NBSIR 76-999

Surveillance Test Procedures

H. W. Aimer

Edited by: Jerry Keller

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

February 1 976

Final

Issued May 1 977

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBSIR 76-999

SURVEILLANCE TEST PROCEDURES

H. W. Aimer

Edited by: Jerry Keller

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

February 1976

Final

Issued May 1977

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Acting Director

SURVEILLANCE TEST

PROCEDURES

H. E. Aimer

Abstract

Surveillance tests are designed to monitor the values of

mass standards between calibrations. T\jo types are

described; both consist of comparisons of the weights of an

ordered set of mass standards with each other. The

differences found are compared with those computed from the

reported mass values. Surveillance limits based on the

precision of both the calibration and the surveillance test

processes are computed. These limits are estimates of the

departure of the measured differences from the expected, or

predicted, differences as computed from the reported values.

A larger change is considered significant. Additional

measurements to identify individual weights v/hich have

changed are required when a given comparison indicates that

the mass of one or more of the weights involved has changed.

Buoyancy corrections are used to correct for the difference

in the buoyant effect on weights of differing densities.

Records document the surveillance test results, and control

charts help detect trends. Judgments concerning

recalibration can be made based on the constancy of the

weights relative to the use requirements.

Key words: Apparent mass; buoyancy; buoyancy correction;

change; comparison; difference; mass; records;

set; surveillance limits; surveillance test;

test interval; true mass; value; weighing

design; weights.

CONTENTS

Page

1. Introduction 1

2. Measurement Procedures 1

2.1 Type I Surveillance Test 2

2.2 Type II Surveillance Test 4

3. Surveillance Limits 6

3.1 Uncertainties of Each of the Summations from the 6

Calibration Mass Measurement Process Known

3.2 Uncertainties for Individuals but not Summations from ^ the Calibration Mass Measurement Process Known

3,2.1 Numerical Example 7

4. Identifying Weights Which Have Changed 8

4.1 Analysis of Measurement Results . 9

4.2 Numerical Examples 10

5. Buoyancy Corrections 11

5.1 Buoyancy Corrections Computed on True 11

Mass Basis

5.2 Buoyancy Corrections Computed on Apparent 13

Mass Basis

5.3 Application of Buoyancy Corrections 15

5.3.1 Buoyancy Correction Application for 15

True Mass

5.3.2 Buoyancy Correction Application 16

for Apparent Mass

6. Records

7. Surveillance Test Interval

REFERENCES 20

Appendix 1. Weighing Designs for Surveillance Tests 21

Weighing Designs for Type I 22

Surveillance Tests

Weighing Designs for Type II 28

Surveillance Tests

Appendix 2. Surveillance Test Examples 36

Type I Surveillance Test Example 36

Type II Surveillance Test Example 51

1. INTRODUCTION

Surveillance test procedures are designed to monitor the values of

mass standards between calibrations. This is important because

the problem of the continuing validity of the values contained in

the report of calibration is always present, and especially so for

those who look to others for calibration service. Surveillance

test procedures, if properly implemented, so provide a means of

detecting gross changes as soon as possible with a minimum expendture of time and effort.

Two types of surveillance tests are described. The first type,

designated Type I, uses a minimum number of measurements that involve all of the weights in the set. The second type, designated

Type II, requires a larger number of measurements which are

grouped so that they are a series of 3-1' s weighing designs? This

method has some redundancy.

Included in the surveillance test procedures are methods of

identifying any weights whose mass values may have changed since

they were calibrated, and methods of correcting for the buoyant

effect of the atmosphere.

2. MEASUREMENT PROCEDURES

A surveillance test consists of a series of comparisons of the

weights of an ordered set of mass standards with each other,

according to an appropriate weighing design, and comparing the

differences in mass value found by these comparisons with those

computed from the values contained in the report of calibration

[1]*. Ideally a suitable known weight, other than one of the

weights in the set being tested, is used as the standard on which

the values found by the surveillance test are based. This also

establishes whether or not the whole set has changed

proportionally. For sets where the largest weight is one

kilogram or less, the nominal value of the weight used as a standard should be that of the largest weight in the set. For

example, a set whose largest v/eight is lOOg is being tested. For

this set, a lOOg weight whose mass value is knovm would be

suitable for use as a standard. For sets having weights greater

than one kilogram, a suitable one kilogram weight may be used as

the standard. For sets in the avoirdupois system having weights

greater than one pound, a suitable one pound weight may be used

as the standard. Generally the uncertainty of the mass value of

a one kilogram, or a one pound standard, is less than the

uncertainty of the value of a larger standard.

^ A title given to the three intercomparisons of three objects

A, B, and C, namely the measurements of the differences A-B,

A-C, and B-C.

* Figures in brackets refer to similarly numbered references

at the end of this paper.
If a Xv'eight of the suggested denomination is not available, a

suitable known weight of a different denomination, if available,

may be used to establish whether or not the whole set has

changed. The nominal value of this weight should be equal to

that of one of the larger weights in the set being tested, say

not less than 20g for a set beginning at lOOg, or less than lOOg

for a set beginning at 1kg. Where the weight used as the

standard has the same nominal value as the largest weight in the

test set, up to one kilogram, the comparison between the standard

and the largest weight of the set is a part of the surveillance

test v;eigl)ing design. VThere the nominal value of the weight used

to establish whether the whole set has changed is not the same as

the largest weight of the test set, the comparison between it and

the corresponding weight of the test set is a side measurement

and not a part of the surveillance test vreighing design.

Wliere a suitable kno\^m weight, other than the v/eights in the set

being tested, is not available, the usual procedure is to base

the values found by the surveillance test on the largest weight

of the set under test, up to one kilogram. Weights larger than

one kilogram may be based on the largest v/eight of the set. The

weighings may be made by either the substitution or the

transposition method of weighing [2].

In general, the capacities of the balances selected for surveillance tests should be the smallest available that will accommodate the maximum load to be placed on it. For example, when

testing a set of vreights ranging from lOOg to Img, a balance

having a capacity of from lOOg to 200g would be used for loads

from lOOg to 20g, and a balance of 20g capacity for loads under

20g. If a balance of say Ig and 2g capacity were available, it

would be used for the fractional weights.

2.1 Type I Surveillance Test

In a type I surveillance test, the first measurement is

the comparison between the largest v/eight of the set and

a summation of the next smaller weights, from the set,

the sum of whose nominal values is equal to that of the

largest v/eight. The next comparison would be between a

selected vrelght from the summation, that is, the

summation used in the first com.parlson, and another

summation whose nom.inal value is equal to that of the

selected weight.

This procedure of selecting

and comparing it with a summa

weights is repeated until a

have been involved in a compa

should involve the fewest wei

the weights of the set to be

comparisons

a weight from each summ.atlon

tlon of the next smaller

11 of the v/eights of the set

rison. Any given comparison

ghts that will permit all of

included in the chain of

- 2 -
If a suitable weight having the same nominal value as the

largest weight of the set is available for use as a

standard, then the first comparison would be between this

weight and the largest weight of the set.

If, for example, a set of weights ranging from lOOg to

Img is to be tested using the Type I surveillance test

procedures where another lOOg weight is to be used as a

standard, the ratios of the weights to each other are 5,

3, 2, 1. The first comparison would be:

lOOg - SlOOg = ai

The second comparison would be:

lOOg - IlOOg = a2

where IlOOg = 50g + 30g + 20g

The third comparison would be:

20g - Z20g = a3

where J:20g = lOg + 5g + 3g + 2g

This procedure is continued until all of the weights have

been compared.

In this example the last comparison V70uld be:

3mg - E3mg = a^^

where ^3mg = 2mg + Img.

The observed differences in mass values (ai,a2»....a )

Tl found by these comparisons are compared with the accepted

differences, as computed from the reported values, to

determine the degree of agreement between the observed

and the accepted differences. If the agreement is within

the limits for surveillance (see section 3) any indicated

changes may be regarded as being insignificant, and the

continuing validity of the reported values may be

assumed. If the agreement between the observed and the

accepted differences is not within the surveillance

limits, the indicated changes should be regarded as

significant, and the weights exhibiting a significant

change should be recalibrated. When the result of a comparison indicates that one or more of the weights has

changed significantly, additional measurements are made

to identify the weight, or weights, that have changed.

