Evaluation of Uncertainty in Basic Error Measurement of DC Resistance Tester

1.Overview

1.1 Measuring method: refer to JJG 837-2003 Verification Regulations of DC Low Resistance Meter

1.2 Environment condition: in most cases, keep the temperature 20 ± 5 ℃ and the relative humidity is no higher than 75%.    

1.3 Measuring standards: BZ3 standard resistance; main technical indicator is 0.01 level

1.4 Test object: DC resistance tester with 0.1 precision level

1.5 Measuring method: adopt 4-terminal connection method; standard resistance is connected to test end of DC resistance tester and then conduct digital comparison to determine the basic error of DC resistance tester.

 2.Mathematical Model

δ= r - r

In the formula: r  display value of DC resistance tester

r— nominal value of standard resistance

3.Transmission Rate of Uncertainty

4.Evaluation of Input Standard Uncertainty

4.1 Evaluation of standard uncertainty u(r) of input r

In most cases, the error of BZ3 standard resistance may cause the uncertainty u(r) of input r. The evaluation is mainly based on technical requirements of standard resistance.

Maximum tolerance error of standard resistance: ± 0.01

1Ω - maximum tolerance error: ± 0.1Ω    half width α = 0.1mΩ 

Within the interval, we can assume that it is subject to uniform distribution and includes the factor 

4.2 Evaluation of the uncertainty u(r) in display resolution of DC resistance tester

In most cases, the component of standard uncertainty is introduced via resolution displayed by digital meter. The resolution is 0.1mΩ. As for the quantization of digital meter, because of the error, it is assumed that the distribution is uniform within the resolution range and it includes factor k. Hence, the standard uncertainty introduced within the range of half width is as follows:    

4.3 Evaluation of the standard uncertainty u(r) of input r

Generally speaking, the uncertainty of input r is caused by measuring repeatability of DC resistance tester. Meanwhile, measuring series are obtained through continuous measurement. Conduct corresponding evaluation via A-type method.   

Connect standard resistance with 1Ω nominal value to test end of DC resistance tester and start the DC resistance tester. Then the measuring series is as follows: 999.9mΩ, 999.8mΩ, 999.9mΩ, 999.9mΩ, 1000.0mΩ, 1000.1mΩ, 1000.2mΩ, 999.9mΩ, 999.9mΩ,, 999.9mΩ, 1000.0mΩ.

u(r)=s=0.111mΩ

 5.Evaluation of synthetic standard uncertainty

5.1 Summary of main standard uncertainties

5.2 Evaluation of synthetic standard uncertainty 

Generally speaking, the input rand r are independent. To some extent, the synthetic standard uncertainty can be calculated according to the following formula:  

Relative standard uncertainty is used to express:

6.Evaluation of expanded uncertainty

k=2, the expanded uncertainty is

U= k × U= 2 ×0.0128% = 0.026%

7.Report and expression of uncertainty in measurement

The DC resistance tester with 0.1 precision level is utilized. Expanded uncertainty of resistance measuring is as follows: 

U= 0.025%  k=2