Quality Assurance in the Calibration of Platinum Resistance Thermometers (Pt-100) at NIS

Doaa Mohamed Abd-ElGalil; Essam Mahmoud; A. El-Matarawey

doi:10.2478/msr-2026-0016

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Quality Assurance in the Calibration of Platinum Resistance Thermometers (Pt-100) at NIS

Measurement Science Review

Volume 26 (2026): Issue 3 (June 2026)

By: Doaa Mohamed Abd-ElGalil , Essam Mahmoud and A. El-Matarawey

Open Access

|Apr 2026

Figures & Tables

Upper control limit (UCL)	UCL = Mean + 3StD = X + 3σ
Upper warning limit (UWL)	UWL = Mean + 2StD = X + 2σ
Control line (CL)	CL = Mean X
Lower warning limit (LWL)	LWL = Mean − 2StD = X − 2σ
Lower control limit (LCL) CL = Mean − 3StD = X − 3σ

[i] Note: UWL and LWL are calculated using the mean $μ \pm k \hat{σ}$ , where $\hat{σ}$ represents an estimate of the process population standard deviation, calculated from sample data using either the sample standard deviation s or the range-based estimator $\hat{σ} = \bar{R} / d_{2}$ where the constants A₂, D₃, D₄, and d₂ are defined in Table 2. Since the population standard deviation is unknown, the sample standard deviation is used as its estimator. These limits provide early warnings before reaching control limits.

Table 1.

Distinction between Shewhart and Westgard rules in quality control.

Aspect	Shewhart rules	Westgard rules
Origin	Walter A. Shewhart (industrial SPC)	James Westgard (clinical chemistry QC)
Application area	Manufacturing, engineering, calibration	Clinical laboratories, patient testing
Focus	Process stability & control	Analytical run validity & error detection
Tools used	X̅, R, S control charts	QC charts with multi-rule criteria
Decision outcome	Detects out-of-control process behavior	Accept/reject patient test runs

Table 2.

Control chart constants (X̅- and R-charts).

Sample size = m	A₂	A₃	d₂	D₃	D₄	B₃	B₄
2	1.880	2.659	1.128	0	3.267	0	3.267
3	1.023	1.954	1.693	0	2.574	0	2.568
4	0.729	1.628	2.059	0	2.282	0	2.266
5	0.577	1.427	2.326	0	2.114	0	2.089
6	0.483	1.287	2.534	0	2.004	0.030	1.970
7	0.419	1.182	2.704	0.076	1.924	0.118	1.882
8	0.373	1.099	2.847	0.136	1.864	0.185	1.815
9	0.337	1.032	2.97	0.184	1.816	0.239	1.761
10	0.308	0.975	3.078	0.223	1.777	0.284	1.716

[i] Note:

A₂, A₃ – factors for calculating control limits in X̅-chart;
D₃, D₄ – factors for calculating control limits in R-chart;
d₂ – factor used to estimate standard deviation from range (σ ≈ R̅/d₂);
B₃, B₄ – control chart constants used for constructing S-chart limits.

Table 3.

The uncertainty budget of the platinum resistance thermometer (Pt-100) at 200 °C.

Symbol	Source uncertainty	Value X_i ± (°C, Ω)	Divisor	Sensitivity coefficient	Uncertainty contribution	Method of estimation
U_st1	Uncertainty of standard	0.005	2	1	0.0025	Calibration certificate
U_res	Resolution	0.0001	3.46	1	2.88675E-05	Digital indicator = 0.5 of resolution
U_mul	Bridge	0.0003	2	2.5	0.00037	Calibration certificate
U_drf	Drift of bridge	0	2	1	0	Maximum difference between two successive calibrations of the standard
U_{res uut}	Resolution of UUT	0.001	3.46	1	0.00028	Digital indicator = 0.5 of resolution
U_axi	Axial of dry block	0.07	1.73	1	0.040	Maximum difference between dry block holes for axial measurement
U_rad	Radial of dry block	0.04	1.73	1	0.023	Maximum difference between dry block holes for radial measurement
U_stab	Stability of dry block	0.05	3.46	1	0.0144	Difference between maximum and minimum value of measurements
U_hyst	Hysteresis effects	0.01	1.73	1	0.007	Maximum difference between increase and decrease measurements
U_rep	Repeatability (A)	0.002	1	1	0.002	Standard deviation of measurements
	Combined uncertainty				0.049
	Expanded uncertainty				± 0.09 oC

Table 4.

The raw calibration readings of Pt-100 thermometer at (200 °C, 150 °C, and 70 °C).

