lAT'L INST. OF STAND & TECH RIC

A 11 10 5 3531D7

Nisr United States Department of Commerce

Technology Administration

National Institute of Standards and Technology

NIST Technical Note 1424

NIST Measurement Assurance

Program for Resistance

Paul A. Boynton, June E. Sims, and Ronald F. Dziuba

QC

100

U5753

NO. 1424

1997
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J0303. me elements ai Boulder. CO.
NIST Technical Note 1424

NIST Measurement Assurance

Program for Resistance

Paul A. Boynton, June E. Sims, and Ronald F. Dziuba

Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899-0001

November 1997

4* C

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•5»

U.S. Department of Commerce

William M. Daley, Secretary

Technology Administration

Gary R. Bachula, Acting Under Secretary for Technology

National Institute of Standards and Technology

Raymond G. Kammer, Director
National Institute of Standards U.S. Government Printing Office For sale by the Superintendent of and Technology Washington: 1997 Documents

Technical Note 1424 U.S. Government Printing Office

Natl. Inst. Stand. Technol. Washington, DC 20402

Tech. Note 1424

57 pages (Nov. 1997)

CODEN: NTNOEF
NIST MEASUREMENT ASSURANCE PROGRAM FOR RESISTANCE

CONTENTS

1. INTRODUCTION 1 1.1 What is a MAP? 1

1 .2 Why a MAP? 1 1.3 How do MAPs work? 2

1 .4 Who should participate? 2

1.4.1 Types of labs 2

1 .4.2 Customer requirements 2

2. DESCRIPTION OF SERVICES 3

2.1 Resistance MAP services 3

2. 1 .

1

Present services 3

2.1.2 Group MAPs 3

2.1.3 Transport standards 4

2.1.4 Limitations 5

2.2 NIST resistance standards and measurements 6

2.3 MAP transfer procedures 6

2.3.1 Setting up a MAP transfer 6

2.3.2 Measuring the resistors and sending data to NIST 9

2.3.3 Returning the MAP package 10

2.3.4 NIST follow-up measurements 10

2.3.5 Generating the report of the MAP 11

3. DATA ANALYSIS 11 3.1 Estimate of the difference 11 3.2 Uncertainty of the estimate of the difference 11

4. ACKNOWLEDGMENTS 14

APPENDIX I: Typical MAP 15

1.1 MAP Packet 16

1. 1.1 Introduction 16

1.1.2 Front data sheet 19

1.1.3 Data Sheet 20

1. 1 .4 Shipping Order and Labels 21

1.2 Analysis of MAP data 22

1.2.1 Introduction 22

1.2.2 Sample "MAPS97.0UT" 24

1.2.3 Sample "Final" Data 26

1.2.4 Sample "COLLECT97" 28

iii
1.3 Results of MAP 44

1.3.1 Introduction 44

1.3.2 Report of Test 45

1.3.3 Appendix A 46

1.3.4 Appendix B 49

1.3.5 Appendix C 51

REFERENCES 52

IV
NIST MEASUREMENT ASSURANCE PROGRAM FOR RESISTANCE

Paul A. Boynton, June E. Sims, and Ronald F. Dziuba

Abstract - The National Institute of Standards and Technology (NIST) offers resistance

Measurement Assurance Program (MAP) transfers at the 1 Q and 1 kQ levels, to provide a method

of assessing and maintaining the quality of a customer's measurement process. This document

describes the basic concepts of a resistance MAP, and the procedures for participating in the

program. A discussion of the data analysis follows, with an explanation of the uncertainty of the

estimate of the transfer. Also included is a sample MAP scenario, with data sheets, analysis results,

and a final test report.

1. INTRODUCTION

1.1 What is a MAP?

The Measurement Assurance Program (MAP) services offered by NIST provide a tool for achieving

quality assurance of the customer's measurement process. The MAP is a method of assessing the

uncertainty of the measurement process, and provides NIST-traceable assigned values to the

customer's standards. This procedure, completed with internal statistical process control techniques,

gives the customer a technique for monitoring the quality of its measurement process.

1.2 Why a MAP?

Many laboratories may find it more advantageous to participate in a MAP rather than use the NIST

calibration service. The calibration service, in which the customer laboratory sends its standards to NIST for calibration, assigns the values ofthe customer's standards relative to NIST's standards, and

their uncertainties, thus indicating the quality of the NIST measurement process, and the short-term

performance of those standards. The NIST MAP service samples the output of the customer's

measurement process rather than checking the standards alone. This provides a picture ofthe quality

of the customer's measurement process as well, and thus is a more effective method of traceability.

As a result, problems with the customer's measurement system that would not necessarily be

revealed by the regular calibration service would possibly be uncovered. A MAP indicates such

deviations from the measurement's assumed quality, thus providing information that can help

improve the precision and uncertainty of the customer's measurement process.

It is true that MAPs can be more expensive in the short term; still, they can save money in the long

term. Often customers discover, that after participating in the program for a few years, the results

allow them to increase the interval between MAPs. For example, some resistance MAP customers

find that after a few years of annual transfers, they can reduce their participation to a biennial

transfer.
1.3 How do MAPs work?

Each specific measurement situation requires its own procedures [1]. Generally, a set of transport

standards is measured at N1ST and then sent to the customer, usually via air freight, for measurement

by the customer's system. After a minimum number of measurements have been taken (enough to assess whether the process is under control), the transport standards are returned to NIST for further

measurements. The NIST data and the customer data are then analyzed, and a report is issued from

NIST to the customer. This report states the offset ofthe customer's measurement process from the

NIST standards, and the total uncertainty of the customer's measurement process. This uncertainty

includes errors resulting from both random and systematic effects.

The transport standards are usually measured by the customer using their normal calibration

conditions, as if they were part of the normal workload of the laboratory. This allows for a realistic

assessment of the quality of the customer's measurement process. Many situations call for the use of a design scheme. In all cases, the customer's measurement process must be in statistical control

while the transport standards are being measured. Thus, check standards or statistical tests need to be used on a regular basis in the laboratory.

1.4 Who should participate?

1.4.1 Types of labs. Standards laboratories that provide calibrations of electrical standards with

an uncertainty within one order ofmagnitude ofthose available by NIST calibration services should

consider participating in a MAP. As a rule, those laboratories that do not aspire to this level of

uncertainty would find that the regular NIST calibration service should suffice. However, NIST

MAP services used on a once-only basis can be used by laboratories to evaluate new calibration

systems.

1.4.2 Customer requirements. The customer who is interested in participating in a NIST MAP

should have the following:

1

)

an extensive comprehension of the particular measurement process in use;

2) an ongoing measurement control program, such as making repeated measurements on inhouse check standards so that the random error of the measurement system can be

estimated and ensure that the measurement process is in control;

3) some understanding ofthe basic concepts of statistical analysis or access to a statistician

(NIST staffmembers are available to explain the detailed analysis ofa MAP report); and

4) a desire to respond creatively to the results of the MAP.

NIST insists that these conditions exist before participating to avoid wasting time and resources both

by the customer and NIST. Ifthe customer needs the analysis that a MAP provides, these conditions

should already exist.
2. DESCRIPTION OF SERVICES

2.1 Resistance MAP services

2.1.1 Present services. NIST offers MAPs at 1 Q and 10 kQ since they represent the two primary

levels at which most customers maintain their unit of resistance. In the past, MAPs at other

resistance levels have been offered, but have not been frequently requested by customers. In the

future, a high-resistance MAP will be offered to help address the special problems at levels above

1MQ.

Transfers at both levels take a minimum of 13 weeks. Data are taken at NIST on the transfer

standards for a minimum of four weeks. During the next four weeks the customer receives and

measures the standards. Then for four additional weeks NIST measures the same transport

standards. An additional week is necessary to process the data and to generate a report. Extra time

may be required during any part of the MAP if unusual circumstances or problems arise.

