SEE

SAMPLING PLANS UNDER CONSIDERAT ION

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-TP-98-550 COMMENT 02EE

SAMPLING PLANS UNDER CONSIDERATION 

FOR COMPLIANCE TESTING 

by 

Oskars Petersons and Ken 8tricklett 

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. 
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 (X), or

- (B) the lower 95% confidence limit of the

mean of the population divided by 0.999

CRITERION FOR COMPLIANCE:

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

0 Represented value ? Mandated efficiency

EE-TP-98-550 COMMENT 02EE

.... 

METHOD 1 

AS DEFINED IN 10 CFR 430, § 430.32 ' 

lOA 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 

followin~ 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 (6) 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 (X), or 

(8) the lower 95% confidence limit of the 

mean of the population divided by 0.999 

CRITERION FOR COMPLIANCE: 

III Represented value 2! Mandated efficiency 

METHOD 1 (CONTINUED) 

STATISTICAL METHOD, SAMPLE SIZE 

III 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)/O.999 

test the represented value for compliance 
i

NORMALLY DISTRIBUTED EFFICIENCIES

Increasing Effidency -•

ME

Mandated efficiency, ME

Probability density for the population, Po

Probability density for the mean of 5 units, PS

True mean efficiency, a

1

METHOD I: Sampling Plan

Increasing Efficiency ----

ME

LCL

0.999

Sample mean, X

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-TP-98-550 COMMENT 02EE

NORMALLY DISTRIBUTED EFFICIENCIES 

looreaslng Elllclency -

ME 

Mandated efficiency, ME 

Probability density for the population, Po 

Probability density for the mean of 5 units, Ps 

True mean efficiency, J.1. 

METHOD I: Sampling Plan 

Sample mean, X 

Standard error, SE(X) 

Increasing ettrclency -

ME 

LCL 

Q.999 

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

For Compliance: 

A) X ~ ME 

B.) i -tSE(X) > ME 

0.999 -

2 
METHOD 2

BASED ON

• statistical t-test

® requirement of minimum sample size

CRITERIA FOR COMPLIANCE

0 X Z ME ®tSE(X )

n = 5or

n ^ (tS/T]2

T is the maximum error in the determination

of the mean (7)

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

L

ME - tSE(X) ....'

meME

Sample mean, .k

Standard error, SE(X)

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

For Compliance:

A) X .> ME - tSE(X)

B) n • Z [tS/T]z

4

EE-TP-98-550 COMMENT 02EE

t.; ..•. 

METHOD 2 

BASED ON 

CD statistical t-test 

CD requirement of minimum sample size , 

CRITER'IA FOR COMPLIANCE 

CD X ~ ME - ,tSE{~) 

CD n = 5 or 

n ;?; [tS/T]2 

T is the maximum error in the determination 

·of the mean (X) 

STEPS IN IMP~EMENTATION' (SIMPLIFIED) 

• measure losses, compute efficiency 

• compu:te the mean (X). standard deviation, 

standard error of the sample, the lower 90% 

confid~nce limit (LCL), and ME - tSE(X ).,. 

CD determine adaquecy of sample size (in most 

cases a sample of 5 will suffice) 

CD test X for compliance 

METHOD II: Sampling Plan 

I 

! 

I 

f 

e t 

11.' 

ME·tSE(X) ~ 

Sample mean, X 

Standard error, SE(X) 

IlIOI'lIulng Efficiency -

ME 

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

For Compliance: 

. A) X.~ ME - tSE(X) 

B) n· ~ [tSffJ2 

4 
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:

0 Complexity

EE-TP-98-550 COMMENT 02EE

Method 1 

Advantages: 

SUMMARY 

CD Simple, flexible. 

• High assurance of meeting EPCA requirements . 

CD Determination assurance increases with sample 

size 

Disadvantages: 

• High burden on producers; risk of false 

determination of noncompliance can be as high as 

50% 

e 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 

FEEDBACK DESIRED 

1. General comments on the two plans -- perceived 

advantages and disadvantages 

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

applicable to 50% and 35% loadings? 

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

method 1 and "T" coefficient in method 2 

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

4. Other sampling plans that should be considered.