Setting	Groups	Reading [°C]
1	2	3	4	5
200 °C	1	200.4	200.5	200.5	200.4	200.5
	2	200.6	200.6	200.5	200.5	200.6
	3	200.3	200.5	200.4	200.6	200.7
4	200.6	200.5	200.5	200.4	200.6
5	200.3	200.4	200.6	200.5	200.5
Setting	Groups	Reading [°C]
1	2	3	4	5
150 °C	1	148.8	148.6	148.7	148.8	148.5
	2	148.7	148.6	148.5	148.7	148.6
	3	148.7	148.6	148.8	148.7	148.7
4	148.9	148.7	148.8	148.7	148.6
5	148.7	148.8	148.7	148.6	148.7
Setting	Groups	Reading [°C]
1	2	3	4	5
70 °C	1	67.5	67.6	67.5	67.3	67.5
	2	67.7	67.6	67.5	67.4	67.6
	3	67.3	67.5	67.4	67.6	67.7
4	67.6	67.7	67.5	67.4	67.6
5	67.2	67.4	67.6	67.6	67.5

Table 5.

Control charts, constants, and calculated limits for Pt-100 calibration subgroup statistics.

X̅	R	S	σ	X̿	R̅	S̅
67.48	0.3	0.109544512	0.130128142	67.512	0.34	0.126802209
67.56	0.3	0.114017543
67.50	0.4	0.129099445
67.56	0.3	0.114017543
67.46	0.4	0.167332005

A₂	B₃	B₄	D₃	D₄	X̅_UCL	X̅_LCL	R_UCL	R_LCL	S_UCL	S_LCL
0.577	0	2.089	0	2.114	67.69664	67.32736	0.718	0	0.2681	0

Table 6.

The calculated control limits for the platinum resistance thermometer (Pt-100) calibration process over multiple years.

Date	Reading [°C]	X̿ [°C]	1σ	2σ	3σ	1σ	2σ	3σ
Date	Reading [°C]	X̿ [°C]	UWL [°C]			LWL [°C]
20 March 2021	67.48	67.512	67.64212814	67.77225628	67.90238443	67.38187186	67.25174372	67.12161557
20 June 2021	67.60	67.512	67.64212814	67.77225628	67.90238443	67.38187186	67.25174372	67.12161557
12 September 2021	67.42	67.512	67.64212814	67.77225628	67.90238443	67.38187186	67.25174372	67.12161557
22 December 2021	67.56	67.512	67.64212814	67.77225628	67.90238443	67.38187186	67.25174372	67.12161557
22 March 2022	67.54	67.512	67.64212814	67.77225628	67.90238443	67.38187186	67.25174372	67.12161557
22 June 2022	67.50	67.512	67.64212814	67.77225628	67.90238443	67.38187186	67.25174372	67.12161557
22 September 2022	67.60	67.512	67.64212814	67.77225628	67.90238443	67.38187186	67.25174372	67.12161557
22 December 2022	67.50	67.512	67.64212814	67.77225628	67.90238443	67.38187186	67.25174372	67.12161557
19 March 2023	67.56	67.512	67.64212814	67.77225628	67.90238443	67.38187186	67.25174372	67.12161557
19 June 2023	67.48	67.512	67.64212814	67.77225628	67.90238443	67.38187186	67.25174372	67.12161557
19 September 2023	67.42	67.512	67.64212814	67.77225628	67.90238443	67.38187186	67.25174372	67.12161557
22 December 2023	67.60	67.512	67.64212814	67.77225628	67.90238443	67.38187186	67.25174372	67.12161557
19 March 2024	67.46	67.512	67.64212814	67.77225628	67.90238443	67.38187186	67.25174372	67.12161557
25 June 2024	67.54	67.512	67.64212814	67.77225628	67.90238443	67.38187186	67.25174372	67.12161557
25 September 2024	67.60	67.512	67.64212814	67.77225628	67.90238443	67.38187186	67.25174372	67.12161557
19 December 2024	67.50	67.512	67.64212814	67.77225628	67.90238443	67.38187186	67.25174372	67.12161557

X̅ control chart for Pt-100 calibration readings.

R control chart for Pt-100 calibration readings.

3σ̂ (estimated from sample data) chart for Pt-100 calibration readings.

Articles in this issue

DOI: https://doi.org/10.2478/msr-2026-0016 | Journal eISSN: 1335-8871

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Language: English

Page range: 127 - 135

Submitted on: Jun 11, 2025

Accepted on: Feb 11, 2026

Published on: Apr 11, 2026

Published by: Slovak Academy of Sciences, Institute of Measurement Science

In partnership with: Paradigm Publishing Services

Publication frequency: Volume open

Keywords:

quality assurance,

Pt-100,

calibration laboratory,

statistical process control,

Related subjects:

Electrical engineering,

Control engineering, metrology and testing

© 2026 Doaa Mohamed Abd-ElGalil, Essam Mahmoud, A. El-Matarawey, published by Slovak Academy of Sciences, Institute of Measurement Science
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 26 (2026): Issue 3 (June 2026)

Quality Assurance in the Calibration of Platinum Resistance Thermometers (Pt-100) at NIS

Figures & Tables

Table 1.

Fig. 1.

Table 2.

Table 3.

Table 4.

Table 5.

Table 6.

Fig. 2.

Fig. 3.

Fig. 4.

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