Unlike many other types of MAPs, a design is not required. Normal laboratory measurement

procedures can be used. The substitution methods used in resistance calibrations do not lend

themselves well to calibration designs. However, errors caused by leakage currents, and lead and

contact resistances are reduced by using substitution balancing techniques [2].

2.1.2 Group MAPs. Some laboratories engage in a regional group MAP, usually involving two

to six companies, where they compare their standards in a round-robin design. One company serves

as a pivot lab, and performs a MAP transfer with NIST, to link the data to the U.S. ohm. One such

scheme is shown in Figure 1 . Each lab begins by measuring a set oftransport standards against their

working standards. They then send the set to the next lab in the sequence, and receive another set of transport standards from another lab to calibrate. Eventually they work around the design until

the lab receives its own transport standards back, and measures them to achieve closure. This

provides traceability to NIST with no interdependence on the other labs.

If funds are available, the group can purchase a set of transport standards (possibly on the used

equipment market) and rotate the package to each lab in a similar sequence. The pivot lab would

begin and end the entire process with a set ofmeasurements to provide closure. This scheme allows

companies to reduce costs by sharing expenses and reducing the amount of effort required by NIST.

Companies presently involved in regional group MAPS have found an additional benefit: they have

discovered that this program provides a forum for the sharing of experience and information, which

aids everyone involved.
Transfer standards sequence Pivot Laboratory a b c d a A

b c d a b B

c d a b c C

d a b c d D

Figure 1 . Typical group MAP scheme.

2.1.3 Transport standards.

properties:

To serve as transfer standards, resistors require the following

1) low temperature coefficient of resistance (TCR) at the temperature of use;

2) long-term stability of resistance; and

3) rugged construction to handle traveling conditions.

The NIST 1 Q package consists of four double-walled manganin Thomas-type resistors [3], [4].

Manganin is an alloy of approximately 84 percent copper, 12 percent manganese, and 4 percent

nickel, and exhibits a small TCR at 25.0 °C and very good stability in resistance over time [3], [5].

The transport standards display TCRs within (( ± 3) x 10

" 6 )/K and drift rates within ((0 ± 0.1) x

10

" 6 )/year. All four of the resistors should be measured in an oil bath maintained at a nominal

temperature of 25.0 °C. This type of resistor has a pressure effect; therefore, the customer is asked

to record the barometric pressure at the time of measurement, as well as the depth of the oil to the

surface of the amalgamated current terminals of the resistor.

The 10 kQ package consists typically of four nickel-chromium alloy resistors [6], two to be

measured in oil at 25.0 °C, and two to be measured in air at 23.0 °C. This alloy consists of
approximately 75 percent nickel, 20 percent chromium, 2.5 percent copper, and 2.5 percent

aluminum [7], [8]. Like manganin, it has a small TCR at the temperature of use, and proves to be

stable in resistance over time. These transport standards have drift rates within ((0 ± 0.2) x 10"

6 )/year, and TCRs within ((0 ± 1) x 10

" 6 )/K. The oil-type resistors (measured at 25.0 °C) are mounted in cylindrical housings, with good thermal conductivity between the resistance element and

the outside metal case to minimize load effects and temperature errors. The air-types (measured at 23.0 °C) are mounted inside rectangular enclosures which are insulated to reduce the effects ofroom

temperature fluctuations. These standards have thermometer wells and temperature sensors in close

thermal contact with the resistance elements to monitor their temperature. The air-types display

slight pressure coefficients.

2.1.4 Limitations. As stated above, the transfer standards exhibit some effects resulting from the

transportation to and from the customer laboratory (see Table 1). This is especially true with the

Thomas-type resistors. Analysis of MAP data over a 3-year period shows that there can be a slight

shift in the mean value of a transfer standard. The 10 kQ level MAP packages reflect a slightly

smaller shift, especially for the air type standards, possibly a result of their more sturdy mounting.

The results in Table 1 were derived by fitting a line to the data that were taken before the standards were shipped, and fitting a line to the data that were taken after the standards were returned to NIST.

To determine the shift in the mean ofeach standard, the differences between the predicted values for

1 5 days after the transfer were averaged for each resistor. The estimated standard deviation is a pooled standard deviation of the standard deviation of each resistor for each transfer.

Table 1 . Effects on NIST MAP transfer standards resulting from transportation between NIST and

customer laboratories

NIST

MAP transfer

standards

shift in

mean

(x 10"6)

estimated standard

deviation

(x 10-6 )

1 Q total 0.028 0.059

10 kQ total 0.021 0.014

oil type 0.024 0.014

air type 0.018 0.013

The measurement results on each resistor are dependent on temperature. Since the temperature scale

is not transferred during the MAP, it is assumed that the customer's temperature scale has been

implemented according to the ITS-90. The recorded temperatures of the 1 Q transport standards and

the 10 kQ transport standards are expected to be known in terms of the ITS-90 to within 0.005 °C

and 0.05 °C, respectively. The temperatures of the air-type 10 kQ standards are measured using
temperature sensors positioned in their thermometer wells. The internal temperature sensors ofthese

resistors are not used, since they have significant load coefficients.

Customers utilize one of several systems for the measurement of resistance, such as current

comparators or one of a variety of resistance-ratio bridges. Some use direct comparison methods

or substitution methods, others use calibration designs. This can make it more difficult to identify

problem areas, since each customer has a unique operating procedure.

2.2 NIST resistance standards and measurements

NIST maintains the U.S. representation ofthe ohm, which has been based on the quantum Hall effect

since January 1, 1990 [9]. A reference group of five 1 Q Thomas-type resistors is maintained as a working standards group for calibration purposes. The mean of the group is predicted as a function

oftime from a linear least-squares analysis based on prior measurements against the quantized Hall

resistance. The group is calibrated periodically against the U.S. representation of the ohm, and the

results are compared to the predicted value to ensure the efficacy ofthe model used in the prediction

and the accuracy of the measurement system. This is described in detail in [2]. Working standards

are calibrated against this 1 Q group using special ratio techniques. The 10 kQ working standards

are calibrated by periodically scaling up from this reference group using Hamon devices or cryogenic

current comparators as ratio standards [2].

The 1 Q transport standards are measured using an automated direct current comparator (DCC)

potentiometer [10]. The 10 kQ transport standards are measured using an automated guarded

resistance bridge system [11]. NIST procedures follow recognized precision dc measurement

practices, including current reversal techniques (to eliminate the effects of constant or linearly

varying thermal emfs), substitution techniques (to reduce errors from leakage currents and lead and

contact resistances), careful selection of dummy resistors, measurements under minimum power

dissipation, and the use of check standards and statistical analyses to monitor the operation of the

measurement system [2]. The statistical tests include comparing the ranges of the readings of each

measurement run to a control value, comparing the measured values to the predicted values of each

resistor under test (including the check standard), and monitoring the bridge zero.

2.3 MAP transfer procedures

2.3.1 Setting up a MAP transfer. A MAP transfer begins when the customer contacts NIST to participate in the program (see Fig. 2). At that time, the customer and the NIST Calbration

Administrator make shipping, receiving, and billing arrangements, and NIST staff members are

available to address technical questions. For first-time MAP customers, the technical staffmember

discusses the customer's measurement process and statistical control procedures.

Next, NIST staff set up special working files. Historical files are kept for each resistance working

standard, including the MAP transport standards. From these files NIST staff create working files for each transport standard involved in the MAP. Each working file contains a header and the results

of the last 1 2 measurements made at NIST. The data taken at the customer's laboratory are added to these files.
Customer calls NIST Calibration Administrator.

Customer discusses measurement process am

statical control procedures with NIST technical starT.

Call NIST immediately!

Customer ships package

back to NIST

Customer and NIST

Calibration Administrator rr arrangements for:

1) scheduling;

2) shipping/receiving,

3) billing.

NIST stan* choose transter package.

NIST starT set up working tiles from history files.

