^1ST1R X092

Analysis of Proposals for Compliance and Enforcement

Testing Under the New Part 431; Title 10, Code of Federal

Regulations

K.L. Strickle tt

M. Vangel

Electronics and Electrical Engineering

Laboratory

and

Information Technology Laboratory

National Institute of Standards

and Technology

Gaithersburg, MD 20899-0001

January 1998

ENT OF CO

rP y N

Z^O6TA OF TES

U.S. DEPARTMENT OF COMMERCE

William M . Daley, Secretary

TECHNOLOGY ADMINISTRATION

Gary Bachula, Acting Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS

AND TECHNOLOGY

Raymond G. Kammer, Director

EE-RM-96-400-CSA COMMENT 58
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EE-RM-96-400-CSA COMMENT 58
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Executive Summary

This report was prepared at the request of the Office of Codes and Standards of

the U.S. Department of Energy (DOE). It analyzes two proposals for establishing

compliance with the average efficiency levels prescribed by section 342(b)(1) of the

Energy Policy and Conservation Act of 1975, as amended (EPCA): The Department

of Energy's Proposed Rule for Electric Motors, at 10 Code of Federal Regulations

Part 431, sections 431.24 and 431.127, published in the Federal Register, November

27, 1996; and the April 18, 1997, "Proposal for the Method of Determining Compliance and Enforcement for Electric Motors under the Efficiency Labeling Program

of DOE, 10 CFR Part 431," submitted by the Motor and Generator Section of the

National Electrical Manufacturers Association (NEMA).

Under section 431.24 of the DOE's Proposed Rule for compliance with EPCA, the

manufacturer would determine the average full-load efficiency of each basic model

of electric motor either by testing or by application of an Alternative Efficiency

Determination Method (AEDM). Under section 431.127 of DOE's Proposed Rule

for enforcement of EPCA, the DOE would ascertain. through an enforcement sampling plan, the accuracy of information disclosed in the labeling and the marking of

the electric motor to indicate its energy efficiency, and whether the motor complies

with EPCA standards.

During the public comment period. NEMA raised issues concerning the DOE's

proposed sampling plans for compliance and enforcement. According to NEM A, the

compliance criteria in the Proposed Rule are inconsistent with NEMA Standards

Publication MG1-1993. "Motors and Generators," and place a high burden on

manufacturers. Moreover, NEMA contends that the Proposed Rule would require

that electric motors covered by EP CA be engineered to exceed the average full-load

efficiency levels prescribed by EPCA.

This report evaluates the operating characteristics of the DOE's and NEM A's proposals within the context of EPCA: Compliance with the energy efficiency levels

for motors prescribed by section 342(b)(1) of EPCA appears to be satisfied when

the true mean full-load efficiency of the population of each basic model of electric

motor equals or exceeds the applicable nominal full-load efficiency.

n1

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Contents

Introduction 1

Methods 1

Compliance testing 3

Enforcement testing 4

Concluding remarks 5

Summary 7

Appendix A: NOPR-Compliance Criteria 15

Appendix B: NOPR-AEDM Substantiation 17

Appendix C: NOPR-Sampling Plan for Enforcement Testing 19

Appendix D: The NEMA Proposal 21

Appendix E: Supplemental Analysis 29

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EE-RM-96-400-CSA COMMENT 58
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Analysis of Proposals for Compliance and Enforcement

Testing Under the New Part 431; Title 10, Code of Federal

Regulations

Introduction

This report was prepared at the request of thf, Office of Codes and Standards of the U.S. Depart.nent

of Energy (DOE). It analyzes various criteria and :,ampling plans proposed for establishing compliance -6th

the nominal full-load efficiency levels prescribed by

the Energy Policy and Conservation Act (EPCA), 42

L.S.C. 6313(b)(1) [1].1 The report discusses, in detail,

two proposals: (1) the Notice of Proposed Rulemaking

(NC-PR) for electric motors published in the Federal

Register on November 27, 1996 [2]; and (2) a proposal

prepared by the National Electrical Manufacturers Association (NEMA), Motor and Generator Section [3],

which was submitted in response to the call for public

comment given in the NOPR.

This report evaluates the operating characteristics of

these proposals in the context of the EPCA requirements. Section 342(b)(1) of EPCA requires that each

electric motor manufactured (alone or as a component

of another piece of equipment) have a nominal full-load

efficiency of not less than the prescribed level. This report assumes that the energy efficiency requirement of

the legislation is satisfied if the mean full-load efficiency

of the entire population of motors of each basic model

covered by the legislation equals or exceeds the applicable nominal efficiency.

Under the NOPR, efficiency testing is required in three

contexts:

1. compliance testing,

2. substantiation of Alternative Efficiency Determination Methods (AEDM), and

3. enforcement testing.

The statement submitted by the NEMA, Motor an

Generator Section [3], raises significant issues regarding

the NOPR:

'Numbers in square brackets refer to articles listed in the

References.

i. The electric motor manufacturers maintain that

the NOPR compliance criteria (1) are inconsistent

with NEMA Standard MG 1-1993 [4], (2) place

a high burden on manufacturers in that the risk

of false determination of noncompliance can be

as high as 50 percent for motors in compliance

with the NEMA labeling guidelines, and (3) in

effect, ensure compliance with the EPCA energy

efficiency levels for electric motors by requiring

that covered equipment be engineered to exceed

the average full-load efficiency levels established

by EPCA.

2. The electric motor manufactureres maintain that

the methods proposed for compliance and enforcement testing by the NOPR are not harmonized.

This report seeks to clarify such issues.

Methods

This report compares the NOPR and NEMA proposals

through model calculations of their operating characteristics, i.e., an estimated probability of demonstrating

compliance for a population of motors having a specific

mean efficiency and standard deviation . Modeling the

operating characteristics of the NOPR and NEMA proposals requires detailed information about the distribution of motor efficiencies. Ideally, such model calculations would be based on energy efficiency data gathered from extensive testing; in the absence of such

data, however, this report must infer information from

the energy efficiency labeling guidelines established by

NEMA Standard MG 1-1993. Such guidelines were developed by consensus among motor manufacturers and

are voluntarily followed by many motor manufacturers.

To quote from NEMA MG1-1993 , paragraph 12.58.2,

Efficiency of Polyphase Squirrel-Cage Medium Motors

with Continuous Rating [4]:

Variations in materials, manufacturing processes, and tests result in motor-to-motor efficiency variations for a given motor design;

1

I

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NISTIR 6092

the full-load efficiency for a large population

of motor of a single design is not a unique efficiency but rather a band of efficiency. Therefore, Table 12-8 [of NEMA MG1-1993] has

been established to indicate a logical series of

nominal motor efficiencies and the minimum

associated with each nominal. The nominal

efficiency represents a value which should be

used to compute the energy consumption of a

motor or a group of motors.

Although the MG 1 guidelines were developed primarily to provide uniformity in motor efficiency labeling,

they are used for I urposes of quality control by many

manufacturers and may, taerefore, provide a reasonable

basis to estimate of iriency performance.