- 3 -
2.2 Type II Surveillance Test

In a Type II surveillance test, the measurements of the

first 3-1 's weighing design series are between the

largest weight of the set, another weight of the same

nominal value, and a summation of the next smaller

weights from the set also having the same nominal value

as the largest weight of the set. The comparisons of the

next 3-1 's weighing would be between a selected weight

from the summation, used in the first 3-1 's series, and

two other summations, of the next smaller weights, whose

nominal values are the same as that of the selected

weight. This procedure of selecting a weight from a

summation and comparing it with other summations of the

next smaller weights according to the 3-1 's weighing

design is repeated until all of the weights of the set

have been involved in the com.parisons

For example, a set ranging from lOOg to Img is to be

tested using the Type II surveillance test procedures,

where another lOOg weight^ is to be used as a standard.

The ratios of the weights to each other are 5, 3, 2, and

1. The first series according to the 3-1 's weighing

design would be:

SlOOg - lOOg = ai

SlOOg - ZlOOg = a2

; lOOg - ZlOOg = a3

where SlOOg is the standard

lOOg is the lOOg of the set being tested

ElOOg = 50g + 30g + 20g

If a suitable known lOOg weight is not available for use as a standard, the first series according to the 3-1 's weighing design

would be:

lOOg - lOOg' = ai

lOOg - ZlOOg - a2

lOOg'- ZlOOg = a3

where

lOOg' is any lOOg weight, or a summation v;hose nominal value is

lOOg, used to fill the series Z]00g = 50g + 30g + 20g. The other

series remain as indicated.

- 4 -
The second series would be:

where

30g - Z30gi = aj

30g - Z30g2 = a2

230gi- E30g2 = ag

Z30gi = 20g + lOg

Z30g2 = 20g + 5g + 3g + 2g

This procedure is continued for each decade until all of the

weights in the set have been compared. Unless the set contains an extra Img weight or another Img weight whose mass

value is known is available, the 3-1 's weighing design cannot

be used for the last decade. Where the set has only one Img

weight and another is not available to fill the series, the

comparisons for the last decade are:

5mg - 3mg - 2mg = a^

3mg - 2mg - Img = a2

These two comparisons are treated as the comparisons in Type

I surveillance test. Where the set has two Img weights, or

another Img weight whose value is known, is available, the

last series is:

where

3mg - i:3mgj = ^1

3mg - ^3mg2 = ^2

2:3mgj- ^:3mg2 = ^3

Z3mgj= 2mg + Inigj

£3mg2= 2mg + lmg2

The lmg2 may be either the second Img weight of the set or

another Img weight whose mass value is known.

If a weight other than one of the same denomination as the

largest weight in the set is used to establish whether or not

all the weights of the set have changed proportionately, then

some other known weight must be compared to a weight of the

set or (e.g. in this case) a known 30g is compared with the

30g of the set.

30g - S30g = a

- 5 -
If this difference agrees with the expected difference as

computed from the reported values of the two weights,

within the surveillance limit, (see section 3), and the

observed differences of the other comparisons are in

agreement with the predicted differences, it may be

assumed that the set as a whole has not changed

significantly.

Because in most of the series used in a Type II

surveillance test one of the weights is part of both

summations used in a given series, the weighings are made

by the substitution method of weighing. For example, in

the series involving the 30g weight, ZBOg^, and Z:30g2,

the 20g weight is part of both summations.

3. SURVEILLANCE LIMITS

3.1 Uncertainties of Each of the Summations from the Calibration

Process Known [l], [3]

Ideally the surveillance limits are calculated from the

standard deviations of the calibration process and

surveillance test process as follows:

si = U + 3a, (1)

c d

where U = uncertainty of calibration process

= standard deviation of one weighing

of the surveillance test process

si = surveillance limit

3.2 Uncertainties for Individuals but not Summations from the

Calibration Process Known

Sometimes only the uncertainties associated with the mass

values of the weights, as reported in the Calibration

Report, are available for estimating the uncertainties of

the summations. In this situation, an approximate estimate of the uncertainties is found by taking the square

root of the sura of the squares of the uncertainties of

the values of the weights in a given comparison [4].

- 6 -
Suppose that the comparison is between a selected weight,

Wj , and a summation consisting of three weights, W2 , and

Wj^ , whose nominal value is equal to that of the selected

weight, Wi . The uncertainty of each value is , U2 , U3

and Uij respectively.

An approximate estimate of the uncertainty, U , for these

weights is:

where is the uncertainty of the calibration mass

measurement process and

\J. is the uncertainty for the individual weights

as reported on the Report of Calibration.

With this procedure, the expression for the surveillance

limit is:

si = + 3a^ (3)

where is the uncertainty as defined above, and

si and oj have the same meaning as in equation (1).

This process is equally applicable for any number of weights

For most designs, this procedure gives a somewhat smaller

uncertainty than the uncertainties from the calibration

process

3.2.1 Numerical Example

Assume that the following weights and their associated un- certainties are involved in the comparison lOOg - I^lOOg.

Weight Uncertainty

lOOg 0.015

50g 0.011

30g 0.012

20g 0.010.

- 7 -
- -^0.0152 + O.OlF + 0.012^ + 0.010?

= ^0.00025 + 0.000121 + 0.000144 + O.OOOl'

0.00059

0.024 mg

This Is an approximate estimate of the uncertainty of the

calibration process for this comparison.

Now let us assume that the standard deviation of one

weighing of the surveillance test process is 0.015 rag.

Then the surveillance limit, si, is:

si = 0.024 + 3(0.015)

si = 0.024 + 0.045

= 0.069 mg

4. Identifying the Weights X\%ich Have Changed

If, in any comparison, the observed difference differs from the

predicted value of the difference by more than the surveillance

limits for that comparison, the weight, or vreights, that have

changed must be identified so that they can be recalibrated. The

identity of the weights that have changed may be established by

additional measurements. In general, these additional

measurements are comparisons between the weights making up the

sum.mation that vras compared with the selected weight.

Suppose, for example, that the observed difference of

20g - Z20g = a

where Z20g = lOg + 5g + 3g + 2g

differs from the predicted value of the difference by more than

the surveillance limits. Assume, also, that the observed

differences in the comparison in which the 20g weight was a part

of the summation, lOOg - ZlOOg, and the comparison in which the 2g

weight was the selected weight, 2g-Z2g, are in good agreement

with their predicted, or accepted, differences as computed from

the reported values. This indicates that neither the 20g weight

nor the 2g weight have changed significantly. The following

measurements are made and their results analyzed to identify the

v/eight, or weights, whose masses have changed:

- 8 -
lOg - (5g + 3r + 2g) a'

5g - (3g + 2g) a

I !

3g - (2g + Ig) a

A.l Analysis of Measurement Results

If a' differs from the predicted value by more than the

surveillance limits and a'' and a''' agree with the

predicted value within the surveillance limits, it is

probable that the lOg weight has changed. If both a' and

a'' differ from the corresponding predicted values by

more than the surveillance limits by about the same

amount, numerically, but with opposite signs, and a'*'

agrees with the predicted value within the surveillance

limit, it is probable that the 5g weight has changed. If

a' and a'' differ from the corresponding predicted values

by markedly difference amounts which are greater than the

corresponding surveillance limits, and a'*' agrees with

the corresponding predicted value within the surveillance

limit, it is probable that both the lOg and the 5g

weights have changed.

If a', a'*, and a'*' all differ from the corresponding

predicted values by more than the surveillance limits,

but by about the same am.ount, it is probable that the 3g

weight is the one that has changed. If a' and a'' differ

from the corresponding predicted values by about the same

amount, but a'*' differs from the corresponding predicted

value by a markedly different amount, it is probable that

both the 5g weight and the 3g v/eights have changed.

If the results of all three measurements differ from the

corresponding predicted values by more than the

corresponding surveillance limits, by markedly different

amounts, it is probable that all three weights have

changed and may require recalibration.

If all three (a', a'', and a''') of the observed

differences are in good agreement with the predicted

differences, it is still possible that the weights involved in either of the comparisons

experienced compensating changes in mass, even though the

agreement between the observed differences and the

predicted differences were within the surveillance

limits. However, this is an unlikely situation. But, if

it does occur, the weights that have changed may be

identified in the manner described for the comparison

between the 20g and I20g weights, as may the weights

involved in any measurements where the observed

difference does not agree with the predicted difference

within the surveillance limits.

lOOg - ElOOg = ai or 2g - Z2g = a

3

- 9

-
In any event, if it is determined that several weights of

a given set require recalibration (more than, say, three

or four weights in a lOOg to Img set, or more in a larger

set) the entire set should be recalibrated.