Working files are analyzed

using COLLECT97 and are

labelled -before" data.

NIST ships MAP transfer package to customer using a approved carrier.

Call NIST to conrirm reception

of transfer package.

Allow the standards to settle In their appropriate temperature

environment for aproxlmately two days.

Customer measures resistors

to check condition Report

data to NIST technical sujff.

NIST creates a MAP file.

Customer ships package

back to NIST

Customer runs measurement

three times during the week

E-mail or ta« data to NIST

NIST adds data to MAP file.

NIST runs analysis or data

using MAP97 and COLLECT97, to check the data

MAP will be rescheduled when

system Is in control.

Customer makes arrangements

With NIST Catfcrauon

Administrator to return transfer package. JC

Figure 2. Flow-chart of resistance MAP procedures.
c

CONTINUE 3

MAP package is shipped to NIST via approved carrier

NIST receives MAP transfer package.

The resistors are allowed to

settle in their appropriate temperature environment for approximately two days.

NIST measures resistors to check condition.

NIST takes measurements three times a week for four weeks.

In the rare case that the MAP

package didn't return well, a new package may have to be

sent.

Data is placed into MAP file, and

analyzed using COLLECT97.

NIST generates a test report, which is checked, signed, and

mailed to the customer

c

STOP J

Figure 2 (continued). Flow-chart of resistance MAP procedures.

NIST staff check the transport standards by running the working files through a NIST program called

COLLECT97, which provides an analysis ofall the transport standards. This program performs a least- squared analysis ofthe data and determines the residual standard deviation. The program fits and plots

the data versus time to ensure that the standards and the measurement system are in control before

shipping. The program output is printed out and labeled "before" data, and the slope and intercept of

the fit of each resistor are noted for later reference.
Then the NIST Calibration Coordinator ships the MAP package to the customer. These transport

standards are rugged and transportable, and they are well characterized for effects of temperature,

pressure, and drift. They are packed and shipped, usually via air freight, to the customer in special

shipping containers. Oil-type resistors are placed in plastic bags prior to shipping, and the air-type

resistors have their lids attached and closed. The shipment includes a folder packed in the transport

box. The folder contains an introduction sheet, data sheets, return shipping labels, and a packing list (see Appendix 1.1).

2.3.2 Measuring the resistors and sending data to NIST. The transport standards should be treated as part of the typical customer workload; the MAP package should be measured in the same manner

as any other resistor that the customer receives for calibration. Thus the MAP data sheets ask only for

the final value assigned to the transport standard along with the appropriate environmental conditions

(temperature and pressure) for the particular measurement run. The customer laboratory has the choice

to correct the data for a transport standard to nominal temperature (23.00 °C or 25.000 °C) and standard

atmosphere (101.325 kPa) or have NIST make the corrections. Occasionally, the customer will be

requested to run a balanced design for one set of measurements in order to access within-run precision

and identify any measurement problems.

The customer performs measurements as outlined on the introduction sheet. The customer will make

approximately 12 measurements, unless unusual circumstances warrant something different. No

deviations from the instructions should be taken without first consulting the appropriate NIST staff.

The customer records the measurement results on the data sheets, as well as environmental conditions,

date and time of measurement, and the operator performing the measurement. The customer returns

the data to NIST at the end of each week, either by e-mail or fax. This allows NIST staff to follow the

progress of the measurements while the MAP package is at the customer's site.

NIST staff create a customer MAP file (see Fig. 3) and give it a filename based on the customer

laboratory, with an extension indicating the value of the MAP (e.g., 0T for 1 Q Thomas types, 4S for

10 kQ specials). This file includes the customer laboratory (e.g., LAB XXX), the resistance value of

the MAP (e.g., IT), the intercept year for the drift (e.g., DFYR 1997), and the depth of the oil (e.g.,

OIL 110) in mm on the first line. The second line labeled TR includes: the serial number of the

transport standard (e.g., 1002), the temperature coefficients (alpha inl0"

6/K and beta in 10"6/K2 ), drift

data (intercept value in 10"6 from nominal and the slope in lO'Vyear), and the pressure coefficient ofthe

standard in 10"9/hPa. The following lines labeled TL (only three of twelve lines indicated) include the

customer laboratory data: the measurement date, correction of the standard from nominal in 10"6

, the

barometric pressure in hPa, and the temperature of the standard in °C.

As data is received from the customer, it is placed in the MAP file. The MAPS97 software program

corrects the data in the MAP file to standard temperature and pressure, and stores the results in a file called ANALYSIS.MAP. The corrected data is then included in the working files (weighted "0") and

run by the COLLECT97 program (see Appendix 1.2). Thus, the data can be checked to see if all is running smoothly. If the COLLECT97 results of the "during" data shows anything unusual, the NIST

staff will notify the customer.
LAB LAB 1T DFYR 1997 OIL 110

TR 1002 2.2448 -0.5225 -0.8508 -0.0825 0.81

TL 02/24/1997 -1.173 1006.18 24.997 Z TL 02/26/1997 -1.172 1010.92 24.997 Z

TL 03/21/1997 -1.153 992.20 24.997 Z END

TR 1005 2.1458 -0.5231 -0.1952 -0.0972 0.90

TL 02/24/1997 -0.528 1006.18 24.997 Z TL 02/26/1997 -0.529 1010.92 24.997 Z

TL 03/21/1997 -0.519 989220 24.997 Z END PAGE

TR 1014 1.6648 -0.4380 1.5006 -0.4592 2.94

TL 02/24/1997 0.939 1006.18 24.997 Z TL 02/26/1997 0.942 1010.92 24.997 Z

TL 03/22/1997 0.915 992.20 24.997 Z END TR 1016 2.1738 -0.5260 -2.1422 -0.5033 3.09

TL 02/24/1997 -2.648 1006.18 24.997 Z TL 02/26/1997 -2.632 1010.92 24.997 Z

TL 03/21/1997 -2.648 992.20 24.997 Z END STOP STOP

Figure 3. Sample customer MAP file "LAB.OT".

2.3.3 Returning the MAP package. After the last customer measurements arrive at NIST, the

technical staffnotifies the Calibration Coordinator, who in turn notifies the customer, so that the return

shipping of the transport standards can be arranged. The customer returns the transport standards in

their original shipping container, using the shipping labels included with the MAP packet. The resistors

must be packed properly to minimize any effects as a result of shipping.

It is essential that the return of the standards be arranged through NIST. The Calibration Coordinator can assure that the shipping company understands the precautions and procedures necessary to lessen

any transportation effects (such as not letting the standards sit out on a hot airport tarmac). Failure to make arrangements through NIST can jeopardize the results of the MAP transfer.

2.3.4 NIST follow-up measurements. As the NIST technical staff take the first follow-up

measurements, they add the data to the transport standards working files. Running the COLLECT97

program determines if the resistors shifted during transit. If all looks well, the NIST staff takes 12

measurements over a period of four weeks, after which all measurements for the MAP are completed.

All of the follow-up data are placed in the working files (see Appendix 1.2).

10
2.3.5 Generating the report of the MAP. After all of the data are taken, the working files contain:

1) NIST "before" data (labeled "WEIGHT 1");

2) Customer "during" data (labeled "LWEIGHT LAB"); and

3) NIST "after" data (labeled "WEIGHT 1").

The COLLECT97 program analyzes the working files one last time, generating the updated slopes and

intercepts for the NIST measurements, slope and intercepts for the customer measurements, and the

random and systematic errors of the MAP (see Appendix 1.2).

Using the data generated by the COLLECT97 program, and information from the test folder, the NIST

technical staff generate a test report for the customer laboratory (see Appendix 1.2 and Appendix 1.3).