The analysis contait.ed in this report is of value primarily as a qualitative comparison of the operating characteristics of the NOPR and NEMA proposals, and,

secondarily, as a quantitativ. estimate of the risk, or

statistical confidence, associat.-d with motor testing under such proposals. The quantitative estimation of risk

can be tenuous, since the results of these calculations

depend on the model assumptions. Consequently, high

significance should not be placed on these estimates of

risk.

Industry practice

Guidelines for motor efficiency labeling are provided

in paragraph 12.58.2 of NEMA Standard MG 1-1993.

Table 12-8 of that section establishes a series of Nominal Efficiencies that are used for purposes of labeling

and a Minimum Efficiency associated with each Nominal value. Under the MG 1 guidelines. two conditions

must be satisfied for a motor to be labeled at a given

Nominal Efficiency:

1 . " ... the Nominal Efficiency... shall be not greater

than the average efficiency of a large population of

motors of the same design."

2. "The full-load efficiency... shall be not less than

the minimum value... associated with the nominal

value..."

The MG 1 guidelines are shown graphically in Fig. 1.

In the figure, the Nominal Efficiencies are indicated

by their full-load losses, where 100 percent of the

full-load losses is equal to the difference, 100 -

Nominal Efficiency. For this discussion, we define the

loss fraction by the ratio,

100 - True Full-load Efficiency x 100,

Loss Fraction = 100 - Nominal Efficiency

01

l i

W 110 100

L*s Fraction (Percent of Full-Load Losses)

Figure 1: Graphical representation of MG I efficiencies.

EPCA nominal efficiencies correspond to the vertical line at

100 percent of f il-load losses. The vertical lines grouped

around 90 percent and 110 percent correspond respectively

to the next higher and lower MG 1 Nominal Efficiencies.

The MG 1 Minimum Efficiencies correspond to the vertical

lines grouped around 120 percent. A normal distribution

with mean of 100 percent and 3a equal to 20 percent is also

shown in the figure.

ANALYSIS OF PROPOSALS FOR

kraeasinp ENiaency --+

which is given in percent. Values of loss fraction corresponding to the EPCA nominal efficiencies are plotted

in Fig. 1, i.e.,

Loss Fraction,

100 - Nominal Efficiency

x 100,

100 - Nominal Efficiencyi

for j = i + 1, i, i -1, and i - 2. The index i is assigned to

the Nominal Efficiencies presented in Table 12-8 of the

MG 1 standard: It is a positive integer that increases

with the efficiency. We have chosen this graphical representation to illustrate the operating characteristics of

the NOPR and NEMA proposals over the full range of

the EPCA nominal efficiencies, and to give an indication of the precision that underlies the MG 1 standard.

The MG 1 guidelines establish efficiency levels that

differ by increments corresponding to 110 percent of

the full-load losses. The vertical lines grouped around

90 percent and 110 percent in the figure correspond

respectively to the next higher and lower Nominal Efficiencies; and the MG 1 Minimum Efficiencies correspond to the vertical lines grouped around 120 percent.

The values of loss fraction fall over a range of values due

to rounding in the least significant digit in the efficiencies given in Table 12-8.

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COMPLIANCE AND ENFORCEMENT TESTING

Model Assumptions

Following methods used by the NEMA, Motor and

Generator Section, we assume that motor efficiencies

are normally distributed [5]. The efficiency distributions are thus characterized by two parameters: the

true mean efficiency and the standard deviation, Q. Expectation values for the minimum average efficiencies

may be clearly established from the MG I guidelines;

however, the standard deviation is not as clearly defined: Since, for normally distributed efficiencies, there

is a finite probability that a motor may test at any arbitrarily low value, there is no minimum efficiency, per

se.

We make the following assumptions for these calculations:

1. The efficiencies of' units of a basic model are normally distributed about the true mean efficiency,

2. The true mean efficiency i; equal to the Nominal

Efficiency,

3. The standard deviation of motor efficiencies is

given by the following formula:

Q= , and (1) Nominal Eff. - Minimum Eff.

3

4. The motors tested are selected at random from a

population of motors that is representative of the

motors sold and in use.

We infer by these assumptions that a manufacturer may

reject some motors due to low efficiency performance,

and that the probability of rejecting a motor on this basis is on the order of one per thousand. We believe that

these conditions approximate a worst-case scenario for

a manufacturer following the MG 1 guidelines. The

true distribution of efficiencies would depend on engineering and business factors and would likely differ

between manufacturers and basic models.

There is an additional complication associated with

these calculations due to the nature of testing under

the NOPR: Under the NOPR, the number of motors

to be tested is not fixed from the outset. In the case of

compliance testing, a manufacturer could test as few as

two motors, but may test any arbitrarily large number

of motors. The NOPR Sampling Plan for Enforcement

Testing specifies an initial sample of five but allows

testing of as many as twenty motors. The scenario in

which the sample size is not fixed from the outset is difficult to characterize statistically, and we have chosen

to treat compliance and enforcement testing under the

NOPR under the approximation that the sample size is

NISTIR 6092

fixed from the outset. The consequence of this approximation is that these calculations provide a lower bound

on the probability of being found in compliance. For

example, a fixed sample size of five includes some cases

for which a manufacturer would have been shown to be

in compliance after testing two motors and could have

stopped testing at that point. but fails after testing five

motors due to the final three test results. The computed probability may thus underestimate the probability of being found in compliance.

15

Wotsasmp Efioency --

ME:

120 110 100 90

Lou Fncflo , (Pe,cei. d Fuk.Load Losses)

Figure 2: Model parameter space . The mean and standard

deviation are given as a percentage of the full-load losses.

The horizontal lines correspond to the standard deviations

such that 3a is equal to the difference (Nominal EfficiencyMinimum Efficiency).

These model assumptions are presented graphically in

Fig. 2. In the figure, standard deviations corresponding to the EPCA nominal efficiencies and calculated

by Eq. 1 are indicated by horizontal lines. The target

performance established by the MG 1 guidelines corresponds to the vertical line at 100 percent. We assume

that product quality control is maintained such that

the standard deviations are at or below the band of

horizontal lines.

Compliance testing

Operating characteristics of the NOPR

compliance criteria

The criteria for establishing compliance with the efficiency levels mandated by EPCA are prescribed in

§431.24(b)(1)(iii) of the NOPR [2], which may be found

in Appendix A of this report.

§431.24(b)(1)(iii) makes reference to K coefficients that

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EE-RM-96-400-CSA COMMENT 58
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are tabulated in Appendix B of Subpart B of the

NOPR. The K coefficients are based on NEMA Standard MG 1-1993 [4) and are calculated by the following

formula:

_ Minimum Efficiency

K Nominal Efficiency

The NOPR assigns K coefficients to all MG 1 Nominal

Efficiencies between 75.5 and 99.0 percent.