4.2 Numerical Example

The following numerical example, using difference

measurement 20g - Z20g, discussed above, illustrates the

procedure.

The observed value of the difference:

20g - Z20g = +0.084mg

The predicted value is +0.052mg. The surveillance limit

is +0.028mg. The difference between the observed value

and the predicted value is:

+0.08Amg - 0.052mg = 0.032mg

This difference exceeds the surveillance limits and

indicates that the mass of one or more of the weights

involved has changed. Three weighings were made to

determine which weight, or weights, have changed. The

results of these measurements are:

Observed Predicted

Value of Value of Surveillance

1

t • I

Observation

lOg - (5g + 3g + 2g) =

5g - (3g + 2g)

3g - (2g + Ig)

Difference Difference Limit

-0.025 mg -0.057 mg 0.024 mg

-0.065 mg -0.032 mg 0.018 mg

+0.031 mg +0.034 mg 0.015 mg

Examining these results, we find that the agreement

between the observed value and the predicted value for

a'" is well within the surveillance limit, thus

virtually ruling out any change in the masses of the 3g

and 2g weights. But, the observed values for a' and a''

do not agree with the predicted values within the

surveillance limits. Further, the observed values for

both a' and a'' differ from the predicted values by about

the same amount, but with opposite signs.

For a' -0.025 - (-0.057) = +0.032 mg

For a" -0.065 - (-0.032) = -0.033 mg

- 10 -
I

Had it been only for a' that the observed value did not

agree with the predicted value, within the surveillance

limit, it would he logical to conclude that the mass of

the lOg weight had changed. But, for both a' and a'',

the observed values of the differences do not agree with

the predicted values by about the same amount,

numerically, though with opposite signs. Therefore,

the conclusion is that the mass of the 5g weight has

changed because it is involved in both a' and a*', while

the lOg weight is involved only in a'. Further, the 5g

weight is in opposed positions in the two equations.

5. BUOYANCY CORRECTIONS

Buoyancy corrections are used to account for the difference in

the buoyant effect of the air on weights of differing densities

[5] . In some instances it will be necessary to apply buoyancy

corrections to the measured differences between weights in surveillance tests because the buoyant effect on the weights may

mask real changes in their masses, or apparent changes in mass

may be indicated v;hen there is no change. This is true whether

the computations of the results are made on the true mass or the

apparent mass basis. In general, the buoyancy corrections

computed on the true mass basis are numerically greater than

buoyancy corrections computed on the apparent mass basis when

weights having widely different densities are involved in a given

comparison.

It is always good practice to compute, at least roughly, the

magnitude of the correction to establish the order of magnitude

with reference to the uncertainty of the surveillance test

measurement [1]. If the correction is not significant, it can be

ignored

5.1 Buoyancy Corrections Computed on True Mass Basis

When the results of the surveillance test weighings are

computed on the true mass basis, the expected differences

being computed from the reported mass (true mass) values,

the true mass buoyancy correction term, pAV, for the

m.easured difference may be derived from the weighing

equation for the difference between two v/eights.

- 11 -
(.^Q - pVc)8 ~ P^D^g = ^8 weighing equation (1)

where: and M^^ = the masses of weights C and D, respectively

and = the volumes of C and D, respectively, from

the Report of Calibration

p = air density when weighing was made

a = the indicated difference in mass units

g = acceleration of gravity

The derivation of the buoyancy correction term, pAV, for

the true mass difference between the two masses C and D

is

(M^ - pVj^)g - (M^ - pVj^)g = ag weighing equation (1)

- pV^ - + pVj^ = a dividing by g (2)

M - = a + p (V - V ) transposing and

collecting terms (3)

M - = a + pAV substituting AV

for (V^ - V^) (4)

It is better to use the form of the buoyancy correction term,

p (V^ - Vp) , in equation (3) above when computing the buoyancy

correction because its sign is more readily apparent. The

following example illustrates this.

The measured difference, a, between 2g and E2g is

0.0388mg.

Weight Volume

2 g 0 .2564 cm^ from Report of

1 g 0 .12820 cm^ II II •1

500 mg 0 .03012 cm3 M II II

300 mg 0 .01807 cm^ II II II

200 mg 0 .01205 cm^ II •1 II

^2g 0 .1884 cm3 II II M

p = 1.17 mg/cra^

- 12 -
The true mass difference:

2g - 12% = +0.0388 + 1.17(0.2564 - 0.1884)

= +0.0388 + 0.0796 = +0.1184 mg

If volumes are not listed on the Report of Calibration,

they may be computed from:

, Mass Volume = Density

5.2 Buoyancy Corrections Computed on Apparent Mass Basis

I'Then the results of the weighings are computed on the

apparent mass^ basis [5], the expected differences being

computed from the reported apparent mass values, the

apparent mass buoyancy correction term, ApAV, for the

measured differences m.ay be derived from the expression

for finding the apparent mass when the true mass and the

volume are known.

where

AM^^ = apparent mass value of weight "W" versus the reference material (R)

= mass (true mass) of weight "W"

p = density of normal air

n

V„ = volume of weight "W" at 20 "C

w

V = volume of equivalent mass of the reference material

(R) at 20 °C

The derivation of the buoyancy correction term, ApAV, for the

apparent mass difference between the weights C and D is:

1 In the United States, the apparent mass is usually expressed as

apparent mass versus normal brass in normal air. Normal brass is

defined as brass having a density of 8.4 g/cm^ at 0 °C and a coefficient of cubical expansion 0.000054 per degree C. Normal air

is defined as air having a density of 1.2 mg/cm^ at 20 "C.

- 13 -
AM,

AM,

- = \ - Pn^^ - \^ subtracting (8)

- AMj^ = M^ - Mj^ - P/C + ^n^

"

substituting a + P (V^ - V^^) for (M^ - M^^)

(see equation (3))

(9)

AM^ - AMp = a + (p - P^) (Vj, - Vjj)

= a + ApAV

combining terms (10)

substituting ApAV for (11)

where AM^ and AM^

M^ and

the apparent mass of weights C and D

the masses of weights C and D

and = the volumes of C and D, respectively,

from the Report of Calibration

V, =

n

the volume of equivalent mass of

normal brass, the reference m-aterial

the air density when the weighing was

made

the density of normal air at 20 °C.

It is better to use the form in equation (10) above when computing

the buoyancy correction term because its sign is more readily

apparent

The following example illustrates this:

The measured difference, a, between 2g and E2g is 0.0388 mg.

Weight Volume

2 g

1 g

500 mg

300 mg

200 mg

0.2564 cm ^ from Report of Calibration

0.12820 cm3

0.03012 cm3

0.01807 cm^

0.01205 cm^

"

g 0.188A cm^

p = 1.17 mg/cm^

Pj^= 1.20 mg/cm^

- 14 -
The apparent mass difference

2g - Z2g = + 0.0388 + (1.17 - 1.20)(0.256A - 0.188A)

= + 0.0388 + (-0.03)(0.0680)

= + 0.0388 - 0.0020

= + 0.0368 mg

5.3 Application of Buoyancy Correction

The buoyancy correction terms derived above are correct

when the mass difference and the volume difference of the

weights are taken in the same direction. That is, if the

difference between the masses of weights C and D is taken

as Hq - Mp then their volume difference must be taken as

V - V or the buoyancy correction will have the wrong

sign.

If, when assigning a mass value to one of the two weights

being compared with each other, the other weight being

used as the standard, a buoyancy correction is used, it

is essential that the correct sign be used for the

buoyancy correction term.

5.3.1 Buoyancy Correction Application for True Mass

Consider the relationship

substituting for a, p, V , and and D their values, we

get the true mass value or C, provided the true mass

value of D was used.

If C, the first v/eight in the difference, C - D, is the

standard (this is the situation in many weighing designs)

then.

C - D = a + p (V^ - V^) (1)

If D is the standard then

C = a + p(V^ - Vp) + D (2)

-D = a + p(Y - V ) - C

C 1)^

and

D = -a - p(V^ - Vj^) + C (3)

- 15 -
Substituting for a, p, V^,, Vp and C their values, we get

the true mass value of D, provided the true mass value of

C was used.

Note that the sign of the buoyancy correction term in (3)

above is minus. This application is illustrated on the

computation sheet for the 3-1 's weighing design.