3. DATA ANALYSIS

3.1 Estimate of the difference between the customer's unit of resistance and the

U.S. ohm representation

Standard resistors usually display a linear drift over a short time period. Therefore, using the leastsquares method [12], a straight line is fitted to the corrections from nominal ofthe "before" and "after"

measurements taken by NIST on the transport standards, after being corrected for temperature and

pressure. The slopes and intercepts of the fitted lines are used to predict the values of the transport

standards on the dates of their measurements by the customer. Straight lines are also fitted to the data

taken by the customer. The estimate of the difference between the unit of resistance as maintained by

the customer laboratory and the U. S. ohm representation as maintained by NIST is determined by

subtracting each NIST predicted value from each customer predicted value for each transfer standard

for each date upon which the customer's measurements were made. Thus, for each resistor an average

difference, Ai?, can be determined. The average over all resistors, ARmea„

, represents the estimate of

the difference between the units.

If this estimate is greater in magnitude than the combined standard uncertainty of the particular

measurement, then NIST recommends adjusting the assigned mean value of the customer's reference

standards such that

OHM^ - OHM =

(1)

where OHMLAB is the unit of resistance at the particular level (either 1 Q or 10 kQ), and OHM is the

U.S. ohm representation. The combined standard uncertainty is determined by dividing the expanded

uncertainty by two (U/2).

3.2 Uncertainty of the estimate of the difference

The uncertainty ofthe estimate ofthe difference consists of the combination of the Type A and Type B

uncertainties resulting from errors in the measurement process [13], where Type A uncertainties are

11
those that are evaluated by statistical methods based on observed data, and Type B uncertainties are those that are not. The expanded, or overall uncertainty can be expressed by the following equation:

2 2 U = 2 { Slab + Snist + t stransfer v 2 \Ul

(2)

The standard deviation of the customer data (sUB) estimates the effect of random error resulting from

the customer laboratory measurements, and is determined by the following equation:

1 2 M N

\ MNJ y= i i=i Vlab ' (3)

where Mis the number of standards in the transfer package, N is the number of measurements at the

customer laboratory for each transfer standard, and where s. . is the estimated standard deviation of

'Jlab

the customer's predicted value of the/* resistor for the i

th measurement at the customer laboratory.

Since s. . is an estimate of the standard deviation of a predicted value for an actual measurement at

the customer laboratory, it is calculated from the customer's data using the following equation [14]:

2 2

'Jlab Jlab N

(*

'Jlab Jlab N

Ec*.

(4)

i=l

'Jlab Xj f) Jlab

where $ is the estimated residual standard deviation determined from the linear regression of the

Jlab

customer's data on the/ resistor, x is the r measurement value of they resistor, and x is

'Jlab J'ub

the mean value of all the customer laboratory measurements on they resistor.

The standard deviation of the NIST predicted data (sN/ST) estimates the effect of random error resulting

from the NIST measurements, and is expressed as

>NIST

( - \2 M N

(5)

12
where s. . is the estimated standard deviation of the NIST predicted value of they'"' resistor for the

iJNIST

i"

1 measurement while at the customer laboratory. The values of s. . are calculated from NIST data

Vmst

using the following equation, which is similar to eq (4):

2 2

'JNIST JNIST

{ \

1 'Jnist Jnist N A I Jj(jf -X. )2

7

J = l

(6)

where s. is the estimated residual standard deviation determined from the linear regression of the

Jnist

"before" and "after" NIST data on the/* resistor, x. . is the i

th measurement value of the/* resistor,

'Jnist

and x is the mean value of all the NIST measurements on the/'' resistor. Although the values of

Jnjst

s.. are determined for actual measurement dates at the customer laboratory and not for Vmst measurement dates at NIST, the measurement dates used in the calculations are inside the range of

NIST measurement dates and using the form of eq (4) is applicable.

The standard deviation of the AR measurements serves as an estimate of the variability of the transfer

standards (stransfer). The value of stransfer can be calculated by the equation:

1 m w= ' n E (**, - ^)2

. (7) M(M- l) 7= i

where

N

Mj N

2^(Rij(pred)IAB Rij(pred)mJ ( 8)

and represents the mean difference of the/* resistor for the i"' measurement, Rij(pred) is the NIST

predicted value of the//l resistor for the i'h measurement at the customer laboratory, and

MJ= i

13
Notice that any shifts in mean or variability resulting from transportation effects are reflected in the

above analysis.

To provide coverage for stransfer, which has a low degree of freedom, it is multiplied by t' , which is defined as

t t =

975 (10)

where 1 97S is a percent point of the Student t distribution. The value of t g75 depends on the number of

transfer standards (M), and can be obtained from Table 2. This value is divided by two to simplify the

expression of eq (2).

Table 2. Percent point of the Student t distribution for various values of M.

Number of Transfer Standards

M

Degrees of

Freedom

Percent Point

'.975

2 1 12.71

3 2 4.30

4 3 3.18

2. The quantity T>uB

in eq (2) is due to Type B uncertainties resulting from maintaining the working

standards in terms of the quantum Hall effect, determining the environmental conditions

(temperature and pressure), lead and contact resistances, leakage resistances, loading effects, and

predicting the values for the NIST resistors while at the laboratory. Other possible Type B

uncertainties in the measurement process are believed to be negligible. For a detailed analysis of

Type B uncertainties, see [2]. They are 0.021 x 10"6 for the 1 Q level and 0.037 x 10"6 for the 10 kQ

level.

The three Type A components and the Type B components are combined in quadrature (root-sumsquare) according to the guidelines recommended by the International Bureau of Weights and

Measure [15]. The uncertainty is multiplied by a coverage factor k = 2 as recommended in [13].

4. ACKNOWLEDGMENTS

The authors wish to express their gratitude to the Calibration Coordinator, Denise Prather, for her

hard work and cooperation in keeping the logistics of the resistance MAPs flowing smoothly. We

also like to thank Ted Moore for his invaluable service of setting up the computer files, entering the

customer laboratory data, and running the computer programs. In addition, we thank Jack Neal (now

retired) who for many years did the 10 kQ calibrations.

14
APPENDIX I: Typical MAP

The following pages contain the introduction, data sheets, analysis, and final report of a typical

resistance MAP. The information follows the outline below.

1.1 MAP Packet: contains procedures for both types of resistance MAPs, data sheets (including

a front data sheet), and packing and return shipping labels.

1.2 Analysis of data: contains the working files of the transport standards, and sample input files and output of the software programs, to reflect the analysis of the MAP process.

1.3 Results of MAP: contains a sample report of test and its associated appendices.

15
1.1 MAP Packet

Introduction: The MAP packet is placed in a folder, shipped with the transport standards, and

contains the following:

1.1 .1 Introduction to Resistance MAPs: explains the suggested measurement procedure

for both the 1 Q and the 10 kQ MAPs.

1.1.2 Front data sheet: gives data on the transport standards, and asks for information on

the customer's reference standards.

1.1.3 Data sheet: one data sheet for each measurement run oftransport standards; asks for

the measurement results, the environmental conditions during the measurement, the

date and time of measurement, and the name of the operator.

1.1.4 Shipping order and labels: shipping order and labels to place on the transport

standards case for return shipping.

Examples of each are contained in the following pages.

16
RESISTANCE MAP - 1 Q

Suggested Measurement Schedule:

1) Place resistors in oil bath @ 25 °C as soon as possible after arrival.

2) Measure resistors after ~ 2 days in oil bath and report measurements to NIST. Report the

data to the Technical Contact for resistance MAPs (301-975-4221). These are preliminary measurements to check the conditions of the resistors.

3) Measure each resistor three times a week from the 2nd through the 5th week for a total of

12 measurements for each resistor. After each week during this time period, send the data

to NIST for analysis. Fax data to:

National Institute of Standards and Technology

Electricity Division

Attn: Calibration Coordinator, Metrology B 146

Gaithersburg, MD 20899

FAX: 1-301-926-3972

4) If no complications arise, this completes the measurements by the customer laboratory.

The resistors are then packaged in their original container and returned to NIST. Contact

the Calibration Coordinator (301-975-4221) for shipping instructions.