To emphasize the salient features of the proposal, we

paraphrase the NOPR criteria for compliance testing

as follows:

Compliance with EPCA efficiencies is demonstrated

provided:

(A) The average full-load efficiency of the sample is not

less than the EPCA nominal efficiency, and

(B) The lower 90 percent confidence limit of the average full-load efficiency of the entire population

divided by the applicable K coefficient is not less

than the EPCA nominal efficiency.

The operating characteristics of the NOPR criteria for

compliance testing are shown in Figs. 3a and 3b, which

present data for sample sizes of two and five, respectively. The contours plotted are for the specific case

where the EPCA nominal efficiency is 80 percent, i.e.,

K has been set equal to 0.963.

Operating characteristics of the NEMA

compliance criteria

The full text of the NEMA proposal may be found in

Appendix D of this report. To emphasize the salient

features of the proposal, we paraphrase the NEMA criteria for compliance testing as follows:

Compliance with EPCA efficiencies is demonstrated

provided:

(A) The average full-load efficiency of a sample of motors is not less than the value given by the following

expression,

100

1+1.05(1°c.-1)'

and

(B) No individual motor in the sample shall have a

full-load efficiency of less than the value given by

the following expression,

100

1+1.15(NE

where NE is the Nominal Efficiency.

ANALYSIS OF PROPOSALS FOR

Operating characteristics of the NEMA criteria for

compliance testing are shown in Fig . 4. The model

calculations shown there are for samples of two and

five.

Enforcement testing

Operating characteristics of the NOPR

sampling plan

The full text of the NOPR proposal for enforcement

testing may be found in Appendix C of this report.

The operating characteristics of the NOPR Sampling

Plan for Enforcement Testing for sarlple sizes of five

and twenty are shown in Figs. 5a and 5b, respectively.

Operating characteristics of the N71MA

enforcement criteria

The full text of the NEMA proposal for enforcement

testing may be found in Appendix D of this report.

To emphasize the salient features of this proposal. we

paraphrase the NEMA criteria for enforcement testing

as follows:

Compliance with EPCA efficiencies is demonstrated

provided:

(A) The average full-load efficiency of a sample of motors is not less than the value given by the following

expression,

100

1+1.150

and

(B) No individual motor in the sample shall have a

full-load efficiency of less than the value given by

the following expression,

100

1+1.20('00 - 1)'

where NE is the Nominal Efficiency.

The operating characteristic of the NEMA criteria for

enforcement testing for a sample sizes of five and twenty

are shown in Figs. 6a and 6b, respectively.

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COMPLIANCE AND ENFORCEMENT TESTING

Concluding remarks

Burden of testing

The data shown here indicate that the NOPR criteria for compliance testing are indeed inconsistent with

NEMA guidelines. Under the NOPR compliance criteria, manufacturers are, in effect, required to have true

mean efficiencies that are significantly above the Nominal values. While the NOPR criteria may allow minimal testing in principle, the premium paid for such

reduced testing, in terms of average efficiency performance above the. Nominal value, is severe. Figure 3a

suggests that the true mean efficiency must lie above

the next higher Nominal value for a manufacturer to

have a 90 percent probability of being found in corr.pliance for a sample size of two.

We note also that the K coefficients given in Appendix B of Subpart B of the NOPR [2] include all

MG 1 Nominal Efficiencies equal to or greater than the

lowest value allowed by EPCA, and that the NOPR

criteria thus establish a protocol for assigning Nominal Efficiencies that applies to all covered motors. It

is particularly important in this case that the labeling

protocol established by the final rule be consistent with

the MG 1 guidelines.

Risk for over-representation of efficiency

The performance of the NEMA proposal in deterring

over-represented values of efficiency should be considered. The model calculations presented in Fig. 4b suggest that the probability of being found in compliance

by testing five motors under the NEMA protocol is on

the order of 90 percent to 95 percent and that the probability of compliance decreases substantially for true

mean efficiencies that are below EPCA nominal efficiencies. However, a full evaluation of the deterrence

against over-represented efficiencies may require costbenefit analyses, which is beyond the scope of this report.

Our conclusions regarding the performance of the

NEMA compliance criteria in deterring systematic

over-representation of efficiencies would be much different, had we assumed product quality control supporting a smaller standard deviation:

6a : Nominal Efficiency - Minimum Efficiency

for example. The NEMA criteria could be fine-tuned

to more strongly favor higher efficiencies: the 1.05 coefficient could be changed to 1.03, for example. However,

to our knowledge, the DOE has no data to suggest that

the NEMA proposal provides a realistic advantage for

systematic over-representation of efficiencies.

NISTIR 6092

Table 1: t coefficients for specified confidence . Adapted

from ASTM Standard E 122-89

t value Confidence Probability o

exceeding E

3 99.7 0.003

2.56 99.0 0.010

2 95.5 0.045

1.96 95.0 0.050

1.64 90.0 0.100

Sample size under the NEMA compliance criteria

We note, as may be readily verified by examination of

the data shown in Fig. 4, that the performance of th?

NEMA proposal for compliance testing depends , ,n the

sanple size. We believe that compliance testiz g for

the purpose of substantiation of an AEDM pro6des

the most compelling argument for establishing a mnimu,n sample size. The criteria for substantiation of

an AEDM are provided in §431.24(b)(3) of the NOPR,

which is reproduced in Appendix B of this report. Substantiation of an AEDM is based on compliance testing:

and the results of such testing may be highly leveraged,

in that testing as few as five basic models may provide

the basis for labeling a substantial portion of a manufacturer's line of covered motors. The DOE thus has

an interest in establishing the validity of such test results. The following discussion estimates the number

of tests needed to support the required 10 percent precision recommended by the NOPR.

The scenario in which testing is required to conform to

a predetermined precision is addressed by ASTM Standard E122-89 [7]. This standard is based on use of the

t statistic and establishes the sample size required to

determine a two-sided confidence interval for an estimate of the mean. The sample size , n, is given by the

following expression:

n - C

ta)2

E

(2)

where E is the required tolerance and t is the coefficient

that corresponds to the desired statistical confidence

(see Table 1). In this case, the desired tolerance, E, is

10% of the total loss, i.e.,

E = 0.10(100 - NE).

Assume that the difference between the NEMA Nominal and Minimum efficiencies corresponds to three standard deviations, and use the approximation,

0.20(100 - NE)

3

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EE-RM-96-400-CSA COMMENT 58
NISTIR 6092

for the standard deviation. Finally, since a high statistical confidence is desired, set the coefficient t equal to

three. Substitution of these values into Eq. 2 gives the

following expression for sample size:

3 x 0.20(100 - NE) 2

{3x0.10(100- NE)1

From this we can conclude that no fewer than four motors should be tested.

Harmonization of compliance and enforcement testing

The NEMA proposal presents motor testing criteria for

compliance and enforcement that are closely related.

While it may be desirable to harmonize such compliance and enforcement testing, the NEMA criteria for

enforcement testing may have unwanted characteristics.

