# Evaluation of Performance and Uncertainty of Infrared Tympanic Thermometers

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Equipment and Methods

#### 2.1. Infrared Tympanic Thermometer

#### 2.2. Standard Temperature

#### 2.3. Testing Procedures

#### 2.4. Data Analysis

#### 2.5. Establish the Calibration

^{2}, t-tests of each parameters and residual plots [21,22].

_{1}is the reading values of infrared thermometer, b

_{0}, b

_{1}, b

_{2}are parameters.

## 3. Sources of the Uncertainty for Infrared Tympanic Thermometer

#### 3.1. The Standard Deviation

_{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.

#### 3.2. The Calibration Equation

_{y}is calculated by follows:

#### 3.3. Uncertainty of the Reference Temperature

_{ref}is the uncertainty source of TC-2000 temperature calibrator, and u

_{ref}is the uncertainty due to the reference temperature.

#### 3.4. Uncertainty Due to Nonlinearity and Repeatability

_{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.

#### 3.5. Uncertainty Due to Resolution

_{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.

#### 3.6. Uncertainty Due to Ambient Temperature Variation

_{tem}is the uncertainty source due to the ambient temperature; and u

_{tem}is the uncertainty due to the ambient temperature.

_{c}then be calculated as follows:

- Uncertainty estimation of a fixed measuring point.$${u}_{{c}_{1}}=\sqrt{{u}_{x}^{2}+{u}_{\mathit{ref}}^{2}+{u}_{\mathit{non}}^{2}+{u}_{\mathit{res}}^{2}+{u}_{\mathit{tem}}^{2}}$$
- Uncertainty estimation include the effect of calibration$${u}_{{c}_{2}}=\sqrt{{u}_{y}^{2}+{u}_{\mathit{ref}}^{2}+{u}_{\mathit{non}}^{2}+{u}_{\mathit{res}}^{2}+{u}_{\mathit{tem}}^{2}}$$

## 4. Results and Discussions

#### 4.1. Performance of OMRON MC-510 Thermometer

_{sta}is the standard temperature and T

_{rea}is the reading temperature of IR thermometer.

#### 4.2. Performance of BRAUN IRT-3020 Thermometer

#### 4.3. The Replicate of the Infrared Tympanic Thermometer

#### 4.4. Calculation of the Uncertainty of Infrared Tympanic Thermometer

#### 4.5. The Combined Standard Uncertainty

_{c}values for two infrared tympanic thermometers at five observations are listed in Table 7.

_{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 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.

_{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 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.

## 5. Conclusions

## Acknowledgments

## References

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**Figure 4.**The relationship between reading values of BRAUN IRT-3020 thermometer versus standard values.

**Figure 7.**The standard deviation of five measurements of OMRON MC-510 thermometer at different standard temperatures and three leaves of ambient temperatures.

**Figure 8.**The standard deviation of five measurements of BRAUN IRT-3020 thermometer at different standard temperatures and three leaves of ambient temperatures.

OMRON MC-510 | BRAUN IRT-3020 | |
---|---|---|

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 2. (≤36.0, ≥39 °C), ±0.3 °C | 1. 37.0–39 °C, ±0.1 °C 2. (≤37 °C, ≥39 °C), ±0.2 °C |

**Table 2.**Analysis of variance ANOVA table for the effect of standard temperature and ambient temperature on the measurement of OMRON MC-510 thermometer.

Variance | SS | df | MS | F | P-value | F-critical value |
---|---|---|---|---|---|---|

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 |

**Table 3.**Analysis of variance ANOVA table for the effect of standard temperature and ambient temperature on the measurement of BRAUN IRT-3020 thermometer.

Source | SS | df | MS | F | P-value | F-critical value |
---|---|---|---|---|---|---|

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 |

Calibration equations | y_{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 |

Description | Estimate value | Standard uncertainty | Probability distribution |
---|---|---|---|

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 |

Description | Estimate value | Standard uncertainty | Probability distribution |
---|---|---|---|

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 |

IR thermometer | Calibration equation | y_{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 |

© 2010 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license ( http://creativecommons.org/licenses/by/3.0/).

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**MDPI and ACS Style**

Chung, W.; Chen, C.
Evaluation of Performance and Uncertainty of Infrared Tympanic Thermometers. *Sensors* **2010**, *10*, 3073-3089.
https://doi.org/10.3390/s100403073

**AMA Style**

Chung W, Chen C.
Evaluation of Performance and Uncertainty of Infrared Tympanic Thermometers. *Sensors*. 2010; 10(4):3073-3089.
https://doi.org/10.3390/s100403073

**Chicago/Turabian Style**

Chung, Wenbin, and Chiachung Chen.
2010. "Evaluation of Performance and Uncertainty of Infrared Tympanic Thermometers" *Sensors* 10, no. 4: 3073-3089.
https://doi.org/10.3390/s100403073