5.3.2 Buoyancy Correction Application for Apparent Mass

Consider the relationship

C - D = a + (p - p ) (V - V_ ) (4)

n L u

If D is the standard, then

C = a + (p - P„)(V_ - V ) + D (5)

n C D

Substituting for a, p, p^, V^^, Vp, and D their values, we

get the apparent mass value of C, provided the apparent

mass value of D was used.

If C, the first v/eight in the difference, C - D, is the

standard (this is the situation in many weighing designs)

then,

-D = a + (p - p ) (V - V_ ) - C

n c u

and

D = -a - (p - p^) (V^ - V ) + C (6)

n L U

Substituting for a, p, Pj^, V^, Vp and C their values, we

get the apparent mass value or D, provided the apparent

mass value of C was used.

Note that the sign of the buoyancy correction term in (6)

above is minus. This application is illustrated on the

computation sheets for the 3-1 's weighing design as used

in the example for the Type II surveillance test (see

appendix 2)

- 16 -
6. RECORDS

Records are an essential part of any measurement program. In a

surveillance test program, adequate records are necessary to

document the continuing validity of the reported mass values and

to realize the full value of the program. Such records may be

simple, or elaborate, as long as they contain the information

needed to document the claimed validity of the mass values. A

notebook or card file should be maintained containing a description of the test system. This should include a statement of the

procedures, a list of standards (if any) and weighing

instruments, test intervals, and a tabulation of the accumulated

results of tests. The records should also include the identity

of the weights, the expected, or predicted, values of the

differences measured as computed from the reported values, and

the surveillance limits. The calibration report should be an

integral part of the records. In addition, where the Type II

Surveillance Test is used, the estimate of the standard deviation

should be compared for each 3-1 's series, compared with the long

term estimate of the standard deviation and recorded. This

information, combined V7ith the original data sheets, forms an

adequate record. A large operation m.ay require a more elaborate

record keeping system.

Control charts [3] similar to the one illustrated on page 18 are

a useful addition to the surveillance test records. Control

charts show more readily than tabulations whether a trend in the

values of the differences being measured is developing. Such

trends, when detected, can signal the need for recalibration before the values of the mass standards become invalid.

7 .SURVEILLANCE TEST INTERVAL

The purpose of surveillance test procedures is to assure continu

ing validity of the values contained in the calibration report

and to prevent, or at least minimize, the possibility of using

the weights as standards when their reported values are no longer

valid. But, when and how frequently should the surveillance test

procedures be used in order to achieve this goal? Because of the

many variables affecting the stability of the weights, such as

the type of weights, the use to which the weights are put, the

care they receive, etc., a categorical answer covering all situations cannot be given.

- 17 -
SURVF.ILLANCE TEST

CONTROL CHART

SET RANGES lOOg - Ig

CALIBRATION TEST NO, NBS 200390

TED rsmsrs

-LI MIX

i:

-it-r- MG

Sims

+d.DZO

D40

m +.020

-c.ico

-1

100

d.o<45 ; <&

7-":""--- - +.00f

:..t.:-.

•4 •-.

" .1 +C^079:6

-I

t

T.

13'

+.07

r --r -1

+O.-0-3Z0 'd

: ft, 0236

I

I 1 -0,049

0.019 <r

1

0:

0:

1
The following suggestions, where they are applicable, may serve

as general guide lines for the use of surveillance tests and the

interval between surveillance tests.

1. Immediately upon the receipt of a newly calibrated

set of weights, comparisons should be made to verify

the values reported.

2. If this is a set for which no history exists, the

comparisons should be repeated monthly, or bimonthly

until the degree of stability of the weights has

been demonstrated.

3. Where sufficient information about a set of weights

has been developed to predict their performance with

some degree of certainty, this information may be

used in determining the interval between surveillance tests.

4. If there has been an accident with the weights, such

as dropping them on the floor, at least the weights

involved in the accident should be given a surveillance test before being used as standards to be sure

that their reported values are still valid.

5. If a facility performs a large number of calibrations, its procedures should provide "built-in"

checks on standards and if the standards checked on

are part of the set in question, the information developed from these "built-in" checks can be used to

determine when a surveillance test is needed.

6. Where the number of calibrations performed is small,

the standards may be given a surveillance test just

prior to using the standards in the calibration of

other weights.

- 19
REFERENCES

[1] Pontius, P. E., Measurement Philosophy of the Pilot

Program for Mass Calibration, Nat. Bur. Stand. (U.S.),

Tech. Note 288, 39 pages (1968).

[2] Aimer, H. E., Method of Calibrating Weights for Piston

Gages, Nat. Bur. Stand. (U.S.), Tech. Note 577, 49 pages

(1971).

[3] Pontius, P. E. , Cameron, J. M. , Realistic Uncertainties

and The Mass Measurement Process, Nat. Bur. Stand.

(U.S.), Monogr. 103, 17 pages (1967).

[4] Youden, W. J., Statistical Methods for Chemists, John

Wiley & Sons, New York (1541).

[5] Nat. Bur. Stand. (U.S.), Handbook 77, Precision Measurement and Calibration, Volume III, Optics, Metrology and

Radiation, Circular 3, pp. 671/53 to 683/65. This handbook is available for reference in. most Government

Depository Libraries throughout the United States.

- 20 -
APPENDIX I. WEIGHING DESIGNS FOR SURVEILLANCE TESTS

The weighing design used in a given surveillance test depends on

the range of the set and ratio of the weights in the set to each

other. Some suggested weighing designs for weight sets having 5,

3,2,1; 5,2,2,1 and 5, 2, 1,1, El ratios are shoxm for various

ranges. Other designs may be developed by using the principles

outlines in section 2 for situations where the suggested weighing

designs do not apply. The surveillance test weighing designs are

shown with metric units of mass. But with a given design,

customary units of mass can be substituted for the metric units,

provided the ratios of the weights to each other are the same in

both systems.

- 21 -
Vjeighing Designs for Type I Surveillance Test

Design 1

Set - Range: Ikg to Img Ratio 5, 3, 2, 1

1kg - Slkg = a^*

Slkg = Standard 1kg

1kg - Zlkg =

Ilkg = 500g + 300g + 200g

200g - Z200g = a^

Z200g = lOOg + 50g + 30g + 20g

20g - Z20g = a^^

Z20g = lOg + 5g + 3g + 2g

2g - E2g = ag

I2g = Ig + 500mg + 300mg + 200mg

200iug - I200tng = a^

6

Z200ing = lOOmg + 50nig + 30mg + 20mg

20mg - Z20ng = a^

Z20ng = lOmg + Sing + 3i!ig + 2mg

3mg - E3mg = ag

Z3ing = 2mg + Img

* If a known 1kg weight suitable for use as a standard is not

available, this "a" is omitted and 1kg - Zlkg becomes the

first "a", 200g - I200g = a^, 20g - Z20g = a^, etc.

- 22 -
Design 2

Set - Range: lOOg to Img Ratio: 5, 3, 2, 1

lOOg - SlOOg = a^*

SlOOg = Standard lOOg Weight

lOOg - ZlOOg = a^

ZlOOg = 50g + 30g + 20g

20g - J:20g = ag

nOg = lOg + 5g + 3g + 2g

2g - E2g = a^^

Z2g = Ig + 500mg + 300mg + 200mg

200rag - Z200mg = a^

Z200mg = lOOmg + 50mg + 30mg + 20mg

20mg - E20nig = a^

Z20ing = lOmg + 5mg + 3mg + 2ing

3mg - Z;3mg =

3mg = 2ing + Img

For sets in which the smallest weight is Ig, the last "a" would

be

3g - Z3g = a

Z3g = 2g + Ig

* If a known lOOg weight suitable for use as a standard is not

available, this "a" is omitted and lOOg - ZlOOg becomes the

first "a", 20g - Z20g = a^y etc.

- 23 -
Design 3

Set - Range: 1kg to Img Ratio: 5, 2, 2, 1

1kg - Slkg = aj*

Slkg = Standard 1kg Weight

1kg - Zlkg =

Slkg = 500g + 200gj + 200g2 + lOOg

lOOg - ElOOg

ElOOg = 50g + 20gj + 20g2 + lOg

lOg - ZlOg =

ZlOg = 5g + 2gj + 2g2 + Ig

Ig - Zlg = ag

Ilg = 500ir«.g H 20Cingj + 200ing2 + lOOmg

lOOmg - ZlOOmg = a^

IlOOmg = 50mg + 20mg^ + 20ingp + lOtng

lOrag - ElOmg = a^

ZlOmg = 5mg + 2iTigj + 2mg2 + Inig

* If a knouTi 1kg weight suitable for use as a standard is not

available, this "a" is omitted and 1kg - Zlkg becomes the

first "a", and lOOg - ZlOOg = a2, lOg - ZlOg = ag, etc.