1. The NEMA criteria for enforcement testing appear

to make little distinction between performance at

and significantly below the EPCA levels: the data

presented in Fig. 6a suggest that the true mean

efficiency could be near the next lower Nominal

value without an appreciable change in the outcome of enforcement testing. Thus, it may be argued that the NEMA enforcement crtieria do not

adequately support the EPCA goals.

2. Although interrelated, compliance and enforcement testing differ in significant ways. For example, the consequences that may follow failure

to pass an enforcement test cannot be foreseen by

the rule. Under the NEMA criteria, the efficiency

performance of a single unit could cause a basic

model to fail the entire test, without recourse. The

NEMA criteria may thus not allow a manufacturer

to test as needed to protect its interests.

Performance of the NOPR Sampling

Plan for Enforcement Testing

One important characteristic for evaluating the performance of the Sampling Plan for Enforcement Testing is

the likelihood that testing could support a false conclusion. As proposed, the Sampling Plan for Enforcement

Testing establishes that testing be consistent with a statistical confidence of not less that 90 percent. This statistical confidence implies that the likelihood of falsely

concluding that a product is not in compliance may be

as high as 10 percent. This level of assurance may not

adequately protect the manufacturer's interests. The

NOPR Sampling Plan for Enforcement Testing could

ANALYSIS OF PROPOSALS FOR

be readily modified to increase the assurance against a

false conclusion.

This modification could be accomplished by a change

in the wording of Step 5 of the NOPR Sampling Plan

for Enforcement Testing. The text could be changed to

read as follows:

Compute the lower control limit (LCL1) for

the mean of the first sample using the applicable statutory full-load efficiency (SFE) as

the desired meats as follows:

LCL1 = SFE - tSE(.Z1).

Here t . s the L percentile of a t-distribution

for a sar.iple size of ni and yields a 99 percent

confiden :e level for a one-tailed t-test,

where the modified text has been underlined.

In principle, specifying a higher statistical confidence

may require a higher level of testing. To estimate the

level of testing required, we estimate the likelihood that

a motor that is labeled in accordance with the MG I

guidelines would fail during enforcement testing due to

insufficient sample size. Step 7 of the NOPR Sampling

Plan for Enforcement Testing sets a condition on the

sample size. To demonstrate compliance, the initial

sample size, n1, must satisfy the following condition:

ItSi(120-0.2SFE)12 nl

SFE(20 - 0.2SFE) (3)

where SFE is the applicable EPCA nominal efficiency

and Si is the standard deviation of the sample. This

equation may be rearranged to yield a condition on the

value of t:

ni SFE(20 - 0.2SFE)

t

S1(120 - 0.2SFE) I (4)

Following the earlier discussion, one can assume that

the difference between the NEMA Nominal and Minimum efficiencies corresponds to three standard deviations, and use the following approximation:

a, _ 0.20(100-SFE)

ni 3 nl

Upon substitution into Eq. 4, the following condition

on t is obtained:

t < 3ni SFE(20 - 0.20SFE)

0.20(100 - SFE)(120 - 0.2SFE)'

For an initial sample of five, t must exceed ten for

the sample to fail due to insufficient sample size for

all EPCA nominal efficiencies . The probability that t

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COMPLIANCE AND ENFORCEMENT TESTING

would exceed ten by chance is less than 1 in 1000, for

a sample of five. We cdnclude that it is highly unlikely

that a product that is labeled in accordance with the

MG I guidelines would require testing beyond the initial sample of five, and argue that any risk of additional

testing is more than offset by the increased value of the

test in assuring that the manufacturer's interests are

protected.

The operating characteristics of the modified Sampling

Plan for Enforcement Testing are shown in Fig. 7.

The figure presents data for initial samples of five and

twenty.

Summary

In this section, we summarize the relative merits of eLch

set of criteria.

Compliance testing

NOPR criteria

Advantages:

• high assurance that the average motor efficiency meets or exceeds EPCA levels with

minimal testing

• the likelihood of a correct determination increases with sample size

Disadvantages:

• high burden on manufacturers, i.e., the risk

of a false determination of noncompliance can

be as high as 50 percent

• complexity

• statistical methods that describe these criteria are not readily available

NEMA criteria

Advantages:

• simplicity

• reduced burden on manufacturers

Disadvantages:

• higher risk. relative to the NOPR criteria, of

overly optimistic estimates of efficiency

• statistical methods that describe these criteria are not readily available

NISTIR 6092

Enforcement testing

NOPR

Advantages:

• robust, i.e.. the t-test is not strongly influenced by the exact form of the underlying

distribution and it is a widely accepted basis for a testing protocol

• the likelihood of a correct determination increases with sample size

Disadvantages:

• complexity

NEMA criteria

Advantages:

• simplicity

Disadvantages:

• these test criteria do nct appear to differentiate between efficiencies at and significantly

below the EPCA nominal values

• statistical methods are not readily available

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EE-RM-96-400-CSA COMMENT 58
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15

a)

0

15

b)

0

ANALYSIS OF PROPOSALS FOR

Increasing Efficiency --

120 110 100 90

Loss Fraction (Percent of Full-Load Losses)

Increasing Efficiency --

.05

.01

.001

120 110 100 90

Loss Fraction (Percent of Full-Load Losses)

Figure 3: Operating characteristics of the NOPR compliance criteria. Model calculations for samples of two and five

motors are shown in a) and b), respectively. The contours indicate the probability of demonstrating compliance, e.g., the

.90 contour corresponds to a 90 percent likelihood of demonstrating compliance.'

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COMPLIANCE AND ENFORCEMENT TESTING

Increasing Efficiency

a)

15

b)

0

120 110 100 90

Loss Fraction (Percent of Full-Load Losses)

Increasing Efficiency -

120 110 100 90

Loss Fraction (Percent of Full-Load Losses)

NISTIR 6092

Figure 4: Operating characteristics of the NEMA criteria for compliance testing. Model calculations for samples of two

and five are shown in a) and b), respectively. The contours indicate the probability of demonstrating compliance, e.g.,

the .90 contour corresponds to a 90 percent likelihood of demonstrating compliance.

9

EE-RM-96-400-CSA COMMENT 58
NISTIR 6092 ANALYSIS OF PROPOSALS FOR

Increasing Efficiency --

a)

n=5

b)

15

10

5

0

120 110 100 90

Loss Fraction (Percent of Full-Load Losses)

Increasing Efficiency ----

120 110 100 90

Loss Fraction (Percent of Full -Load Losses)

Figure 5: Operating characteristics of the NOPR proposal for enforcement testing. Model calculationds for samples of

five and twenty are shown in a) and b), respectively.

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Increasing Efficiency --

a)

b)

N

120 110 100 90

Loss Fraction (Percent of Full-Load Losses)

Increasing Efficiency --

15

10 -+

120 110 100 90

Loss Fraction (Percent of Full-Load Losses)

0

NISTIR 6092

Figure 6: Operating characteristics of the NEMA criteria for enforcement testing. Model calculations for sample sizes

of five and twenty are shown in a) and b). respectively. The probabilities of being found in compliance are indicated by

the contours, e.g., the contour labeled .90 corresponds to a 90 percent probability of being shown in compliance.

