SAMPLING PLANS UNDER CONSIDERATION

FOR COMPLIANCE TESTING

by

Oskars Petersons and Ken Stricklett

Electricity Division

National Institute of Standards and Technology

February 10, 1998

Note: This draft material is prepared for a presentation at the Workshop on

Distribution Transformer Test Procedures organized by the Department of Energy,

February 10, 1998 to stimulate discussion at the workshop and submission of peer

review comments. Since the draft is of a preliminary nature and has not received

full review by NIST, it may not be cited and referenced for the purposes other than

those stated here.

EE-DET-97-550 COMMENT 05
METHOD 1

AS DEFINED IN 10 CFR 430, § 430.32

"A sample shall be selected and tested comprised of units

which are production units, or are representative of production

units of the basic model being tested and shall meet the

following applicable criteria . For each basic model of

distribution transformers, as defined in §430.2, a sample of

sufficient size shall be tested to insure that any represented

value of transformer efficiency shall be no greater that the

lower of (A) the mean of the sample or (B) the lower 95%

confidence limit of the estimated true mean divided by 0.999."

DETERMINE THE REPRESENTED VALUE OF

EFFICIENCY

• the smaller of

(A) the mean of the sample (R), or

(B) the lower 95% confidence limit of the

mean of the population divided by 0.999

CRITERION FOR COMPLIANCE:

• Represented value >_ Mandated efficiency

METHOD 1 (CONTINUED)

STATISTICAL METHOD, SAMPLE SIZE

• not specified

• if t-test selected

- select sample size, measure losses,

compute efficiency

compute the mean (X), standard deviation,

standard error of the sample, the lower

95% confidence limit (LCL), and

(LCL)/0.999

test the represented value for compliance

EE-DET-97-550 COMMENT 05
I

NORMALLY DISTRIBUTED EFFICIENCIES

Increasing Efficiency --+

ME

Mandated efficiency, ME

Probability density for the population, Po

Probability density for the mean of 5 units, P5

True mean efficiency, μ

1

METHOD I: Sampling Plan

Increasing Efficiency --

ME

Sample mean,

Standard error, SE(X)

Lower 95% confidence limit, LCL =X - tSE(X)

For Compliance:

A) X > ME

B) X-tSE(X)

0.999 > ME

2

EE-DET-97-550 COMMENT 05
METHOD 2

BASED ON

• statistical t-test

• requirement of minimum sample size

CRITERIA FOR COMPLIANCE

• X > ME - tSE(X)

• n = 5or

n [tS/T]2

- T is the maximum error in the determination

of the mean (X)

STEPS IN IMPLEMENTATION (SIMPLIFIED)

• measure losses , compute efficiency

• compute the mean (-X), standard deviation,

standard error of the sample , the lower 90%

confidence limit (LCL), and ME - tSE(X )

• determine adaquecy of sample size (in most

cases a sample of 5 will suffice)

• test X for compliance

METHOD II : Sampling Plan

Increasing Efficiency --

ME

Sample mean, X

Standard error, SE(X)

Lower 95% confidence limit, LCL =X - tSE(X)

For Compliance:

A) X > ME - tSE(X)

B) n , >- [tS/T]2

4

EE-DET-97-550 COMMENT 05
SUMMARY FEEDBACK DESIRED

Method 1

1. General comments on the two plans -- perceived

Advantages: advantages and disadvantages

• Simple, flexible.

2. Statistical significance of the 6% loss tolerance. Is it

• High assurance of meeting EPCA requirements applicable to 50% and 35% loadings?

• Determination assurance increases with sample

size

3. Suggestions for the values of constants: the divisor in

method 1 and "T coefficient in method 2

Disadvantages: 3. Do the actual test data support the modeling results?

• High burden on producers; risk of false

determination of noncompliance can be as high as 4. Other sampling plans that should be considered.

50%

• Statistical methods for analyses of operating

characteristics are not readily available

Method 2

Advantages:

• Rigorous and widely used statistical method

• Can balance producer and consumer risks

Disadvantages:

• Complexity

EE-DET-97-550 COMMENT 05