- 2A -
Design 4

Set - Range: lOOg

lOOg

lOOg

lOg

Ig

lOOmg

lOmg

For the set in which the smallest weight is Ig, the last "a"

would be:

5g - ESg = a

ESg = 2gj + 2g2 + Ig

* If a known lOOg weight suitable for use as a standard is

not available, this "a" is omitted and lOOg - ElOOg becomes the first "a", and lOg - ElOg = a^ , etc.

- Img Ratio: 5, 2, 2, 1

- SlOOg = a^*

SlOOg = Standard lOOg Weight

- ZlOOg =

ZlOOg = 50g + 20g^ + 20g^ + lOg

- SlOg = a^

ZlOg = 5g + 2g^ + 2g^ + Ig

Zlg = 500mg + 200mg^ + 200mg^ + lOOmg

- ZlOOmg = a^

ZlOOmg = 50mg + 20mg^ + 20mg^ + lOmg

- ZlOmg = a

6

ZlOmg = 5mg + 2iag + 2mg + Img

- 25 -
Design 5

Set - Range: 30kg - Img Ratio: 5, 3, 2, 1

30kg - Z30kg = a

J Z30kg = 20kg + 10kg

10kg - ElOkg = a2

ZlOkg = 5kg + 3kg + 2kg

2kg - Z2kg = a

3

Z2kg = 1kg J + lkg2

1kg J- Elkg = a^^

Zlkg = 500g + 300g + 200g

200g - Z200g = a^

Z200g = lOOg + 50g + 30g + 20g

20g - Z20g = ag

Z20g = lOg + 5g + 3g + 2g

2g - Z2g = a^

Z2g = Ig + 500mg + 300iug + 200ng

200ng - Z200ing = ag

Z200mg = lOOmg + 50mg + 30mg + 20mg

20ing - Z20mg = ag

Z20mg = lOmg + 5mg + 3ing + 2rag

2mg - E2ing = a^Q

Z2iag = Img J - lmg2

- 26 -
Weighing Designs for Type I Surveillance Tests

Design 6

Set - Range: lOOg - Img Ratio: 5, 2, 1, 1, Zl

lOOg - SlOOg = ai*

SlOOg = Standard lOOg weight

lOOg - ZlOOg = a2

ElOOg = 50g + 20g + lOgi + 10g2 + ZlOg

lOgi - ZlOg = a^

ZlOg = 5g + 2g + Ig^ + lg2 + Zlg

Zlg = 500mg + 200mg + lOOmgj^ + 100mg2 + ZlOOmg

lOOmgj - IlOOmg =

ZlOOmg = 50mg + 20ing + lOmg^ + 10mg2 + IlOmg

lOmgj - ElOmg ~

ZlOmg = 5ing + 2mg + Img^ + lmg2 + Inig^

\^/hen comparing the unit of weight of a given decade of weights

with summation of smaller v/eights from a weight set in which the

ratio of the weights to each other 5, 2, 1, 1, 1, it is

necessary to include all of the set's weights smaller than the

unit weight to which summation is being compared. For example:

in the comparison lOOg - ElOOg, the SlOOg includes all of the

weights in the set smaller than lOOg; and in the comparison lOg - ZlOg the ZlOg includes all of the weights smaller than lOg and so

on.

If a known lOOg weight suitable for use as a standard is

not available, this "a" is omitted and lOOg - ZlOOg

becomes the first "a" and lOg - ElOg = a2, etc.

- 27 -
Weighing Designs for Type II Surveillance Tests

Design 7

Set - Range: 1kg to Img Ratio: 5, 3, 2, 1

Series 1 Slkg - 1kg = a^*

Slkg - Elkg = aj

1kg - Zlkg = ag

Slkg = Standard 1kg

Elkg = 500g + 300g + 200g

Series 2 300g - SSOOg^ = a^

300g - Z300g2 = 32

E300gj - Z300g2 = 33

Z300gj = 200g + lOOg

I300g2 = 200g + 50g + 30g + 20g

Series 3 30g - I30g^ = a^

30g - Z30g2 = ^2

Z30gj - J^30g2 = ag

Z30gi = 20g + lOg

i:30g2 = 20g + 5g + 3g + 2g

Series 4 3g - ^3g-^ a 1 3g - I3g2 = a2

Z3gj - I3g2 = ag

ngi = 2g + Ig

J:3g2 = 2g + 500mg + 300mg + 200mg

- 28 -
Series 5 300mg - Z300mgj =

300mg - Z300mg2 = a2

S300mgj - Z300mg2 =

Z300mgi = 200nig + lOOmg

Z300mg2 = 200mg + 50mg + 30mg + 20mg

Series 6 30mg - iSOmgj = a^^ 30mg - Z30mg2 = 32

Z30mg2 - Z30Tng2 =

E30mgj = 20mg + lOmg

E30mg2 = 20ing + 5mg + 3ing + 2mg

Series 7 3mg - Z3mgj = a^

3mg - Z3mg2 = 32

Z3mgj - E3mg2 =

E3mgj = 2mg + Irngj

, Z3mg2 = 2mg + lrag2**

* If a knovm Ikg weight, suitable for use as a standard is not

available, any 1kg or Elkg may be used to fill the series.

Then the 1kg of the set is used as the standard and the first

series of measurements is:

1kg - 1kg' = aj

1kg -Zlkg = 32

1kg' -Ukg = 33

where 1kg' is either the 1kg weight or the Zlkg used to comple

the series.

** The lmg2 is an extra Img weight used to fill the last series.

- 29 -
Design 8

Series - Range: lOOg to Img Ratio: 5, 3, 2, 1

Series 1

Series 2

Series 3

SlOOg - lOOg = aj*

SlOOg - ZlOOg = ag

loog - J:ioog = 33

ElOOg = 50g + 30g + 20g

30g - ESOgj = aj

30g - Z30g2 = a2

S30gi - i:30g2 = ag

ESOgi = 20g + lOg

Z30g2 = 20g + 5g + 3g + 2g

3g - 23gi = aj

3g - 23g2 = a2

Z3gi - Z3g2 = ag

T>3gi = 2g + Ig

Z3g2 = 2g + 500ing + 300mg + 200mg

Series 4 300mg - Z:300mgi = aj

300mg - Z300mg2 = a2

J:300mgi- J:300mg2 =

Z300iagi = 200mg + lOOmg

E300mg2 = 200mg + 50mg + 30mg + 20mg

- 30 -

I
Series 5 30mg - E30mgj =

30ing - Z30mg2 = 32

Z30mg-[ - Z]30mg2 = a

3

Z30mgj = 20mg + lOmg

E30mg2 = 20mg + 5mg + 3mg + 2mg

Series 6 3mg - Z3mgi =

3mg - i:3mg2 =

Z3mgj - I3mg2 =

Z3Tngi = 2mg + Imgj

Z3mg2 = 2Tng + lTng2

* If a known lOOg weight suitable for use as a standard is not

available, any lOOg weight or ElOOg weight may be used to fill

the first series. Then the lOOg of the set is used as the

standard and the first series of measurement is:

lOOg - lOOg' = aj

lOOg - ElOOg = 32

lOOg' - ^lOOg = 33

where lOOg' is either the lOOg or the ZlOOg used to complete

the series.