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NISTIR 6092 ANALYSIS OF PROPOSALS FOR

Increasing Efficiency --

a) .99 .999

n=5

b)

0

15

10 --I

I

120 110 100 90

Loss Fraction (Percent of Full-Load Losses)

Increasing Efficiency -

n=20

0

120 110 100 90

Loss Fraction (Percent of Full-Load Losses)

Figure 7: Operating characteristics of the NOPR proposal for enforcement testing at 99 percent confidence. Model

calculations for sample sizes of five and twenty are shown in a) and b) respectively. The contours indicate the probability

of being shown in compliance, i.e., the contour labeled .90 corresponds to a 90 percent probability of being found in

compliance.

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COMPLIANCE AND ENFORCEMENT TESTING

References

[1] Section 122(d), Energy Policy Act of 1992, Public

Law 102-486, October 24, 1992.

[2] "10 CFR Part 431, Energy Conservation

Program for Certain Commercial and Industrial

- Equipment: Test Procedures. Labeling. and

Certification Requirements of Electric Motors;

Proposed Rule," Federal Register, Vol. 61,

No. 230, Wednesday, November 27, 1996,

pp. 60439-60475.

[3] "Proposal for the Method of Determining

Compliance and Ei.forceinent for Electric Motors

Under the Efficiency' Labeling Program of DOE

10 CFR Part 431," NEMA Motor and Generator

Section, Friday, Apr 1 18, L)97 (Docket No.

EE-R.M-96-400, NEI I A, No 23).

[4] "Motors and Generators," NEMA Standards

Publication No. MG 1-1.993, -vith Revisions,

National Electrical Manufacturers Association,

Rosslyn, VA 22209, 1996

[5] "Statistical Methods for Motor Efficiency Data."

Motor and Generator Section Publication,

National Electrical Manufacturers Association,

Washington, DC 20037, May 1978.

[6] K.L. Stricklett and M. 'angel, "Electric Motor

Efficiency Testing Under the New Part 431 of

Chapter II of Title 10. Code of Federal

Regulations: Enforcement Testing," NIST

Technical Note 1422. National Institute of

Standards and Technology, Technology

Administration. US Department of Commerce,

December, 1996.

[7] "Standard Practice for Choice of Sample Size to

Estimate a Measure of Quality for a Lot or

Process." ASTAI Std E 122-89, American Society

for Testing and Materials, Philadelphia. PA.

NISTIR 6092

13

EE-RM-96-400-CSA COMMENT 58
flI

EE-RM-96-400-CSA COMMENT 58
I

Appendix A

NOPR-Compliance Criteria

The criteria for establishing compliance with the efficiency levels mandated by EPCA are prescribed in

§431.24(b)(1)(iii) of the NOPR [2].

§431.24(b)(1)(iii) makes reference to K coefficients that are tabulated in Appendix B of Subpart B of the NOPR.

The K coefficients are based on NEMA Standard MG 1-1993 [4] and are calculated by the following formula:

_ NEMA Minimum Efficiency

K NEM A Nominal Efficiency

The table assigns K :.oefficients to all MG 1 Nominal Efficiencies between 75.5 percent and 99.0 percent.

§431.24(b)(1)(ii)

For each basic model selected for testing, a sample of units shall be selected at random and tested in

accordance with 3§431.23 and 431.25, and Appendix A, of this subpart. The sample shall be comprised of

production units of the b, ,sic model, or units that are representative of such production units, and shall be

of sufficient size to ensure that any represented value of the nominal or average full-load efficiency of the

basic model is no greater than the lesser of

(A) The average full-load efficiency of the sample, or

(B) The lower 90 percent confidence limit of the average full-load efficiency of the entire population divided

by the coefficient "K" applicable to the represented value. The coefficients are set forth in appendix B

of this subpart.

15

EE-RM-96-400-CSA COMMENT 58
NISTIR 6092 ANALYSIS OF PROPOSALS FOR

Appendix B of Subpart B of Part 431-Nominal Full-load Efficiency and Corresponding Coefficient K

Nominal full-load

efficiency Coefficient K

N ominal u

efficiency Coefficient K

99.0 0 .998 94.1 0.988

98.9 0 . 998 93 .6 0.987

98.8 0.998 93.0 0.986

98.7 0.998 92 .4 0.985

98.6 0.998 91 . 7 0.984

98.5 0.997 91.0 0.984

98.4 0.996 90.2 0.981

98.2 0.996 89. 5 0.916

98.0 0.996 88.5 ().11, 7.,

97.8 0.996 87.5 0.977

97.6 0 . 995 86.5 0.971

97.4 0.994 85.5 0.965

97.1 0.994 84.0 0.970

96.8 0.994 82.5 0.970

96.5 0.993 81.5 0.963

96.2 0 . 992 80.0 0.963

95.8 0.992 78.5 0.962

95.4 0.991 77. 0 0.961

95.0 0.990 75.5 0.954

94.5 0.990

16

EE-RM-96-400-CSA COMMENT 58
Appendix B

NOPR-AEDM Substantiation

Criteria for substantiation of an AEDM are provided in §431.24(b)(3) of the NOPR [2].

§431.24(b)(3)

Substantiation of an alternative efficiency determination method. Before an AEDM is used, its accuracy

and reliability must be substantiated as follows:

(i) The AEDM must be applied to at least five basic models that have been selected for testing and tested

in accordance with paragraph ( b)(1) of this section, and

(ii) The predicted total power loss for each basic model, calculated by apph ing the AEDM , must be within

plus or minus ten percent of the mean total power loss determined fron the a,•tual testing of the basic

model.

17

EE-RM-96-400-CSA COMMENT 58
81

EE-RM-96-400-CSA COMMENT 58
I

Appendix C

NOPR-Sampling Plan for Enforcement Testing

The Sampling Plan for Enforcement Testing proposed by the NOPR [2].

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

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

Step 2. Compute the mean (..I) of the measured energy performance of the n1 units in the first sample as

follows:

1 °' X1 = F, xi,

n

1 =1

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

Step 3. Compute the sample standard deviation (SI) of the measured full-load efficiency of the n1 units in

the first sample as follows:

Si =

(Xi -

1 )2

n1 - 1

(C2)

Step 4. Compute the standard error (SE(. 1)) of the mean full-load efficiency of the first sample as follows:

SE(X1) = S'n (C3)

Step 5. Compute the lower control limit (LCL1) for the mean of the first sample using the applicable

statutory full-load efficiency (SFE) as the desired mean as follows:

LCL1 = SFE - tSE(.91). (C4)

Here t is the 10th percentile of a t-distribution for a sample size of nl and yields a 90 percent

confidence level for a one-tailed t-test.

Step 6. Compare the mean of the first sample (.91) 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

noncompliance 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.