5) If the resistors have not settled after the first week, additional measurements may be

necessary. You will be notified by NIST if this is the situation.

6) If problems arise with the resistors or time schedule, please notify the Technical Contact

for resistance MAPs.

17
RESISTANCE MAP - 10 kQ

Suggested Measurement Schedule:

1) Place resistors in their respective temperature environments (air temperature ~ 23 °C, oil

bath temperature = 25 °C) as soon as possible after their arrival.

2) Measure resistors after « 2 days in oil bath and report measurements to NIST. Report the

data to the Technical Contact for resistance MAPs (301-975-4221). These are preliminary measurements to check the conditions of the resistors.

3) Measure each resistor three times a week from the 2nd through the 5th week for a total of

12 measurements for each resistor. After each week during this time period, send the data

to NIST for analysis. Fax data to:

National Institute of Standards and Technology

Electricity Division

Attn: Calibration Coordinator, Metrology B 146

Gaithersburg, MD 20899

FAX: 1-301-926-3972

4) If no complications arise, this completes the measurements by the client laboratory. The

resistors are then packaged in their original container and returned to NIST. Contact the

Calibration Coordinator (301-975-4221) for shipping instructions.

5) If the resistors have not settled after the first week, additional measurements may be

necessary. You will be notified by NIST if this is the situation.

6) If problems arise with the resistors or time schedule, please notify the Technical Contact

for resistance MAPs.

18
FRONT DATA SHEET

FILL OUT THIS SHEET AND RETURN WITH FIRST RUN

ADDRESS

XYZ Resistance Laboratory Name P. P. Ems

Ohm City. MP 20899 phone #= 1-999-123-4567

SERIAL NUMBER CORRECTION NOM. TEMP. ALPHA BETA PRESSURE COEFF

,

(ppm) (°C) (ppm/°C) (ppm/°C2

) (ppb/hPa)

X0001 1.29 25.00 -1.26 -0.508 2.0

X0002 -0.35 25.00 4.81 -0.525

X0003 -2.45 25.00 -2.01 -0.512

X0004 6.01 25.00 3.65 -0.530

X0005 -0.87 25.00 2.54 -0.519

X0006 4.22 25.00 -1.22 -0.532

1002 25.00 2.2448 -0.5225

1005 25.00 2.1458 -0.5231

1014 25.00 1.6648 -0.4380

1016 25.00 2.1738 -0.5260

1.9

3.7

2.1

2.8

1.6

.61

.68

2 . .21

2 , ,32

INFORMATION NEEDED ON THIS SHEET

1. Corrections to the laboratory standards in ppm.

2. Nominal temperature of laboratory standards in degrees Celsius.

3. Temperature coefficients to the laboratory standards in ppm/°C and ppm/°C2

,

4. Pressure coefficients to the laboratory standards in ppb/hPa; if known.

19
Data Sheet No. 1

Laboratory: xyz Date: 2/24/1997 Time : 9 = 35 am

Assignment of corrections to the NIST transport standards by the Laboratory (LAB)

Serial Number Correction

(ppm)

Temperature

(°C)

Barometric

Pressure

(hPa)

Depth of Oil to

Mercury Wetted

Surface of Resistor

in mm

1002 -1.173

1005

1014

1016

-0.528

0.939

-2.648

24.997

24.997

24.997

24.997

1006.2

1006.2

1006.2

1006.2

Error Evaluation (if known)

Average Left -Right Error of Days Measurement

Standard Deviation of an Individual Measurement

Degrees of Freedom Associated with Std. Dev. Above

110.0

110.0

110.0

110.0

NA

N/\

N/\

II. The above corrections are based on intercomparison with the following laboratory

standards

.

Depth of Oil to

Barometric Mercury Wetted

Serial Number Correction Temperature Pressure Surface of Resistor

(ppm) (°C) (hPa) in mm

X0001

X0002

X0003

X0004

X0005

X0006

1.29

-0.36

-2.44

6.00

-0.88

4.22

24.997

24.997

24.997

24.997

24.997

24.997

1006.2

1006.2

1006.2

1006.2

1006.2

1006.2

110.0

110.0

110.0

110.0

110.0

110.0

In the above assignment of laboratory standard corrections

:

1. Were temperature corrections applied? Yes No i/

If Yes, to what temperature?

2

.

Were barometric pressure corrections applied? Yes No %/

If Yes, to what pressure?

3

.

Were corrections for depth of the oil to the mercury wetted surfaces applied?

Yes No •

20
Shipping Order and Labels

This form will be made out on a typewriter. Care should be taken to make the last copy legible. The last copy may be retained for your files. The first five copies should be left attached to the stub. 1

FORM NIST-386

(REV. 11- 88

SHIPPING ORDER

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

1. FOR FURTHER INFORMATION CALL - TELEPHONE NUMBER Calibration

Administrator (301) 975-4221

2. DIVISION 811

3. COST CENTER NUM8ER AND REQUISITION NUMBER 8111234 811-99994. DATE 2/19/97

5. SHIP FROM

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

RT. 270 & QUINCE ORCHARD ROAD

GAITHERSBURG, MD. 20899

6. SHIP TO XYZ Resistance Laboratory

51130 Thomas Drive

Ohm City, MD 20899

Attn: P.P. Ems

7. DESCRIPTION (Include NIST property and manufacturer's serial number when pertinent and itemize all separate parts or attachments)

HAZARDOUS MATERIAL D^S [S NO 4 - One-Ohm Resistors, Serial Nos. 1002, 1005, 1014, 1016

(It necessary, continue on plain paper with 4 carbon copies) 8. ESTIMATED VALUE S 20,000.00

9. SUGGESTED METHOD OF SHIPMENT Messenger Service

10. Q PREPAID Q COLLECT

11 PURPOSE (E.G. , RETURN OF TEST MATERIAL, LOAN, REPAIRS. ETC.) Participation in the Resistance Measurement Assurance

Program

12. AUTHORIZED

Group Leader, 811

(Signature and Title)

13. NUMBER PIECES 1

14. GROSS WEIGHT 15. ESTIMATED SHIPPING COST 16. B/L NUMBER 17. SHIPPED VIA 18. DATE

19. remarks please keep in controlled environment

between 18 & 28°C

20. RECEIVED BY

USCOMM-DC 89-6029

21
1.2 Analysis of MAP data

1.2.1 Introduction. This section discusses the working files and the input and output files of the

software analysis at different points in the MAP process, showing a step-by-step analysis ofthe data.

The outline below describes the sequence of data and analysis.

1. "Before" data:

a. Historical files: Data files are kept on all of NIST's working standards, including the

transport standards. To begin a MAP, working files containing the most recent 12 data

points are created from these historical files.

b. COLLECT97: Before NIST ships the transport standards to the customer, a least-squared

analysis is performed on the data for the transport standards, using the COLLECT97

program, to check the performance of the package. The output is labeled "before" data, and

the slope and intercept for each resistor are noted for future use in the MAP file.

2. "During" data:

a. MAP file: When the customer begins sending data on the transport standards back to NIST,

the data are placed in a special MAP file, which also contains the following information on

each standard: serial number, slope and intercept based on the "before" data, temperature

coefficients (a and (3), pressure coefficient, and nominal temperature. In addition, the file contains the customer name in abbreviated form, and the depth of the resistors below the oil

in the customer's oil bath.

b. MAPS97: The MAPS97 program takes the newly created MAP file, and corrects the

customer data for temperature and pressure, and stores all the data in a file called

MAPS97.0UT. A listing of a sample MAPS97.0UT file is shown in Appendix 1.2.2.

c. ANALYSIS.MAP: This file is also an output ofthe MAPS97 program. It contains only the

measurement dates and the corresponding "corrected" customer data that are to be entered

in the working files.

d. Working files: The data from ANALYSIS.MAP are added to the working files. A listing

of sample working files, containing the output data from ANALYSIS.MAP, are shown in

Appendix 1.2.3. The customer data are labeled "LWEIGHT LAB", while the NIST data are labeled "WEIGHT 1."

e. COLLECT97: A least-squares analysis is performed on the customer data and the NIST

data using the COLLECT97 program. This program fits the NIST data, then fits the

customer data, and then finally determines the uncertainty of the measurement process.