** The lmg2 is an extra Img weight used to fill the last series,

- 31 -
Design 9

Set - Range: 1kg to Img Ratio: 5, 2, 2, 1

Series 1 Slkg - 1kg = a^*

Slkg - Zlkg = Eg

1kg - Zlkg = ag

Zlkg = 500g + 200gj + 200g2 + lOOg

Series 2 200gj - 200g2 = a^

200gj - I200g = 32

200g2 - 5:200g = ag

E200g = lOOg + 50g + 20gj + 20g2 + lOg

Series 3 20gj- 20g2 =

20gj - Z20g = a2

20g^ - Z20g = ag

r20g = lOg + 5g + 2gi + 2g2 + Ig

Series 4 2g^ - =

2gj - r2g = ag

2g2 - T.2g = ag

i:2g = Ig + SOOmg + 200mgj + 200mg2 + lOOmg

- 32 _
Series 5 200mgj - 200mg2 =

200mgj - Z200mg = 82

200mg2 - E200mg =

E200mg = lOOrag + 50mg + 20mgj + 20mg2 + lOmg

Series 6 20mgj - 20ing2 ^1

20mgj - Z20mg = 32

20mg2 - E20mg =33

r20mg = lOmg + 5mg-^ + 2mgi + 2mg2 + Img

Series 7 2ing-^ - 2ing2 =

2mgi - Z2mg = a2

2mg2 - J^2ing =

Z2mg = Img J + lmg2**

* If a known 1kg weight suitable for use as a standard is not

available, any 1kg weight or Zlkg weight may be used to fill

the series. Then the 1kg of the set is used as the standard

and the first series of measurements is:

1kg - 1kg' = ai

1kg - Elkg = 32

1kg' - llkg = 33

where 1kg' is either the 1kg weight or the Zlkg used to

complete the series.

** The Img^ is an extra Img weight used to fill the last series

- 33 -
Design 10

Set - Range: 30kg to Img Ratio: 5, 3, 2, 1

Series 1 30kg - Z30kgj = aj

30kg - E30kg2 = ag

Z30kgi - E30kg2 =

E30kgi » 20kg + 10kg

i:30kg2 = 20kg + 5kg + 3kg + 2kg

Series 2

Series 3

3kg - E3kgi = aj

3kg - E3kg2 = a2

Z3kgi - 2:3kg2 = a3

E3kgi = 2kg + 1kg.

Z3kg2 = 2kg + 1kg..

1kg. - 1kg.. = aj

1kg. - Elkg = ag

1kg. . - £lkg = a3

Zlkg = 500g + 300g + 200g

Series 4 300g - Z300gi = ai

300g - E300g2 = 32

E300gi - i:300g2 = ag

J:300gi = 200g + lOOg

J:300g2 ' 200g + 50g + 30g + 20g

- 3A -
Series 5 30g - S30gj^ =

30g - i:30g2 =

Z30gj - I30g2 = 33

Z30gi = 20g + lOg

E30g2 = 20g + 5g + 3g + 2g

Series 6 3g - I3gj =

3g - Z3g2 = a2

Z3gi - 23g2 = 33

E3gi = 2g + Ig

E3g2 = 2g + 500mg + 300mg + 200ing

Series 7 300mg - i:300mgj =

300mg - Z300mg2 = a2

i:300mgj - E300mg2 = 83

S300mgj = 200mg + lOOmg

2:300mg2 = 200ing + 50mg + 30mg + 20mg

Series 8 30ing - I130mgj =

30ing - E30mg2 = a2

Z30mg-^ - 230nig2 = a

3

i:30mgj = 20mg + lOmg

E30ing2 = 20Tng + 5mg + 3ing + 2ing

Series 9 3mg - I^3nigj = a^

3mg - J;3mg2 = a2

Z3ingj - I3mg2 = a.^

Z3ing^ = 2mg + Imgj

i:3mg„ = 2mg + lmg„

- 35 -
Appendix 2. Surveillance Test Examples

Type I Surveillance Test Example

Example of a Type I surveillance test for a set of metric mass

standards according to design 2, appendix 1. This set was calibrated by the National Bureau of Standards. The National Bureau

of Standards Report of Calibration Test No. 200390 is reproduced

on pages 45-48. The standards used (other than the set) are listed

below together with their apparent mass corrections and

uncertainties. The balances used and their standard deviation

for one double substitution weighing are also listed. The double

substitution weighing method is used. The standard deviation of

the calibration mass measurement process is not known, so an

estimate is computed from the reported uncertainties, as

described in section 3.2, and used in computing the surveillance

limits.

Standards

SlOOg

h lOmg

h 5mg

Apparent Mass

Corr. (mg)

- 0.019

+ 0.0450

+ 0.0045

Volume

12.822

0.0037

0.0018

Uncertainty

fag)

0.015

0.0006

0.0005

Balance

Laboratory Designation

H - 200

M - 10

Standard

Deviation

(ins) . 0.015

0.003

Capacity

200g

20g

- 36 -
Computation of Surveillance Limits (si)

In the following, "Ug" will denote the uncertainty of the

standard and "S.D." the standard deviation of the process;

For lOOg - SlOOg

Ug = O.OlSmg

S.D. = 0.015mg

si = 0.015 +3(0.015) = O.OeOmg

In the following, "U^," will denote the uncertainty (see

Equation (2) Page 7, and "S.D." the standard deviation

of the process:

For lOOg - IlOOg

Uj, = -^0152 + .011^ + .0122 + oio2

= -y|r000225 + . 00012 r+"000044^ ToOOl

= -^.00059

= 0.024mg

S.D. = 0.015mg

si = 0.024 + 3(0.015) = 0.069mg

For 20g - E20g

V 0102 + .0132 + .0072 + .0042 + .0032

-y/.OOOl + .000169 + .000049 + .000016 + .000009

\/. 000 34 3.

U^, = 0.019mg

S.D. = 0.003mg

si = 0.019 + 3(0.003) = 0.028Tng

37 -
For 2g - E2g

Uc = -^00322 + .0030^ + .00162 + .ooil^ + .OOOS^

= -^.00001 + .000009 + .00000256 + .0000012 + .00000064

=

-^f. 00002 341

Uc = 0.0048

S.D. = 0.003mg

si = 0.0048 + 3(0.003) « 0.014mg

For 200mg - E200mg

U^, = -^.00082 + .0008^ + .00052 + .00052 + .00052

= -^0000064 + .00000064 + .00000025 + .00000025 + .00000025

= V- 00000203

\]^ = 0.0014mg

S.D. = 0.003ing

si = 0.0014 + 3(0.003) = O.OlOmg

For 20mg - E20mg

= -^000422 + .000592 + .000492 + .000522 + .000452

= -^.000000176 + .000000348 + .000000240 + .000000270 + .00000020

= -^.000001234

Uj, = O.OOllmg

S.D. = 0.003mg

si = 0.0011 + 3(0.003) = O.OlOmg

- 38 -
For 3mg i:3mg

-^.000522 + .000452 + .000592

^00000270 + .000000202 + .000000349

^.00000082

Uc = 0.00091ing

S.D. = 0.003tng

si = 0.00091 + 3(0.003) = 0.0099mg

For the weighings made on the smaller balance, the uncertainty of

the values of the weights is small compared to the standard deviation of that balance. Therefore, for all practical purposes,

three times the standard deviation of the balance may be taken

as the surveillance limit for these weighings.

- 39 -
Computation of Bu&yancy Corrections

The buoyancy corrections, ApAV, are computed according to the procedure set forth in section 5.2, using the formula:

buoyancy correction = (p - p^) (V^ - V^^)

Consider the weighing lOOg - SlOOg = a

where p = 1.17mg/cm^ air density at time of weighing

= 1.20mg/cm^ density of normal air

= 12.821cm^ volume of lOOg weight of set under

test, from Report of Calibration

= 12.822cm3 volume of SlOOg standard

buoyancy correction = (1.17 - 1.20) (12.821 - 12.822)

= (-0.03) (-0.001)

= +0.00003mg

This amount is insignificant compared to the surveillance limit of 0.060mg

and may be ignored. Similarly, the differences in the volumes in the

weighings lOOg - ^lOOg and 20g - E20g are small enough so that the buoyancy

corrections are negligible. But, in the weighings 2g - S2g and 200mg

Z200mg weights of differing densities are involved. Consequently, the volumes of the individual weight and the summation of weights are different.

The volumes are:

For the weighing 2g - E2g:

Weights Volumes

2g 0.2564cm3

Ig 0.1282cm3

500mg 0.0301cm3

300mg 0.0181cm3

200mg 0.0120cm3

Z2g 0.1884cm3

The actual air density, p, is the same as for lOOg - ElOOg.

buoyancy correction = (1.17 - 1.20) (0.2564 - 0.1884)

= (-0.03) (+.0680)

= -0.0020mg

This buoyancy correction, while relatively small compared to the surveillance limit, is not insignificant and must be applied to the

measured difference between 2g and I2g.

