for physical and chemical sensors [

The objectives of this study are to evaluate the accuracy and to calculate the uncertainty of two types of infrared tympanic thermometer according to ISO GUM (Guide to the expression of uncertainty in measurement). An adequate calibration equation is first established. Then the effect of the calibration equation on the accuracy and uncertainty was compared.

Two types of infrared tympanic thermometers were adopted in this study. One is the OMRON MC-510 Gentle Temp model (OMRON Co., Japan). The other is the BRAUN IRT-3020 Themoscan model (Braun Co., Germany). The operating procedures for ear temperature measurement were described in detail in their manual. The specifications of the two thermometers are listed in

The standard temperature was prepared by a temperature calibrator and a blackbody cavity. This standard temperature was simulated as the tympanic temperature to evaluate the performance of two types of infrared thermometers. The standard temperature served as the standard for performance testing.

The model of temperature calibrator is TC-2000 Scan Sense (Instrutek Co., Norway). The operating temperature was ranged from −40 °C to 150 °C. The inner temperature of oil bath for calibration was detected by a four-wire Pt-100 thermometer. The uncertainty of this calibrator is 0.03 °C according to its specifications.

An aluminum cylinder was inserted into the oil bath of the calibrator. The length of the cylinder was 14.5 cm and the diameter was 0.485 cm. The emissivity of this cylinder was assembled to be unity calculated from the calculation equation of blackbody cavity [

The target temperature for calibration of infrared thermometer was maintained at 34.5, 36.0, 37.5, 39.0 and 40.5 °C. The performance test experiment was executed in an environmental chamber at three levels of ambient temperature: 25 °C, 30 °C and 35 °C. The variation of the setting temperature was controlled within ±1 °C.

Each infrared thermometer was randomly measured at five sets of standard temperatures at the same ambient temperature. Five replicates were made for each standard temperature. As one measurement was made, the infrared thermometer was taken out of the blackbody cavity for five minutes and then put into the cavity again for further measurement.

The performance of infrared thermometers was assessed by their accuracy and repeatability. The definition of accuracy is the closeness with which a measurement approaches true value [

The standard deviation of data sets was calculated from replicates. These values were then further analyzed by one and two way ANOVAs (Analysis of Variance) and other statistical procedure. Significance was taken as P < 0.05. The P value is the smallest level of significance that would be to reject the hypothesis.

The regression analysis technique was applied to establish the calibration equation from the relationship between the standard values and the reading values. The criteria for selecting of the best equation are the coefficient of determination R^{2}, t-tests of each parameters and residual plots [

To establish the calibration equation, the standard values of the standard temperature made by a temperature calibrator were selected as the dependent value y. The reading values of the infrared thermometer were viewed as an independent variable. The ambient temperature of the experiment testing is assumed as the other independent variable. This calibration equation f(x) is called as the inverse equation [

The form of y(x) can be expressed as follows:
_{1} is the reading values of infrared thermometer, b_{0}, b_{1}, b_{2} are parameters.

Many texts dealing with the calibration equation reported that the reading values of the thermometer were viewed as the independent variable and the standard values of temperature were viewed as the dependent variable. This equation is called as the classical equation. However, the inverse equation has shown the better predictive ability [

According to the ISO GUM [

The standard uncertainty due to the estimate values of standard deviation of replicates u_{x} is a Type A uncertainty. It was easy to calculate from the replicates of the measurement made using the IR thermometer at different conditions.

The standard uncertainty due to the calibration of infrared thermometer is a Type A uncertainty. The uncertainty in a predicted value u_{y} is calculated by follows:

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:
_{ref} is the uncertainty source of TC-2000 temperature calibrator, and u_{ref} is the uncertainty due to the reference temperature.

The source U_{non} 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 u_{non} is calculated as:
_{non} is the uncertainty source due to the nonlinear and repeatability that represents a specification interval provided by the manufacturer; and u_{non} is the uncertainty due to the nonlinear and repeatability made using the IR thermometer.

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 u_{res} is estimated as the follows:
_{res} is the uncertainty source due to the resolution effect, and u_{res} is the uncertainty due to the resolution effect.

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:
_{tem} is the uncertainty source due to the ambient temperature; and u_{tem} 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 u_{c} then be calculated as follows:

Uncertainty estimation of a fixed measuring point.

Uncertainty estimation include the effect of calibration

The relationship between reading values of MC-510 thermometer

The relationship between standard temperature values and reading values of MC-510 thermometer was established by regression analysis. The best equation is:
_{sta} is the standard temperature and T_{rea} is the reading temperature of IR thermometer.

The predicted errors of calibration

The relationship between reading values of BRAUN IRT-3020 thermometer

The relationship between standard values and reading values of IRT-3020 thermometer was established by regression analysis. The adequate equation is:

The predicted errors of

The standard deviation of five measurements of MC-510 thermometer at different standard temperatures and three levels of ambient temperatures are shown in

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

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 (

The two-way ANOVA table for the evaluation of the factors affecting the standard deviations of the IRT-3020 thermometer is listed in

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

The type B uncertainty analysis for the two infrared tympanic thermometers was calculated by

The u_{c} values for two infrared tympanic thermometers at five observations are listed in

According to _{c1} 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

The values of u_{c} 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

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 [

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 [

Many studies have been reported that compare the performance of the rectal thermometer and infrared tympanic thermometer [

The uncertainty evaluation in this study included the Type A uncertainty for standard deviations of replicates or predicative uncertainty of calibration and the Type B uncertainty for reference temperature, nonlinear and repeatability and resolution source. The ambient temperature variation effect was excluded. The uncertainty sources of different operators or different parts of human body were not discussed in this study. The uncertainty analysis has become the basic information for the instrument. No literature or related reports were found that mentioned the evaluation of infrared tympanic thermometers. The method of uncertainty calculation for two types of infrared tympanic thermometers in this study has been developed. This method could be applied for other infrared thermometers.