These data are labeled "during" data.

22
standards. This allows NIST staff to monitor the MAP in progress, and to identify and possibly

correct any errors.

3. "After" data:

a. Working files: After the transport standards have returned from the customer, initial measurements are made and stored in the working file, and labeled "WEIGHT 1 ."

b. COLLECT97: COLLECT97 is run on the working files to determine if any shift has

occurred upon returning. These data are labeled "after" data.

For a period of about 4 weeks, NIST staff continues to take data, storing the results in the

transport standard working files.

4. "Final" data:

a. Working files: NIST stafftake measurements on the transport standards and enters the data

in the working files until 12 or more measurements have been taken since the return of the

MAP package (see Appendix 1.2.3).

b. COLLECT97: The final least-squares analysis on all the customer data and on all the NIST

data is performed using COLLECT97. A listing of a completed COLLECT97 output is shown in Appendix 1.2.4. The output of this program includes all the information needed to generate a test report for the customer laboratory: the customer laboratory's corrected data,

the difference data between the customer laboratory and NIST, the Type A and Type B

uncertainties, and the expanded uncertainty.

Note that the generalized equation for the standard deviation of a predicted value (STDPV)

listed in the COLLECT97 output is given in matrix notation and is equivalent to the form of

eqs (4) and (6) in the text. In the matrix equation, A and B correspond to the variances ofthe

slope and intercept, respectively, and C is the covariance element, or off-diagonal term, of

the variance-covariance matrix. The time variable, T, in the equation corresponds to the

x-variable in the text equations. For a more detailed explanation on the equivalency of these

equations refer to pages 82-83 in [14] or a similar text book on regression analysis.

23
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25
1.2.3 Sample "Final" Data

Working Files

File: M1002M.0T

HEADER ANALYSIS OF NIST 1 Q RESISTOR 1002 INTERCEPT 1997 UNITS PPM SCALE 1.0 ITEM 1002 DATA 01/20/1997

01/22/1997

01/24/1997

01/27/1997

01/29/1997

01/31/1997

02/03/1997

02/05/1997

02/07/1997

02/10/1997

02/12/1997

02/14/1997

LWEIGHT LAB 02/24/1997 -1.1681 02/26/1997

02/28/1997

03/03/1997

03/05/1997

03/07/1997

03/10/1997

03/12/1997

03/14/1997

03/17/1997

03/19/1997

03/21/1997

WEIGHT 1 03/31/1997

04/02/1997

04/04/1997

04/07/1997

04/09/1997

04/11/1997

04/14/1997

04/16/1997

04/18/1997

04/21/1997

04/23/1997

04/25/1997

END

File: M1005M.0T

-0.9288

-0.9333 -0.9274

-0.9268

-0.9163

-0.9215 -0.9212

-0.9164 -0.9183

-0.9100

-0.9100

-0.9150

-1.1709

-1.1393 -1.1567

-1.1546

-1.1408

-1.1551 -1.1757

-1.1347

-1.1354

-1.1601

1, 1368

-1.0131 -1.0116

-1.0106

-1.0090 -1.0118

-1.0108

-1.0028

-1.0081

-1.0101 -1.0058

-1.0105 -1.0127

HEADER ANALYSIS OF NIST Q RESISTOR 1005 INTERCEPT 1997 UNITS PPM SCALE 1.0 ITEM 1005 DATA 01/20/1997 -0.3077

01/22/1997 -0.3056 01/24/1997 -0.3088 01/27/1997 -0.3113 01/29/1997 -0.2931 01/31/1997 -0.3011 02/03/1997 -0.2970 02/05/1997 -0.2957

02/07/1997 -0.2992 02/10/1997 -0.2929 02/12/1997 -0.3020 02/14/1997 -0.2980

LWEIGHT LAB 02/24/1997 -0.5236 02/26/1997 -0.5289 02/28/1997 -0.4942 03/03/1997 -0.5158 03/05/1997 -0.5167

03/07/1997 -0.4980 03/10/1997 -0.5141 03/12/1997 -0.5262 03/14/1997 -0.4977

03/17/1997 -0.4994 03/19/1997 -0.5247

03/21/1997 -0.5020 WEIGHT 1 03/31/1997 -0.3688 04/02/1997 -0.3625 04/04/1997 -0.3652 04/07/1997 -0.3693 04/09/1997 -0.3644 04/11/1997 -0.3624 04/14/1997 -0.3633 04/16/1997 -0.3647

04/18/1997 -0.3641 04/21/1997 -0.3622 04/23/1997 -0.3663 04/25/1997 -0.3633

END

26
HEADER ANALYSIS OF NIST 1 Q RESISTOR 1014 INTERCEPT 1997 UNITS PPM SCALE 1.0 ITEM 1014 DATA 01/20/1997 1.1906 01/22/1997 1.1866 01/24/1997 1.1907 01/27/1997 1.1835 01/29/1997 1.1874 01/31/1997 1.1877 02/03/1997 1.1927 02/05/1997 1.1861 02/07/1997 1.1892 02/10/1997 1.1879 02/12/1997 1.1901 02/14/1997 1.1871 LWEIGHT LAB 02/24/1997 0.9374 02/26/1997 0.9264 02/28/1997 0.9695 03/03/1997 0.9478

03/05/1997 0.9461 03/07/1997 0.9675 03/10/1997 0.9484

03/12/1997 0.9343 03/14/1997 0.9720

03/17/1997 0.9700 03/19/1997 0.9388

03/21/1997 0.9545 WEIGHT 1 03/31/1997 1.0963 04/02/1997 1.0889 04/04/1997 1.0897

04/07/1997 1.0900 04/09/1997 1.0909 04/11/1997 1.0935 04/14/1997 1.0917 04/16/1997 1.0930 04/18/1997 1.0958 04/21/1997 1.0950 04/23/1997 1.0980 04/25/1997 1.0957

END

HEADER ANALYSIS OF INTERCEPT 1997 UNITS PPM SCALE 1.0 ITEM 1016 DATA 01/20/1997 -2.4108 01/22/1997 -2.4131 01/24/1997 -2.4132 01/27/1997 -2.4056 01/29/1997 -2.3992 01/31/1997 -2.4058 02/03/1997 -2.4094 02/05/1997 -2.4131 02/07/1997 -2.4105 02/10/1997 -2.4101 02/12/1997 -2.4069 02/14/1997 -2.4111 LWEIGHT LAB 02/24/1997 -2.6485 02/26/1997 -2.6471 02/28/1997 -2.5977

03/03/1997 -2.6254 03/05/1997 -2.6271 03/07/1997 -2.6033 03/10/1997 -2.6254 03/12/1997 -2.6350 03/14/1997 -2.5964 03/17/1997 -2.5993 03/19/1997 -2.6342 03/21/1997 -2.6053 WEIGHT 1 03/31/1997 -2.4738 04/02/1997 -2.4787 04/04/1997 -2.4804 04/07/1997 -2.4792 04/09/1997 -2.4846 04/11/1997 -2.4801 04/14/1997 -2.4776 04/16/1997 -2.4786 04/18/1997 -2.4804 04/21/1997 -2.4808 04/23/1997 -2.4739 04/25/1997 -2.4736

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1.3 Results of MAP

1.3.1 Introduction. The following pages contains the test report for a typical 1 Q resistance MAP.

The 10 kQ report is similar. The report contains the following:

1.3.2 Report of Test, reports the difference between the unit of resistance as maintained by the

customer, and the U. S. legal ohm, as maintained by NIST, and states the total uncertainty;

1.3.3 Appendix A, which explains the derivation of the uncertainty;

1.3.4 Appendix B, which summarizes the results between NIST and the customer; calculates the

uncertainty, and

1.3.5 Appendix C, which contains information on the customer's reference standards based on the

results of the MAP.

