10 CFR Appendix A to Subpart U of Part 431 - Sampling Plan for Enforcement Testing of Electric Motors

Step 1. The first sample size (n1) must be five or more units.

Step 2. Compute the mean (X

1 of the measured energy performance of the n1 units in the first sample as follows:

${\stackrel{—}{X}}_1=\frac{1}{n_1}\sum _{i=1}^{n_1}{X}_i\text{(1)}$

where Xi is the measured full-load efficiency of unit i.

Step 3. Compute the sample standard deviation (S1) of the measured full-load efficiency of the n1 units in the first sample as follows:

$S_1=\sqrt{\frac{\sum _{i=1}^{n_1}{(X_i-{\stackrel{—}{X}}_1)}^2}{n_1-1}}\text{(2)}$

Step 4. Compute the standard error (SE(X

1)) of the mean full-load efficiency of the first sample as follows:

$\mathrm{SE}\left({\stackrel{—}{X}}_1\right)=\frac{S_1}{\sqrt{n_1}}\text{(3)}$

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

$LC{L}_1=RE-tSE\left({\stackrel{—}{X}}_1\right)\text{(4)}$

where: RE is the applicable EPCA nominal full-load efficiency when the test is to determine compliance with the applicable statutory standard, or is the labeled nominal full-load efficiency when the test is to determine compliance with the labeled efficiency value, and 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 6. Compare the mean of the first sample (X

1) 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 7.

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

$n={\left[\frac{t{S}_1\left(120-0.2RE\right)}{RE\left(20-0.2RE\right)}\right]}^2\text{(5)}$

where S1, RE and t have the values used in Steps 3 and 5, respectively. The factor

$\frac{120-0.2RE}{RE\left(20-0.2RE\right)}$

is based on a 20 percent tolerance in the total power loss at full-load and fixed output power.

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 (X

1) 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 in non-compliance. 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 20−n1, set n2 equal to 20−n1.

Step 8. Compute the combined (X

2) mean of the measured energy performance of the n1 and n2 units of the combined first and second samples as follows:

${\stackrel{—}{X}}_2=\frac{1}{n_1+n_2}\sum _{i=1}^{n_1+n_2}{X}_i\text{(6)}$

Step 9. Compute the standard error (SE(X

2)) of the mean full-load efficiency of the n1 and n2 units in the combined first and second samples as follows:

$\mathrm{SE}\left({\stackrel{—}{X}}_2\right)=\frac{S_1}{\sqrt{n_1+n_2}}\text{(7)}$

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

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

${\mathrm{LCL}}_2=\mathrm{RE}-\mathrm{tSE}\left({\stackrel{—}{X}}_2\right)\left(8\right)\sqrt{b^2-4\mathrm{ac}}$

where t has the value obtained in Step 5, and compare the combined sample mean (X

2) to the lower control limit (LCL2) to find one of the following:

(i) If the mean of the combined sample (X

2) 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 (X

2) 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 10, of this appendix A, 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 full-load efficiency, standard error, and lower control limit of the new combined sample in accordance with the procedures prescribed in Steps 8, 9, and 10, of this appendix A.

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.