Appendix B to Subpart K of Part 431 - Sampling Plan for Enforcement Testing

Step 1. The number of units in the sample (m1) shall be in accordance with §§ 431.198(a)(4), 431.198(a)(5), 431.198(a)(6) and 431.198(a)(7) and shall not be greater than twenty. The number of tests in the first sample (n1) shall be in accordance with § 431.198(a)(8) and shall be not fewer than four.

Step 2. Compute the mean (Xi) of the measured energy performance of the n1 tests in the first sample by using equation 1 as follows:

$ER27AP06.031$ where Xi is the measured efficiency of test i.

Step 3. Compute the sample standard deviation (S1) of the measured efficiency of the n1 tests in the first sample by using equation 2 as follows:

$ER27AP06.032$

Step 4. Compute the standard error (SE(X1)) of the mean efficiency of the first sample by using equation 3 as follows:

$ER27AP06.033$

Step 5. Compute the sample size discount (SSD(m1)) by using equation 4 as follows:

$ER27AP06.034$ where m1 is the number of units in the sample, and RE is the applicable EPCA efficiency when the test is to determine compliance with the applicable statutory standard, or is the labeled efficiency when the test is to determine compliance with the labeled efficiency value.

Step 6. Compute the lower control limit (LCL1) for the mean of the first sample by using equation 5 as follows:

$ER27AP06.035$ where t is the 2.5th percentile of a t-distribution for a sample size of n1, which yields a 97.5 percent confidence level for a one-tailed t-test.

Step 7. 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 in non-compliance 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 non-compliance can be made; proceed to Step 8.

Step 8. Determine the recommended sample size (n) by using equation 6 as follows:

$ER27AP06.036$ where S1 and t have the values used in Steps 3 and 6, respectively. The factor $ER27AP06.037$ is based on an 8-percent tolerance in the total power loss.

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, and no additional units are available for testing, testing is at an end and the basic model is in non-compliance. If the value of n is greater than n1, and additional units are available for testing, select a second sample n2. The size of the n2 sample 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 20-n1, set n2 equal to 20-n1.

Step 9. After testing the n2 sample, compute the combined mean (X2) of the measured energy performance of the n1 and n2 tests of the combined first and second samples by using equation 7 as follows:

$ER27AP06.038$

Step 10. Compute the standard error (SE(X2)) of the mean efficiency of the n1 and n2 tests in the combined first and second samples by using equation 8 as follows:

$ER27AP06.039$ (Note that S1 is the value obtained above in Step 3.)

Step 11. Set the lower control limit (LCL2) to,

$ER27AP06.040$ where t has the value obtained in Step 5 and SSD(m1) is sample size discount from Step 5. Compare the combined sample mean (X2) to the lower control limit (LCL2) to find 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 in non-compliance 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.

Manufacturer-Option Testing

If a determination of non-compliance is made in Steps 6, 7 or 11, above, the manufacturer may request that additional testing be conducted, in accordance with the following procedures.

Step A. The manufacturer requests that an additional number, n3, of units be tested, with n3 chosen such that n1+n2+n3 does not exceed 20.

Step B. Compute the mean efficiency, standard error, and lower control limit of the new combined sample in accordance with the procedures prescribed in Steps 8, 9, and 10, above.

Step C. Compare the mean performance of the new combined sample to the lower control limit (LCL2) to determine one of the following:

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

(b) If the new combined sample mean is less than the lower control limit and the value of n1+n2+n3 is less than 20, the manufacturer may request that additional units be tested. The total of all units tested may not exceed 20. Steps A, B, and C are then repeated.

(c) Otherwise, the basic model is determined to be in non-compliance.