The data for calculating the uncertainty in Appendix B are obtained from the output of the

COLLECT97 program. As an example, the a, b, c, and d quantities indicated on page 39

(page 12 of the COLLECT97 output) correspond to the terms in eq (2) in the text or to the

identical equation in the Report of Test. They are calculated in the following manner, using

12 as the number of measurements (N), and 4 as the number of transfer standards (M):

a) This quantity (sLAB )is calculated using eq (3). The s. values are found on pages 36

and 37 (pages 9 and 10 ofthe COLLECT97 output) under the "SDPV" headings for the four

MAP transfer standards. For this example "a" is equal to 0.816 x 10" 18.

b) This quantity (sNIST ) is calculated using eq (5). The s

tJ values are found on page 30

(page 3 of the COLLECT97 output) under the "SDPV" headings for the four MAP transfer

standards. For this example, "b" is equal to 0.128 x 10" 18.

c) This quantity (t stransfer ) is obtained using eqs (7), (8), (9), and (10). The percent point

of the Student t distribution in eq (10) is found in Table 2 and, for this example, is equal to

3.18. The Ai?' s and AT? are calculated using eqs (8) and (9) with the data found on page 30

(page 3 of the COLLECT97 output). As listed on page 30, the AR' s for the four transfer

standards are -0.187 ppm, -0. 1 79 ppm, -0. 1 90 ppm, and -0. 1 77 ppm, respectively; the value

of AR is -0.183 ppm. The result of eq (7) then becomes 0.100 x 10"4

. Squaring eq (10) and

multiplying it with eq (7) results in a value for "c" equal to 0.254 x 10" 16

.

d) This quantity ( / , uB ) is the Type B variance of the measurement process and is equal

to (0.021 x 10"6)

2 for the 1 Q level (see [2] for a detailed analysis).

44
REPORT OF TEST

RESISTANCE MEASUREMENT ASSURANCE PROGRAM

AT THE 1 Q LEVEL

XYZ Resistance Laboratory

Ohm City, MD 20899

The difference between the unit of resistance at the 1 Q level maintained by the above laboratory

(LAB) and the U.S. legal ohm, as maintained by the National Institute of Standards and Technology

(NIST) in terms of the quantum Hall effect, was determined during the period between

February 24, 1997 and March 21, 1997, and found to be:

OHMLAB - OHM = ( 0.183 ± 0.043 ) ppm

The above value is based upon the test procedure described in Appendix A and the data summarized

in Appendix B of this report. The expanded uncertainty of this difference given above is equal to

<> J 2 2 /

2 2 ^2 yW

Z I SLAB SNIST X Stransfer + ^UB I '

where sLAB and sNIST are the estimated Type A standard uncertainties based on the standard deviation

of the measurements at the customer laboratory and NIST, respectively, t'stransfer is the estimate of

the variability of the transfer standards, and uB

(i) is the estimated Type B standard uncertainty for

each known component of uncertainty arising from a systematic effect (see Appendix A). The

coverage factor 2 used by NIST is consistent with international practice.

If the measured difference between the unit of resistance as disseminated by the above laboratory

and the U.S. legal ohm is greater in magnitude than the combined standard uncertainty (0.022 ppm),

it is recommended that the assigned mean value of the laboratory's reference resistors be adjusted

so that OHMLAB - OHM = 0. Appendix C has been included in this report to facilitate recommended

adjustments.

Measurements performed by: For the Director,

(Technical Staff) (Group Leader), Group Leader

Electricity Division Electricity Division

Test Report No.: 81 1/012345-97

Reference: ABC- 123

Date: April 1, 1997

Telephone Contact: 301-975-4221

45
Appendix A

Before and after the client laboratory measurements were taken on the transport resistors,

determinations were made of the corrections to nominal of the transport resistors at NIST in terms

of the U.S. legal ohm. Since resistors of this type usually exhibit a linear change in resistance with

time, a straight line was fitted to the corrections to nominal determined at NIST for each resistor

using the method of least squares, after adjustment to nominal temperature and barometric pressure.

The resultant straight line was also fitted to the laboratory-assigned corrections to nominal for each

ofthe transport resistors. The estimate ofthe difference, AR, in ppm, between the assignment ofthe

resistance value of a transport resistor by the client laboratory and NIST was determined by

subtracting the NIST predicted value from each laboratory predicted value for the same date.

The uncertainty of the estimate of the difference consists of the combination of the Type A and

Type B uncertainties resulting from random and systematic errors of the measurement process,

where Type A uncertainties are those that can be evaluated by statistical methods based on observed

data, and Type B uncertainties are those that cannot. The expanded, or overall uncertainty can be

expressed by the following equation:

U = 2 { sly, + sIjsj. + t' 2slansfer + £fij(0 }

m .

The standard deviation of the customer's data (sUB) estimates the effect of random error resulting

from the customer's laboratory measurements, and is determined by the following equation:

SLAB

1 \2 M N

V mnJ JL, Z-j slab„

j- 1 i- l

where Mis the number of standards in the transfer package, Wis the number ofmeasurements at the

customer's laboratory for each transfer standard, and where 5 is the estimated standard

•th : „* c *i .-th

,

deviation ofthe customer's predicted value ofthe/ resistor for the 1 measurement at the customer's

laboratory.

The standard deviation of the NIST predicted data (sNIST) estimates the effect of random error resulting from the NIST measurements, and is expressed as

SNIST

1 . \2^ n

I S EE NIST„ '

where 5 is the estimated standard deviation of the NIST predicted value of the/1 resistor for

the i

th measurement at the customer's laboratory.

Test Report No.: 81 1/012345-97

46
The standard deviation of the AR measurements serves as an estimate of the variability of the

transfer standards (stransfer). The value of stransfer can be calculated from the equation:

1 M

'transfer M(M~ 1) pi

£ (A*, - AR)2

,

where

N

M

j ~ -7rT,(Rij ~ Rij(pred)) > N ,= i

and represents the mean difference of they resistor for the i measurement, Rij(pred) is the NIST

predicted value for/h resistor for the f" measurement at the customer's laboratory, and

i m

AR = -£A# . MjTx J

Notice that any shifts in the mean or variability resulting from transportation effects are reflected in

the above analysis.

To provide coverage for stransfer, which has a low degree of freedom, it is multiplied by f , which is defined as

t =

'.975

where t 915 is a percent point of the Student t distribution. The value of 1 975 depends on the number

of transfer standards (M), and can be obtained from Table 1 . This value is divided by 2 because in

the expanded uncertainty equation (C/) it is effectively multiplied by the coverage factor 2.

Table 1. Percent point of the Student t distribution for various values of M

Number of Transfer Standards

M

Degrees of

Freedom

Percent Point

'975

2 1 12.71

3 2 4.30

4 3 3.18

Test Report No.: 811/012345-97

47
The Type B uncertainties (uB

(i)) result from: a) maintaining the working standards in terms of the

quantum Hall effect; b) determining the environmental conditions (temperature and pressure), lead

and contact resistances, leakage resistances, loading effects; and, c) predicting the values for the

NIST resistors while at the laboratory. Other possible Type B uncertainties in the measurement

process are believed to be negligible. For a detailed analysis ofType B uncertainties, refer to "NIST

Measurement Service for DC Standard Resistors," by R. F. Dziuba, P. A. Boynton, R. E. Elmquist,

D. G. Jarrett, T. P. Moore, and J. D. Neal, NIST Technical Note 1298 (USGPO, Washington, DC,

November 1992). The standard Type B uncertainties are 0.021 ppmforthe 1 Q level and 0.037 ppm

for the 10 kQ level.