- 40 -
For the weighing 200ing - Z200mg:

Weights Volumes

200mg 0. 01205 cm^

lOOmg 0.00 602 cm^

50mg O.OOaOlcm^

30mg O.Ollllcm^

20mg 0.00741cm^

Z200mg 0.02755cm3

buoyancy correction = (1.17 - 1.20) (0.01205- 0.02755)

= (-0.03) (+0.01550)

= -0.00046mg

This buoyancy correction Is small compared to the surveillance limits

for this comparison and in most cases can be ignored.

For the weighing 20mg - Z20mg:

Weights Volumes

20mg 0.00741cm3

lOmg 0.00371cm3

5mg 0.00185cm3

3mg O.OOlllcm^

2mg 0.00074cm^

Z20mg 0.00741cm3

The volumes of the two masses are equal, therefore the buoyancy correction is zero.

For the weighing 3mg - I3mg:

Weights Volumes

3mg O.OOlllcm^

2mg 0.00074cm3

Img 0.00037cm3

Z3mg O.OOlllcm^

The volumes of the two masses are equal, therefore the buoyancy correction is zero.

- 41 -
Computation of Predicted or Expected Differences

The expected differences are computed from the reported values as

follows: (see report on page 47).

For the weighing lOOg - SlOOg:

Weights

lOOg

SlOOg

Sums

Expected Dif:

For the weighing lOOg - ZlOOg:

Weights

lOOg

50g

30g

20g

Sums

Values

lOOg SlOOg

-0.058mg

-0.019mg

-0.058mg -0.019mg

-0.039mg

Values

lOOg ZlOOg

•0.0589mg

-0.0133mg

-0.013Amg

-K).0330mg

-0.0589mg -K).0063mg

Expected Diff. = -0.065 mg

For the weighing 20g - Z20g:

Weights

20g

lOg

5g

3g

2g

Sums

Values

20g

+0.0330mg

i:20g

-0.0378mg

-0.0065mg

+0.0191mg

+0.006 6mg

+0.0330mg -0.0186mg

Expected Diff. = +0.05l6mg

- 42 -
For the weighing 2g - E2g:

Weights Values

2g

2g +0.0066mg

Ig

500mg

300mg

200mg

Sums

Expected Diff. =+0.037 7mg

I2g

-0.0216ing

-0.0005mg

-0.004lmg

-0.0049mg

+0.006 6mg -0.0311mg

For the weighing 200mg - Z200mg:

Weights

200ing

lOOmg

SOmg

30mg

20mg

Sums

Expected Diff.

For the weighing 20mg - E20mg:

Weights

20mg

lOrag

5mg

3mg

2mg

Sums

Expected Diff. =

Values

200mg

-0.0049mg

Z200mg

+0.0008mg

+0.0074mg

-0.0049mg

-0.0020mg

-0.0049mg

-0.006 2 mg

+0.00 13 mg

Values

20mg

-0.0020mg

Z20mg

+0.0028mg

+0.0065mg

+0.0030mg

-0.0142mg

-0.0020mg

-O.OOOlmg

-0.0019mg

- 43 -
For the weighing 3mg - E3mg:

Weights Values

3mg Z 3mg

3mg +0.0030mg

2mg -0.0142mg

Img -K).0091ing

Sums -K).0030mg -0.005 Img

Expected Diff. = +0.0081mg

- 44 -
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TC-Q MASS VALUES

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r T

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MF VALHFS BASEL' CU

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Tiorjs AND ARE

AMOUNT SHO/.fl m

rnj OF '.^FIGHTS TO

I A T I 0 '! r R 0 H M 0 » I -

O F • M 0 P K A L 8 R A S S

•

I- T T H r P P . A E L 0 A' ) THI'; rou^•TRY a:jo

S or THF /V O K L fJ . F I T M r n p A S I ^ .7 F rrrisi^T'^riT Atvio

IS, HO '"EVER, A rpFUCf "^FT-iLFli THE

OM EACH RASIa, THF

A S I S 'ir • DM'S I T Y r^OG^AMcj/r. L/»p_

MF OM TMF HASI-> OF

THIS SYSTF >^ A T I C

flFARlY OFTECTA'LE

t-AOirir, OAI. AraCES.

rooi-FrTl^' a - 'APPAPF-jT ilASS

\/rr. 9 11'^ n'^f'c^ct OP •f'Flf^HT IM a IP

A A I

'

I S T r. r ' )\ c; .

j c; n F T r r> j M p q (. y ^ M Y " n T ur I I r A I. '•rjf;HlMr- OF IMF

•'.rir, KT T ?i' fEI. •^lUS 1'! ATR h A V ' f-I r;

A nr-i-TTY OF 1 .

-> rr,/ri-i^ I T H A ff|,-)P'-M c^PA'^. S) «;TAMr^APr) HAv/IM; A

0'- MSI TV r, r J., ^

14 r,/rM3 AT .1 CLLSIUS

""los' ^rlFFFI^lr^•T oF VOLUTT'^-IC

r Y p H r- T " M IS o .

' "> " r s y r F *^ 0 L G R E F

r r I s » ' I , A M ^ M O S f V A I M F IS R A F P

OM ITS Tf^iM" '»ASS or- •rir, MT 1 '!

V a 1 1 n .

SAMPLE REPORT

- A5 -
COMPANY X

NEW YORK, NEW YORK

SET OF MASS STANDARDS 100G TO IMG

TEST NUMBER 252.09/200390

CORRECTION B - 'APPARENT MASS

VERSUS DENSITY 8.0' IS DETERMINED

BY A HYPOTHETICAL WEIGHING OF THE

WEIGHT, IN AIR HAVING A DENSITY OF

1.2 MG/CM3, WITH A STANDARD HAVING

A DENSITY OF 8.0 G/CM3 AT 20

CELSIUS, AND WHOSE VALUE IS BASED

ON ITS TRUE MASS OR WEIGHT IN

AIR.

SAMPLE REPORT (CONTINUED)
Tr^T fill* \i " -> V'» • TO / 3" ••

T A f\ L r T

Mft <;<; lIMrroT A i fiT Y VOI AT 70 C^FF OF

( r- ) ( r,

( r«3

1 .^or , n t -> 7 «4 7 ! . T"!

l} 1 n A I 7, R7nAi4

,

f^ - -»'; 7 R A.M 1 n32

3 J , 'J 3 1 1 *. P , n n , > rj , 1 /, ^ . A I 9 , 0 n 0 n q

r.

''jr. , m7 << 7 1 ,

-»«••,'• I' o o '.'iAM 1 3

1 , n 7 /I A , T '•: ,;, 1 7 H 7 1 . 7T">6

t; ,

-< -. r - p /, A 7 . A " 1 3

3- » , o -< -> r c;1 r, ^ .

•-< •-. o M A .3n«A? , 0 rj

?r- . n - "-l 7 H 1 J i ("1 r t; . ? A 'M

• f , ^ ^ •

!

• -

. 7 T . 1 ?n?r , r r. M 5

, U o 9 9 /, q r f> , o > ,n 1 r,c. .'^^T 1 ? , n n n n 2 ,T

, ><)•)•-} 7 H ji, 1 , o - " :- >-

1 -17 . n > c 7 9 r. , ) 9 o t? p • ; C , " o o <-, 7 9 . » 7 s

1 '1 It • r, ,T7 09p-j7r, , n -1 - • - 7 A ^ n n n r* 7 T

c. ' n f. . r ; - .-. > r, 4 .0 '3^ 1 ^ n T r> p 2 'J

^ :->>"<- r '4 1 ^ . m t 1 1 • '^^'^'^69

9 •, M r. , r -. -, -, 0 a /, .r»'^7M 1 , 1 p n 0 6 V

1 ~ ' < r. , If -iipf^pT ,0 > T c; . ^ 3 7 I . 1C1?69

, r ' r, p> q r > ^

.'• 1- <^ .-^ 14 9 . 0

"

«

. 0 T-f^ 69

3"'"-

. r. M 1 1 . " ? 0 6 9

7"r, ,

r, . . ) 9 n A 3 , np'jOAV

1

• • r, ,-, J r > o o 3 ,

" 1

!

