Appendix C to Subpart C of Part 429 - Sampling Plan for Enforcement Testing of Distribution Transformers

Appendix C to Subpart C of Part 429 - Sampling Plan for Enforcement Testing of Distribution Transformers

(a) When testing distribution transformers, the number of units in the sample (m₁) shall be in accordance with § 429.47(a) and DOE shall perform the following number of tests:

(1) If DOE tests four or more units, it will test each unit once;

(2) If DOE tests two or three units, it will test each unit twice; or

(3) If DOE tests one unit, it will test that unit four times.

(b) DOE shall determine compliance as follows:

(1) Compute the mean (X₁) of the measured energy performance of the n₁ tests in the first sample as follows:

where X_i is the measured efficiency of test i.

(2) Compute the sample standard deviation (S₁) of the measured efficiency of the n₁ tests in the first sample as follows:

(3) Compute the standard error (SE(X₁)) of the mean efficiency of the first sample as follows:

(4) Compute the sample size discount (SSD(m₁)) as follows:

where m₁ is the number of units in the sample, and RE is the applicable DOE efficiency when the test is to determine compliance with the applicable energy conservation standard, or is the labeled efficiency when the test is to determine compliance with the labeled efficiency value.

(5) Compute the lower control limit (LCL₁) for the mean of

(6) Compare the mean of the first sample (X₁) with the lower control limit (LCL₁) to determine one of the following:

(i) If the mean of the first sample is below the lower control limit, then the basic model is not compliant and testing is at an end.

(ii) If the mean is equal to or greater than the lower control limit, no final determination of compliance or noncompliance can be made; proceed to Step (7).

(7) Determine the recommended sample size (n) as follows:

Given the value of n, determine one of the following:

(i) If the value of n is less than or equal to n₁ and if the mean energy efficiency of the first sample (X₁) is equal to or greater than the lower control limit (LCL₁), the basic model is in compliance and testing is at an end.

(ii) If the value of n is greater than n₁, the basic model is not compliant. The size of a second sample n₂ is determined to be the smallest integer equal to or greater than the difference n−n₁. If the value of n₂ so calculated is greater than 21−n₁, set n₂ equal to 21−n₁.

(8) Compute the combined (X₂) mean of the measured energy performance of the n₁ and n₂ units of the combined first and second samples as follows:

(9) Compute the standard error (SE(X₂)) of the mean full-load efficiency of the n₁ and n₂ units in the combined first and second samples as follows:

(Note that S₁ is the value obtained above in (2).)

(10) Set the lower control limit (LCL₂) to,

where t has the value obtained in (5) and SSD(m₁) is sample size discount determined in (4), and compare the combined sample mean (X₂) to the lower control limit (LCL₂) to determine one of the following:

(i) If the mean of the combined sample (X₂) is less than the lower control limit (LCL₂), the basic model is not compliant and testing is at an end.

(ii) If the mean of the combined sample (X₂) is equal to or greater than the lower control limit (LCL₂), the basic model is in compliance and testing is at an end.

[76 FR 12451, Mar. 7, 2011; 76 FR 24781, May 2, 2011]