The Type A components and the Type B components are combined in quadrature (root-sum-square)

according to the guidelines recommended by the International Bureau of Weights and Measures in

order to obtain the combined standard uncertainty. This combined standard uncertainty is multiplied

by a coverage factor k = 2 to obtain the expanded or overall uncertainty (U) as recommended in

"Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results," by B.

N. Taylor and C. E. Kuyatt, NIST Technical Note 1297 (USGPO, Washington, DC, 1992).

Ifthe measured difference between the unit ofresistance as disseminated by the customer laboratory

and the U.S. legal unit ofresistance is greater in magnitude than the characteristic standard deviation

of a measurement of this type (U/2), it is recommended that the assigned mean value of the

laboratory's reference resistors be adjusted so that OHMLAB - OHM = 0.

Test Report No.: 81 1/012345-97

48
Appendix B

Summary of results between NIST and LAB

Table 2. Summary of corrections to NIST transport standards.

Corrections in parts per million to nominal value are given for the NIST transport standards at a

standard temperature of 25.00 °C and a standard pressure of 1013.25 hPa, which also includes a

correction for the depth of oil to the mercury wetted surface of the resistor.

The results of this test were determined from data supplied by LAB taken from February 24, 1997

to March 21, 1997.

DATE RUN

02/24/97 1 02/26/97 2

02/28/97 3

03/03/97 4

03/05/97 5

03/07/97 6

03/10/97 7

03/12/97 8

03/14/97 9

03/17/97 10

03/19/97 11

03/21/97 12

mean

ymMn

S/N 1002 S/N 1005 S/N 1014 S/N 1016

-1.168 -0.524 0.937 -2.648

-1.171 -0.529 0.926 -2.647

-1.139 -0.494 0.970 -2.598

-1.157 -0.516 0.948 -2.625

-1.155 -0.517 0.946 -2.627

-1.141 -0.498 0.968 -2.603

-1.155 -0.514 0.948 -2.625

-1.176 -0.526 0.934 -2.635

-1.135 -0.498 0.972 -2.596

-1.135 -0.499 0.970 -2.599

-1.160 -0.525 0.939 -2.634

-1.137 -0.502 0.954 -2.605

-1.152 -0.512 0.951 -2.620

0.004 0.004 0.004 0.006

Test Report No.: 81 1/012345-97

49
Appendix B

(Continued)

Table 3. Summary of differences between LAB and NIST.

Values for AR are given, in parts per million.

AR == CorrLAB - CorrNIST DATE RUN S/N 1002 S/N 1005 S/N 1014 S/N 1016

02/24/97 1 -0.211 -0.195 -0.212 -0.201

02/26/97 2 -0.208 -0.192 -0.209 -0.197

02/28/97 3 -0.204 -0.190 -0.205 -0.193

03/03/97 4 -0.198 -0.186 -0.200 -0.187

03/05/97 5 -0.194 -0.183 -0.196 -0.183

03/07/97 6 -0.190 -0.181 -0.192 -0.180

03/10/97 7 -0.184 -0.177 -0.187 -0.174

03/12/97 8 -0.180 -0.174 -0.183 -0.170

03/14/97 9 -0.177 -0.172 -0.180 -0.166

03/17/97 10 -0.171 -0.168 -0.174 -0.160

03/19/97 11 -0.167 -0.166 -0.171 -0.156

03/21/97 12 -0.163 -0.163 -0.167 -0.152

mean -0.187 -0.179 -0.190 -0.177

^mpan 0.005 0.003 0.004 0.005

AR Mean = -0.183 ±U

Summary of uncertainty determination:

Number of Runs = 12

Total Degrees of Freedom = 1

U = 2 x { 0.0082 x 10"4 + 0.0013 x 10 4 + 0.2538 x 10"4 + 4.4100 x 10"4

}'A

U = ± 0.043 ppm

Test Report No.: 81 1/012345-97

50
Appendix C

Recommended adjustment to LAB reference resistors

Laboratory: XYZ Resistance Company Laboratory Standards: 6

CorrLAB - CorrNIST -0.183

The table below contains information about your reference standards. Laboratory assigned

corrections are the corrections used in determining the results of this experiment. The NIST

assigned correction to each standard is the calculated mean of all values assigned to the standards

in the experiment adjusted to the A R mean value found in Appendix B.

If the measured difference between the unit of resistance as disseminated by the above laboratory

and the U.S. legal unit ofresistance is greater in magnitude than the combined standard uncertainty

(0.021 ppm), it is recommended that the assigned mean value of the laboratory's reference resistors

be adjusted so that QLAB - Q = 0.

Table 4. Recommend adjustment to LAB reference resistors.

LAB NIST

SERIAL ASSIGNED ASSIGNED

NUMBER CORRECTION CORRECTION TEMPERATURE

(ppm) (ppm) (°C)

X0001 +1.29 +1.47 25.00

X0002 -0.35 -0.17 25.00

X0003 -2.45 -2.27 25.00

X0004 +6.01 +6.19 25.00

X0005 -0.87 -0.69 25.00

X0006 +4.22 +4.40 25.00

Mean +1.31 +1.49

Test Report No.: 81 1/012345-97

51
REFERENCES

[1] C. Croarkin, "Measurement Assurance Programs Part II: Development and

Implementation," Natl Bur. Stand. (U.S.), Spec. Pub. 676-11 (USGPO, Washington, DC,

April 1984).

[2] R. F. Dziuba, P. A. Boynton, R. E. Elmquist, D. G. Jarrett, T. P. Moore, and J. D. Neal,

"NIST measurement service for dc standard resistors," NIST Technical Note 1298

(USGPO, Washington, DC, November 1992).

[3] J. L. Thomas, "A new design of precision resistance standard," NBS Journal of Research,

vol.5, 1930, pp. 295-304.

[4] J. L. Thomas, "Stability of double-walled manganin resistors," NBS Journal of Research,

vol. 36, January 1946, pp. 107-1 10.

[5] J. L. Thomas, "Precision resistors and their measurement," NBS Circular 470, October

1948, pp. 2-3.

[6] G. D. Vincent and R. M. Pailthorp, "Experimental verification of the five-terminal ten- kilohm resistor as a device for dissemination of the ohm," IEEE Trans. Instrum. Meas.,

IM-17, December 1968, pp. 239-244.

"New alloy has improved electrical resistance properties," Materials and Methods, vol.

28, pp. 62-63, Aug. 1948.

[8] C. P. Marsden, "Three design considerations in selecting resistance alloys," Electrical

Manufacturing, vol. 42, pp. 116-121, Aug. 1948.

[9] N. B. Belecki, R. F. Dziuba, B. F. Field, and B. N. Taylor, "Guideline for implementing

the new representations of the volt and the ohm effective January 1, 1990," Natl Inst. Stand. Tech., Tech Note 1263 (USGPO, Washington, DC, June 1989).

[10] K. R. Baker and R. F. Dziuba, "Automated NBS 1 Q measurement system," IEEE Trans.

Instrum. Meas., IM-32, pp. 154-158, Mar. 1983.

52
[11] R. F. Dziuba and L. L. Kile, "An automated guarded bridge system for the comparison of

10 kQ standard resistors," IMTC/97 Digest, IEEE Cat No. 97CH36022, pp. 394-396,

May 1997.

[12] J. M. Cameron, "The use of the method of least-squares in calibration," NBS Interagency

Report 74-587, September 1974.

[13] B. N. Taylor and C. E. Kuyatt, "Guidelines for evaluating and expressing the uncertainty

of NIST measurement results," NIST Technical Note 1297, 1994 Edition, (USGPO,

Washington DC, 1994).

[14] N. R. Draper and H. Smith, Applied Regression Analysis. John Wiley & Sons, 1981.

[15] International Bureau of Weights and Measures (BIPM) Working Group on the Statement

of Uncertainties, Metrologia, vol. 17, pp. 73-74, 1981.

53



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