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

tS1(120 - 0.2SFE) 2

n = [SFE(20 - 0.2SFE)] (C5)

where S1 and t have the values used in Steps 4 and 5, respectively. The factor

120 - 0.2SFE

SFE(20 - 0.2SFE)

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:

19

EE-RM-96-400-CSA COMMENT 58
NISTIR 6092 ANALYSIS OF PROPOSALS FOR

(i) If the value of n is less than or equal to ni and if the mean energy efficiency of the first sample

(11) 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 noncompliance . 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 mean (X2) of the measured energy performance of the n1 and n2 units of

the combined first and second samples as follows:

1 n1 +nz

X2 = E Xi.

ni + n2 1

(C6)

Step 9. Compute the standard error (SE(.92)) of the mean full-load efficiency of the n1 and n2 units in the

combined first and second samples as follows:

SE(2)

Sl

ni +n,.

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

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

LCL2 = SFE - tSE(X2),

(C7)

(C8)

where t has the value obtained in Step b, and 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 noncompliance 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 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, 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 noncompliance.

20

EE-RM-96-400-CSA COMMENT 58
Appendix D

The NEMA Proposal

The following statement was prepared by the NEMA. Motor and Generator Section, and was submitted to the

DOE on Friday, April 18, 1997, in response to the call public comment given in the..NOPR [2]. The text of the

original NEMA statement [3] has been modified to conform with the pagination and the figure labeling scheme

used in this report.

PROPOSAL FOR THE METHOD OF DETERMINING COMPLIANCE AND

ENFORCEMENT FOR ELECTRIC MOTORS UNDER THE EFFICIENCY LABELING

PROGRAM OF DOE 10 CFR PART 431

Submitted by

NEMA Motor and Generator Section

Background - Analysis of Testing Samples from Total Population

The basis behind the NEMA proposal is best illustrated by way of examples. A normal distribution for a total

population of motors having a nominal efficiency rating of 91.0% is shown in Figure D1 based on the assumption

that three sigma (standard deviation) corresponds to the NEMA minimum efficiency of 89.5%. Also shown are

the normal distributions for the means of samples of size 2 or five which are normally distributed about the true

mean of the population and have a standard deviation proportional to that of the total population divided by

the square root of the sample size n. The normal distribution of the total population also corresponds to the

distribution of the means of samples of size 1.

Per Table 12-8 of NEMA MG 1 the values of efficiency in the vicinity of 91.0% which a manufacturer can mark on

appropriately rated motors are 89.5%, 90.2%, 91.0%, 91.7%, and 92.4%.. It remains to be determined which level

of efficiency is supported by testing samples selected from the total population. For this example, a reasonable

compliance criteria should show that the nominal efficiency is 91.0% within a desired degree of confidence.

Figure D2 illustrates the probability that the mean of a sample selected from the total population will be less

than various levels of efficiency. The DOE proposed rule for compliance in 431.24.b.l.iii.A requires that the

represented value of nominal efficiency for the basic model (total population) cannot be greater than the average

(mean) full-load efficiency of the sample. From Figure D2 it can be seen that there is a probability of 50%

that the mean efficiency of a sample of any size will be less than the nominal efficiency of the total population.

91.0% in this particular example. Combining this DOE proposed rule with the NEMA Standard for selection

of efficiency levels for marking, there is then a probability of 50% that for any sample selected from the total

population the declared value of nominal efficiency could not be greater than 90.2%. From Figure D2 the

probability that the mean of the sample would actually be less than 90.2% and that the nominal efficiency must

be selected to be the next lower value, 89.5%, is 5% for a sample of 1, 1.2% for a sample of 2, and a negligible

value for a sample of 5. It should be apparent that the DOE proposed rule places an unreasonable burden (risk)

on the manufacturer to show compliance to the actual true mean nominal efficiency. A rule based on the average

efficiency of a sample not being less than some efficiency level lower than the nominal efficiency, 91.0% in this

example, would appear to offer a reasonable risk for the manufacturer to show compliance to 91.0%.

Background - Analysis of Testing Samples from Limited Population

Because motors based on a basic model design are produced over a long period of time, the total population for

which compliance is being determined will not be available at the time a sample must be selected for testing. As

a result, the sample will be selected from production lot(s) which may incorporate a limited range of variation of

all of the factors which can affect the efficiency of each individual motor; the variations in materials, variations in

manufacturing processes, and variations in testing (see NEMA MG 1-12.58.2). It is not possible to include in a

compliance rule, when testing is likely to take place in only one location, the allowance in the NEMA standard for

the variation in testing results when a motor is tested at different locations. It is then reasonable to assume that

21

EE-RM-96-400-CSA COMMENT 58
NISTIR 6092 ANALYSIS OF PROPOSALS FOR

if the distribution of efficiencies of the total population tested at any facility are as shown in Figure D1 then the

distribution of the total population when tested at a single facility must have a lower value of standard deviation.

Further, it should be evident that the standard deviation of any particular limited production lot should be even

lower because it will not incorporate all of the possible variations in materials and manufacturing processes that

can occur over the extended period of time the basic model is produced. For example, the electrical steel used to

construct the stator and rotor laminated cores is purchased in large quantities at a time. The amount purchased

may be sufficient to handle the production of motors for several months. The characteristics of the material in

that stock will determine the efficiency in the motors selected for testing from those produced using that stock.

A new stock of material having somewhat different performance characteristics will not be available for use until

the present stock: is depleted.

For the purpose of this illustration, it will be assumed that the processes under the manufacturer's control

limit the minimum efficiency for any acceptable motor to 89.8%. The difference between 89.8% and the NEMA

minimum efficiency of 89.5% allows for variations in the test value of efficiency when the tests are performed at

facilities not under the direction of the manufacturer. It will be further assumed that the mean efficien -,v of the

limited population is equal to 90.6% as a result of the effect of variations in materials, manufacturing processes,

and testing performed at a single facility. The difference between efficiencies of 91.0% and 90.6% is eq•ivalent

to a reasonable variation of 5% in the total losses. A normal distribution on the basis of these assumr tions is

.;hoar in Figure D3. Included are the normal distributions of the means of samples of size 2 and 5 as well ss

:. From Figure D2 it can also be observed that the probability of a production lot of motors having mean

efficient-3 less than 90.6% is 21%.

The probability distribution function for the limited population in Figure D3 is shown in Figure D4. From

Figure D4 the probability that a sample mean would exceed 91.0% is only 8% for a sample of 1, 2% for a sample

of 2, and 'J% for a sample of 5. In other words, a sample taken from such a limited population, even if the

number of motors was in the hundreds or thousands, would be unlikely to support compliance to the correct

true mean of the total population when following DOE's proposed rule.

This example does, however, provide additional guidance as to what the compliance rule could be. From

Figure D4 there is a probability of 90% that the mean efficiency of a sample from this limited lot size will be

greater than 90.25% for a sample of 1, 90.35% for a sample of 2, or 90.44% for a sample of 5. From Figure D2

for the total population there is a probability of 93% that any motor from the total population has an efficiency

greater than 90.25%, a probability of 90% that any motor will have an efficiency greater than 90.35%, or a

probability of 87% that any motor would have an efficiency of 90.44%.