The authors would to thank the National Science Council of the Republic of China for financially supporting this research under Contract No NSC-95-2313-B-005-019.

The relationship between reading values of MC-510 thermometer

The error distribution of OMRON MC-510 thermometer at three ambient temperatures.

The predicted errors of calibration equation of OMRON MC-510 thermometer.

The relationship between reading values of BRAUN IRT-3020 thermometer

The error distribution of BRAUN IRT-3020 thermometer at three ambient temperatures.

The predicted errors of calibration equation of BRAUN IRT-3020 thermometer.

The standard deviation of five measurements of OMRON MC-510 thermometer at different standard temperatures and three leaves of ambient temperatures.

The standard deviation of five measurements of BRAUN IRT-3020 thermometer at different standard temperatures and three leaves of ambient temperatures.

Specification of the infrared clinical thermometers.

Sensing element | thermopile | thermopile |

Measuring range | 34–42.2 °C | 34–42.2 °C |

Resolution | 0.1 °C | 0.1 °C |

Nonlinearity and repeatability | 1. 36.0–39 °C, ±0.2 °C |
1. 37.0–39 °C, ±0.1 °C |

Analysis of variance ANOVA table for the effect of standard temperature and ambient temperature on the measurement of OMRON MC-510 thermometer.

Standard temp. | 0.003717 | 4 | 0.000929 | 5.9318 | 0.01614 | 3.8379 |

Ambient temp | 0.000832 | 2 | 0.000416 | 2.6552 | 0.1305 | 4.4590 |

Errors | 0.001253 | 8 | 0.000157 | |||

Total | 0.005802 | 14 |

Note: SS is the sum of square, df is the degree of freedom, MS is the mean square and F-critical value is the smallest level of significance that be to reject the hypothesis of F test.

Analysis of variance ANOVA table for the effect of standard temperature and ambient temperature on the measurement of BRAUN IRT-3020 thermometer.

Standard temp. | 0.000133 | 4 | 3.321E-05 | 0.1926 | 0.9355 | 3.8379 |

Ambient temp. | 0.000617 | 2 | 0.000309 | 1.7924 | 0.2274 | 4.4590 |

Errors | 0.001377 | 8 | 0.000172 | |||

Total | 0.002127 | 14 |

The type A uncertainty of several observations for two infrared tympanic thermometers.

_{obs} of different temperatures | ||||||
---|---|---|---|---|---|---|

34.5 | 36.0 | 37.5 | 39.0 | 40.5 | ||

OMRON | None | 0.1799 | 0.2193 | 0.1767 | 0.1408 | 0.1506 |

MC-510 | Polynomial equation | 0.2026 | 0.1990 | 0.1986 | 0.1989 | 0.2100 |

BRAUN | None | 0.0884 | 0.0535 | 0.0567 | 0.0594 | 0.05606 |

IRT-300 | Linear equation | 0.0711 | 0.0704 | 0.0701 | 0.0703 | 0.0709 |

The type B uncertainty analysis for OMRON MC-510 thermometer.

Reference (u_{ref}) |
0.03 °C | 0.0153 | Normal |

Resolution (u_{res}) |
0.1 °C | 0.0289 | Rectangular |

Nonlinear and repeatability | |||

U_{non1} 36–39 °C |
0.2 °C | 0.1155 | Rectangular |

U_{non2} ≤ 36 °C, ≥39 °C |
0.3 °C | 0.1732 |

The type B uncertainty analysis for BRAUN IRT-3020 thermometer.

Reference (u_{ref}) |
0.03 °C | 0.0153 | Normal |

Resolution (u_{res}) |
0.1 °C | 0.0289 | Rectangular |

Nonlinear and repeatability | Rectangular | ||

U_{non1} 37–39 °C |
0.1 °C | 0.0577 | |

U_{non2} ≤ 37 °C, ≥39 °C |
0.2 °C | 0.1155 |

The combined uncertainty for two IR thermometers.

_{obs} of different temperature | ||||||
---|---|---|---|---|---|---|

34.5 | 36.0 | 37.5 | 39.0 | 40.5 | ||

OMRON | None | 0.2 | 0.2 | 0.2 | 0.1 | 0.23 |

MC-510 | Polynomial equation | 519 | 499 | 136 | 851 | 18 |

0.2 | 0.2 | 0.2 | 0.2 | 0.27 | ||

BRAUN | None | 685 | 324 | 321 | 246 | 41 |

IRT-300 | Linear equation | |||||

0.1 | 0.0 | 0.0 | 0.0 | 0.13 | ||

491 | 873 | 872 | 890 | 24 | ||

0.1 | 0.0 | 0.0 | 0.0 | 0.13 | ||

395 | 965 | 965 | 967 | 94 |