26.1 The precision, bias and lower limit of detection of Method B have been evaluated by a statistical examination of the results of an inter-laboratory test of mineral oil test specimens. A lower limit of repetition is defined here as an aid in the testing of transformers in factories.
26.2 Precision - Repeatability - The expected difference between successive results obtained on identical test specimens by the same operator using the same apparatus and normal and correct operation of the test method.
26.2.1 Combustible Gases and Carbon Dioxide - Repeatability of the determination of each individual combustible gas and of carbon dioxide was found to vary linearly with individual gas concentration level. The repeatability interval at the 95 % confidence level for the determination of a combustible gas n or of CO2, ln(r)95 % can be represented by:
26.2.2 Oxygen and Nitrogen - The ranges of concentrations of oxygen and of nitrogen in the test specimens analyzed in the interlaboratory test were relatively narrow. Therefore the relationships between repeatability intervals and concentrations of dissolved O2 or of N2 are not well defined. The coefficients of variation, S(r), at the 50 % confidence level for the repeatability of the determination of O2 and of N2 and the concentration ranges tested are given in Table 2.
26.3 Precision - Reproducibility - The expected difference between two results obtained on identical test specimens by different operators working in different laboratories and normal and correct operation of the test method.
26.3.1 Combustible Gases and Carbon Dioxide - Reproducibility of the determination of each individual combustible gas and of carbon dioxide was found to vary linearly with individual gas concentration level. The reproducibility interval at the 95 % confidence level for the determination of a combustible gas n or of CO2, ln(R)95 % can be represented by:
26.3.2 Oxygen and Nitrogen - The ranges of concentrations of oxygen and of nitrogen contained were relatively narrow in the specimens analyzed in the inter-laboratory test. Therefore the relationships between reproducibility intervals and concentration of dissolved O2 or N2 are not well defined. The coefficients of variation, S(R), at the 50 % confidence level for the reproducibility of the determination of O2 and of N2 and the concentration ranges tested are given in Table 2.
26.4 Bias - The difference between the mean of results obtained for a gas in a test specimen and the "true" (that is, spiked) value of the concentration of that gas in the tested material.
26.4.1 Combustible Gases - Bias of the determination of each individual combustible gas was found to vary linearly with individual gas concentration level. The relative bias, Bn, for the determination of a combustible gas, n, can be represented by:
NOTE 8 - The distributions of results for the determination of hydrogen by Method B are bipolar (see Fig. 6). The results from twelve laboratories form primary nodes centered about the "true" concentrations of test specimens. The biases reported in Table 2 are based on these primary nodes. The results from five labs form secondary nodes at or near concentrations of zero. This emphasizes the need for a routine QA protocol for the determination of H2 by Method B.
26.4.2 Carbon Dioxide - Bias for the determination of carbon dioxide decrease with increasing CO2. No analytical transformation adequately fits the results; these results are shown graphically in Fig. 5. It is possible that the positive bias at lower concentrations results, in part, from contamination by air.
26.4.3 Oxygen and Nitrogen - The bias for determinations of O2 and of N2 are positive and variable. It is possible that positive bias is, in part, the result of contamination by air. Also, the ranges of concentrations of oxygen and of nitrogen in the test specimens analyzed in the interlaboratory test were relatively narrow. The relationships between bias and dissolved concentration of O2 or of N2 then are not well defined. The coefficients of variation, S(R), at the 50 % confidence level for the reproducibility of the determination of O2 and of N2 and the concentration ranges tested are given in Table 2.
26.5 Method Detection Limit - The method detection limit (MDL) for a gas is the minimum value of concentration of that gas that can be distinguished from zero with a confidence of 95 %. The MDL for each gas is determined from the reproducibility found for the analysis of that gas at levels near the MDL.
26.5.1 Combustible Gases - The MDL for each of the combustible gases determined from the reproducibility of the method and the concentration ranges tested are given in Table 3.
26.5.2 Carbon Dioxide, Oxygen and Nitrogen - The MDL of CO2, of O2 and of N2 could not be determined from the test specimens analyzed in the interlaboratory test because the concentrations were too high.
26.6 Method Repetition Limit - A Method Repetition Limit (MRL) is defined here as an aid in determining whether the concentration of a combustible gas truly changes during a factory test. This MRL is the minimum value by which the results of determinations of a gas must differ for these results to be statistically different at the 95 % confidence level. Changes in concentrations of combustible gases at values near minimum detection limits are useful in evaluating the performance of a newly manufactured or repaired transformer during factory testing prior to shipment for installation. Analyses of gases during factory test are usually conducted in a single laboratory; the MRL for each gas then is determined from the repeatability found for the analysis of that gas at levels near the MDL.
26.6.1 Combustible Gases - The MRL for each of the combustible gases determined from the repeatability of the method and the concentration ranges tested are given in Table 3.
26.6.2 Carbon Dioxide, Oxygen and Nitrogen - The MRL of CO2, of O2 and of N2 could not be determined from the test specimens analyzed in the interlaboratory test.