Background - Overlapping Nominal Efficiency Distributions

The final criteria which must be examined for determining a practical compliance rule is the probability that

the sample test may indicate an incorrect nominal efficiency for the basic model (total population). To aid

in the discussion of this issue, Figure D5 is presented which illustrates the normal distribution of efficiencies

for a population of motors which have a nominal efficiency of 91.0% and a population of motors which have a

nominal efficiency of 90.2%. In this case 90.2% is the next lower level of nominal efficiency which the NEMA

MG 1 Standard permits to be used for the marking of motors. Again, distributions based on test samples of

sizes 1 (equivalent to the distribution for the total population), 2, and 5 are provided for each population. The

corresponding probability distributions are shown in Figure D6.

From Figure D5 it can be observed that the various distributions of efficiency of the two populations tend to

intersect each other in the region of an efficiency of 90.6%. This varies slightly based on the sample sizes because

of the difference in the NEMA criteria permitted for the two nominal efficiency levels. For a nominal efficiency

of 91.0% the NEMA minimum efficiency is 89.5% for a standard deviation of 0.5%. For a nominal efficiency of

90.2% the NEMA minimum efficiency is 88.5% for a standard deviation of 0.57%. This slight distortion in the

relationships of the distribution functions is a result of basing the curves on efficiency when in fact the NEMA

criteria for selecting discreet values of nominal efficiency for the use in marking motors was based on step changes

in the total losses. The increase in losses in going from an efficiency of 91.0% to 89.5% is 19.6%. The increase

in losses is 18.6% when going from an efficiency of 90.2% to 88.5%. This slight difference in the change in losses

was introduced by rounding off the nominal efficiency values used for marking motors to 3 significant figures.

22

EE-RM-96-400-CSA COMMENT 58
COMPLIANCE AND ENFORCEMENT TESTING NISTIR 6092

Per Figure D6 the probability that a motor from a population with a nominal efficiency of 91.0% would have

an efficiency below 90.6% is 21%. The probability that a motor from a population with a nominal efficiency of

90.2% would have an efficiency above 90.6% is 24%. There is a probability of 13% that the mean of a sample

of size 2 selected from the population with a nominal efficiency of 91.0% would be less than 90.6%. Similarly

there is a probability of 16% that the mean of a sample of size 2 selected from the population with a nominal

efficiency of 90.2% would be greater than 90.6%. There is a probability of 4% that the mean of a sample of size

5 selected from the population with a nominal efficiency of 91.0% would be less than 90.6%. Similarly there is

a probability of 6% that the mean of a sample of size 5 selected from the population with a nominal efficiency

of 90.2% would be greater than 90.6%.

This suggests that a reasonable criteria for the compliance rule that balances the manufacturer's and consumer's

risks is that the minimum permissible value of average efficiency fdr the sample should be a value between the

nominal efficiency to be declared and the next lower value of nominal efficiency in Table 12-8 of NEMA MG 1.

Proposed Test for Determining Compliance (Section 431.24.b.l.iii of Part 431)

Basing the test condition for compliance on the values of nominal efficiency in Table 12-8 would introduce a

complexity of having to use a table of values in which the increment in efficien7i between values is not fixed. It

is simpler to use the basic principle under which the table was developed. TL is is the same principle that the

DOE recognized in the proposed rule for enforcement testing in Appendix B to Subpart G of Part 431. The

increment in efficiency between the nominal values in Table 12-8 were based on approximately a 10% change

in total losses. The point at which the manufacturer's and consumer's risks are balanced between two NEMA

nominal values of efficiency suggested above corresponds to a 5% change in losses.

It is therefore proposed that one of the conditions required to determine conformance is that the "average fullload efficiency of the sample is not less than the value of efficiency equal to the nominal efficiency reduced by

an amount equivalent to a 5% "increase in losses at full-load, i.e. the value given by

100 r

I+1.05(1VE 1)

This proposal could also be written in a manner consistent with the DOE proposed rule 431.24.b.1.iii.A "as the

represented value of the nominal full-load efficiency of the basic model is not greater than the value calculated

from

105X

100 + 0.05.k

where t is the average full-load efficiency of the sample."

The second condition that must be satisfied by the sample is related to the standard deviation of the efficiencies

of the motors in the sample. In Appendix B to Subpart G of Part 431 the DOE proposed a test on the sample

size based on a 20 percent tolerance in the total power loss at full-load. This recognizes the complete variation

in efficiency testing at different facilities as identified in the NEMA MG 1 standard. It is recommended that

this value of 20% can be reduced to 15% for the purpose of compliance testing at a single facility. The principle

behind the incorporation of this recognized variation in Appendix B to Subpart G of Part 431 can be applied

here by incorporating it in a simpler method as a requirement that "the full-load efficiency of each motor in the

sample must be greater than the value of efficiency equal to the nominal efficiency NE reduced by an amount

equivalent to a 15% increase in total losses at full-load, i.e. the value given by

100

1+1.15(' °0-1)

Proposed Test for Enforcement (Appendix B to Subpart G of Part 431)

It is proposed that the rules for enforcement testing be similar to those for compliance. The primary difference

being that the rules for enforcement testing be based on the total permissible variation in measured efficiency

permitted by the NEMA MG 1 Standard. The recommended rules for enforcement testing would then be that

23

EE-RM-96-400-CSA COMMENT 58
NISTIR 6092 ANALYSIS OF PROPOSALS FOR

the "average full-load efficiency of the sample is not less than the value of efficiency equal to the nominal efficiency

NE reduced by an amount equivalent to a 15% increase in losses at full-load. i.e. the value given by

100

1+1.15('x°E°°0 - 1)

The second condition that must be satisfied by the sample is the again similar to that for determining compliance

that "the full-load efficiency of each motor in the sample must be greater than the value of efficiency equal to

the nominal efficiency NE reduced by an amount equivalent to a 20% increase in total losses at full-load, i.e.

the value given by .. • - 100 „

-1 + 1.2 ( T - 1)

24

EE-RM-96-400-CSA COMMENT 58
COMPLIANCE AND ENFORCEMENT TESTING NISTIR 6092

89.5

Example of Normal Distribution of Total Population and

Distribution of Means of Samples

90.0 90.5 91.0 91.5 92.0

Efficiency In Percent

L- - Total Popu on - - - Samples 0( 2

Figure Di:

100

90

so

70

60

50

40

30

20

10

0

89.5

- - Samples of 5

Probability That Mean of Sample is Below Efficiency Value

90.0 90.5 91.0 91.5

Efficiency In Percent

I

Sampiea of 1 - - - Sampbs of 2

Figure D2:

92.0

- - Samples of 5

92.5

92.5

25

EE-RM-96-400-CSA COMMENT 58
NISTIR 6092 ANALYSIS OF PROPOSALS FOR

3.5

3.0

2.5

2.0

1.5

1.0

0.5

Example of Normal Distribution of Limited Population and

Distribution of Means of Samples

0.0

89.5 90.0 90.5 01.0 91.5 02.0 02.5

Efficiency In Pei ent

100

Figure D3:

90

80

70

0

50

30

20

10

88s

0

LM11Ied Pope aDo l - - - . Simple.; of 2 - - SampbsOf 5

Probability That Mean of Sample Is Below Efficiency Value

i

90.5 91.0 91.5

Efficiency in Percent

92.0

Samples of 1 - - - Samples of 2 - - Samples of 5

Figure D4:

92.5

26

EE-RM-96-400-CSA COMMENT 58
i

COMPLIANCE AND ENFORCEMENT TESTING NISTIR 6092

1.8

1.6

1.4

12

1.0

0.6

0.6

0.4

0:.

