This extract from the chart comparing standards, which was included in full earlier in this application note, shows that each standard specifies different conditions that must be met if the results of a test are to be accepted as valid.
(1) Mean is the average of the breakdown values recorded in the test sequence. For example, if the breakdown values are 33 kV, 37 kV, 32 kV, 35 kV, 38 kV and 34 kV, the mean value would be the total of these results - 209 - divided by the number of results - 6 - which gives a mean value of 209/6 = 34.83 kV. (Note that in this example there are six results as required by the IEC standard. The ASTM standards require either five or ten results.)
(2) Range of breakdown voltage is referred to in the ASTM standards. For example, D877 specifies that the test sequence must be repeated if the range of breakdown voltages recorded is more than 92% of their mean value. Two examples will make this easier to understand.
- In the first example, the breakdown voltages recorded are 43, 45, 52, 40 and 38 kV. The lowest value is 40 kV and the highest is 52 kV, so the range is 12 kV. The mean of the recorded values is 43.6 kV, so the range is only 12/43.6 x 100% = 27.5% of the mean value. These test results are, therefore, valid.
- In the second example, the breakdown voltages recorded are 33, 45, 52, 18 and 20 kV. The lowest value is 18 kV and the highest is 52 kV, so the range is 34 kV. The mean of the recorded values is 33.6 kV, so the range is 34/33.6 x 100% = 101%. This is above the 92% limit, which means that the test must be repeated.
(3) Standard deviation - In IEC 60156, there is a graphical representation of standard deviation - otherwise known as the coefficient of variation - versus the mean breakdown voltage. Calculation of the mean has already been covered, but what about the standard deviation? IEC 60156 does not explain how to calculate this. The procedure however, is to calculate the difference between each of the six test results and the mean value of those test results. Square each of the differences and add them together. Divide the figure obtained by 2, and then take the square root. The final answer is the standard deviation for the set of test results.
IEC 60156 states that, for the test results to be considered valid, the following procedure must be followed:
(1) Perform six tests
(2) Calculate the mean of the results
(3) Calculate the standard deviation (see above)
(4) Divide the standard deviation by the average value, noting that scatter is expected and acceptable. (See the chart at the end of IEC 60156)
(5) If the value is acceptable, conclude testing
(6) If not, perform six more tests
(7) Repeat the calculations using all 12 results