0.0 L.:-

-Efficiency Distribution for Populations of 2 Different Motor

Designs

83.5 89.0 89.5 91.5 92.0

Efficiency In Percent

Population 1 - - - Sample of 2

- Population 2 - - - Sample of 2

Sample of5

Sample of 5

Figure D5:

100

90

so

70

60

so

40

30

20

10

0

Probability That Mean of Sample Is Below Efficiency Value

/ .

88.5 89.0 89.5

Samples of 1, Pop 1

90.0 90.5 91.0

90.0 90.5 91.0

Efficiency In Percent

- - - Samples of 2, Pop 1

91.5 92.0

- - Samples of 5, Pop 1

Samples of 1, Pop 2 - - - Samples of 2, Pop 2 -- - Samples of 5, Pop 2

Figure D6:

92.5

925

r

27

EE-RM-96-400-CSA COMMENT 58
8Z

EE-RM-96-400-CSA COMMENT 58
Appendix E

Supplemental Analysis

As noted on page 5, the operating characteristics of the NEMA compliance criteria are influenced by the value

of the coefficient used in criterion (A) (see page 4). The NEMA proposal recommends that compliance testing

be based on the use of 1.05 for this coefficient. The operating characteristics of the NEMA compliance criteria

for this value are shown on page 9. The analyses presented in this Appendix were performed at the request

of the DOE in order to evaluate modification of the value of the (A) coefficient, 'and to compare the operating

characteristics of the NOPR sampling plan for enforcement testing with the NEMA criteria for compliance

testing. These supplemental analyses include: Model calculations of the operating characteristics of the NEMA

compliance criteria with the (A) coefficient set to values of 1.03 and 1.01. These data are presented in Figs. El and

E2, respectively. In the remaining figures, the operating characteristics of the NOPR protocol for enforcement

testing and the NEMA compliance criteria are compa- ed. F)r these comparisc ns, the operating characteristics of

the NOPR enforcement protocol at 90 percent and 99 percent statistical confic ence a.-e plotted together with the

.90 contours for the NEMA compliance criteria. Data for the NEMA compliai ce cr;toria with an (A) coefficient

of 1.05, 1.03, and 1.01 are plotted in Figs. E3, E4, an,i E5, respectively-.

29

EE-RM-96-400-CSA COMMENT 58
ANALYSIS OF PROPOSALS FOR

a)

b)

15

10-_^

5-

0

15

0

Increasing Efficiency -

120 110 100 90

Lass Fraction (Percent of Full-Load Losses)

Increasing Efficiency --

120 110 100 90

Loss Fraction (Percent of Full-Load Losses)

Figure El: Operating characteristics of a modified NEMA compliance protocol. Here the coefficient in criterion (A) of

the NEMA protocol for compliance testing is 1.03. Model calculations for samples of two and five are shown in a) and

b), respectively. The contours indicate the probability of demonstrating compliance, e.g., the .90 contour corresponds to

a 90 percent likelihood of demonstrating compliance.

30

EE-RM-96-400-CSA COMMENT 58
I

COMPLIANCE AND ENFORCEMENT TESTING

15

a)

b)

Increasing Efficiency ---

10 -I

0

120 110 100 510

Loss Fraction (Percent of Full-Load Losses)

Increasing Efficiency --

120 110 100 90

Loss Fraction (Percent of Full-Load Losses)

NISTIR 6092

Figure E2: Operating characteristics of a modified NEMA compliance protocol. Here the coefficient in criterion (A) of

the NEMA protocol for compliance testing is been 1.01. Model calculations for samples of two and five are shown in a)

and b), respectively. The contours indicate the probability of demonstrating compliance, e.g., the .90 contour corresponds

to a 90 percent likelihood of demonstrating compliance.

31

EE-RM-96-400-CSA COMMENT 58
NISTIR 6092

b)

15

CD

10

m

OJ

i

C

C

CO CD 5

CD

o0

ANALYSIS OF PROPOSALS FOR

Increasing Efficiency

120 110 100 90

Loss Fraction (Percent of Full-Load Losses)

Increasing Efficiency ----

120 110 100 90

Loss Fraction (Percent of Full-Load Losses)

Figure E3: A comparison of the operating characteristics of the NOPR protocol for enforcement testing and the NEMA

compliance protocol. The operating characteristics of the NOPR protocol at 90 percent and 99 percent statistical

confidence are indicated respectively by the solid lines in a) and b). The .90 contours of the NEMA compliance protocol

are shown for samples of two (------) and five (- - -)• Here the coefficient in criterion (A) of the NEMA protocol

for compliance testing is 1.05.

32

EE-RM-96-400-CSA COMMENT 58
I

COMPLIANCE AND ENFORCEMENT TESTING

Increasing Efficiency

a)

NISTIR 6092

r

15

b )

0

120 110 100 90

Loss Fraction (Percent of Full-Load Losses)

Increasing Efficiency

120 110 100 90

Loss Fraction (Percent of Full-Load Losses)

Figure E4: A comparison of the operating characteristics of the NOPR protocol for enforcement testing and the NEMA

compliance protocol. The operating characteristics of the NOPR protocol at 90 percent and 99 percent statistical

confidence are indicated respectively by the solid lines in a) and b). The .90 contours of the NEMA compliance protocol

are'shown for samples of two (------) and five (- - -). Here the coefficient in criterion (A) of the NEMA protocol

for compliance testing is 1.03.

f

EE-RM-96-400-CSA COMMENT 58
NISTIR 6092

a)

b)

15

5 -^

0

15

H

CD

ANALYSIS OF PROPOSALS FOR

Increasing Efficiency --

120 110 100 90

1 r

Loss Fraction (Percent of Full-Load Losses)

Increasing Efficiency -

n=5

n=5--

n2---•

I I --I

120 110 100 90

Loss Fraction (Percent of Full-Load Losses)

Figure E5: A comparison of the operating characteristics of the NOPR protocol for enforcement testing and the NEMA

compliance protocol. The operating characteristics of the NOPR protocol at 90 percent and 99 percent statistical

confidence are indicated respectively by the solid lines in a) and b). The .90 contours of the NEMA compliance protocol

are shown for samples of two (------) and five (- - -). Here the coefficient in criterion (A) of the NEMA protocol

for compliance testing is 1.01.

34

EE-RM-96-400-CSA COMMENT 58