• n r' c; 9 .n -.n -57 , p 1 1 n 9

SAMPLE REPORT

(continued) - A7
M t • Y 0 V K , "t I': Y O V SFf or •' A *;TAMOA^f^^ 1'"'-''- T r) |Kr

T AmT 1

ITfM CnP.A(f"'0 COP. i»

1 0 "X^ • A •» tl 3

c. ') C , -

» :^ 3 . 33A 1

1 !? G , ') I M 7

, p -» 7 <j q .17 777

1

. 3 7 p 1 , Ti 3 7 n 9

Sr, , ;

• 0 A ^ « ^ 7 Q u u 3G , I 0 r ^ " 44 p 1 7

. 7

1 G "6 » s r f; , •-; n f s ,

-1 7 9 M

3 •} M r- . • M r 9 -.""199

- . '1 3 A

1 n " G , •- R 7 ^ '» m 7

C, T ^- '"l , 7 q T , 7 7

,

. • n n R -,on«AP

? 9 M C, - .

'< n 1 q i<

\ ^ r , r - 7 p 7 .

•!'^ 7 B 9

r " A5 7

37 M r.

, J ? H - . ':» M 7

1 Mr , r '"9 I 1 .'"'91 3

SAMPLE REPORT

-^continued) - A8 -
Humidity

Barometer

von>* NBS.34S.0& U.S. OSPANTHLHT OF COMMtr CE

NATIOMAC BUnCAU OF •TANOAR09

SUBSTITUTION WEIGHING

SingI* Pon Dompvd Bolanc«s

OBSERVATION SHEET

Sheet /

Uaii fCr. * Dill.)

7m

Obierrer baUoce Date Set NBS Test No.

Load Dial Settiog Scale Readiae Computations

6 Jo^

-aoi X ^^^^^ 'pIW.

-"7

/c2. y/

2£>

/I

J?0J •f-J\^ lOrrr^^ a -5-7

Obs. Os =
A3. 6 "C^

Humidity

Saramcier

/./7

FORM HBS.34S.04 U.S. DEPARTMENT OF COMHErjCE NATIONAL BUREAU OP TANOAflD9

SUBSTITUTION WEIGHING

Single Pan Dompvd Balanc»s

OBSERVATION SHEET

Shr

Vaix (Cr. tt Dill,/

Obiier»er _ ^ BaUoce DateJD-JA- 7A

Set NBS Test No.

Load Dial Sectiag Scale Rea4!B£ Ceoiputations

0' 39X 1 0. (?y/

a. 3oA. '7*\

i3

S'- Sol

^ 00 m\ 6 .3<o

£ goo

^

f X

«

n

0 ' 02-

O-oao X

3

J3

3 ^'^^

d . 00

3. S90

^ O.OIO

r-oos^v

Cos. Dj, r

- 50 -
Type II Surveillance Test Example

This example of a Type II Surveillance Test is for a set of metric

mass standards according to Design 7 , appendix 1. This set was

calibrated by the National Bureau of Standards and reported under

National Bureau of Standards Report of Calibration, Test No. 200390.

The report is reproduced on page 47. This is the same set which

was used for the example of the Type I Surveillance Test. The only

standards (other than the set under test) used in this example are

the sensitivity weights listed below, with their apparent mass corrections and uncertainties. The balances used and their standard

deviation for a double substitution weighing are also listed. The

double substitution method of weighing is used. The standard deviation of the calibration mass measurement is not known, so an estimate is computed from the reported uncertainties of the weights

being tested, as described in section 3.2, and used in computing the

surveillance limits.

Sensitivity

Weight

Apparent Mass

Corr. (mg)

Uncertainty

(rog)

hlOmg + 0.0450 0.0006

h 5mg + 0.0045 0.0005

Balance

(Laboratory Designation)

Standard Deviation Capacity

g

H-200 0.015 200g

M-10 0.003 20g

- 51 -
Computation of Surveillance Limit (si)

In the following "U^" will denote the uncertainty (see Equation (2)

Page 7) and "S.D," the estimate of the standard deviation. Og denotes the standard deviation of the balance used.

For series 1: lOOg, lOOg' , Z lOOg

Weight U(,(mg)

lOOg 0.015

lOOg' UNKNOWN MASS USED TO FILL SERIES

50g 0.011

30g 0.012

20g 0.010

Standard deviation of balance H-200 = O.OlSmg

Uj. = yj.0l5^ + .011^ + .012^ + .010^

= -^00225 + .000121 + .000144 + .0001

= -^.00059

U^ = 0.024rag

S.D. = 3/273ag

= 3y/2Ui .015)

= 3/766666 ( .015)

= 3( .81649)( .015)

S.D. = 0.037mg

si for ElOOg = 0.024 + 0.037 = 0.061mg

Since lOOg* is assumed to be an unknown weight, a surveillance limit

for it cannot be computed.
For series 2: 30g, E30gj, E30g2

Weight Uc ( rag

)

30g 0.012

20g 0.010

lOg 0.013

5g 0.0067

3g 0.0045

2g 0.0032

Standard deviation of balance H-200 = 0.015mg

Uj, = ^.012^ + .010^ + .013^

= ^.000144 + .0001 + .000169

= \. 000413

Uj, = 0.020mg

S.D. = SAME AS IN SERIES 1 (0.037mg)

si for Z30gi = 0.020 + 0.037 = 0.057mg

Uc = "^.0122 + .010^ + .0067^ + .0045^ + .0032^

= -^.000144 + .0001 + .0000448 + .00002025 + .00001024

= -^.000319

Uc = O.OlSmg

S.D. = SAME AS IN SERIES 1 (0.037mg)

si for E30g_ = 0.018 + 0.037 = 0.055mg

- 53 -
For series 3: 3g, E3gp I3g2

Weight Uj, (mg)

3 g .0045

2 g .0032

1 g .0030

500mg .0016

300mg .0011

200ing .0008

Standard deviation of balance M-10 = 0.003ing

Uc =-^.0045^ + .0032^ + .0030^

= -^.00002025 + .00001024 + .000009

= V-00003949

Uc = 0.0063mg

S.D. = 3/2/30^

= 3/273( .003)

= 3/.66666 (.003)

= 3( .81649)( .003)

S.D. = 0.0073mg

si for E3gj = 0.0063 + 0.0073 = 0.014mg

Uc = -^.0045^ + .0032^ + .0016^ + .0011^ + .OOOB^

= •^.'06062"025 + .00001024 + .00000256 + .00000121 + .00000064

= V- 0000349

U^ = 0.0059mg

S.D. = SAME AS FOR 5:3g^ (0 .0073mg)

si for E3g2 = 0.0059 + 0.0073 = 0.013mg

- 54 -
For series 4: SOOmg, ZSOOmgj, I300mg2

Weight Uc (mg)

300mg 0.0011

200rag 0.0008

lOOrag 0.0008

50mg 0.0005

30mg 0.0005

20mg 0.0005 ^

Standard deviation of balance M-10 = O.OOSmg

Uc = -yj.OOll^ + .0008^ + .0008^

= -^.00000121 + .00000064 + .00000064

= ^.00000249

Uj. = 0.0016mg

S.D. = SAME AS IN SERIES 3 (0.0073mg)

si for 2:300gj = 0.0016 + 0.0073 = 0.0089mg

Uj, = -^.0011^ + .00082 + .0005^ + .0005^ + .0005^

= -^.00000121 + .00000064 + .00000025 + .00000025 + .00000025

= / 0000026

Uj, = 0.0016mg

S.D. = SAME AS FOR Z300mg ^ (0 . 0073rag)

si for Z300mg2= 0.0016 + 0.0073 = 0.0089mg

- 55 -
For series 5: 30rag, E30nigj, I]30mg2

Weight (mg)

30mg 0.00054

20mg 0.00046

lOmg 0.00059

5mg 0.00049

3ing 0.00052

2mg 0.00045

Standard deviation for balance M-10 = 0.003mg

= ^.00054^ + .000462 + .00059^

=-^.000000291 + .0000002116 + .0000003481

= -^.0000008513

U = 0.00092rag

c °

S.D. = SAME AS IN SERIES 4 (0.0073mg)

si for Z30nigj = 0.00092 + 0.0073 = 0.0082mg

Uc = ^.00054^ + .00046^ + .00049^ + .00052^ + .00045^

= V-0000002916 + .0000002116 + .0000002401 + .0000002704 + .0000002025

= V.0000012162

Ue = O.OOllmg

S.D. = SAME AS FOR Z 30mg ^ (0 . 0073mg)

si for E30mg2 = 0.0011 + 0.0073 = 0.0084mg

- 56 -
For 5nig - ^5mg:

Weight Uc (mg)

5mg 0.00049

3rag 0.00052

2aig 0.00045

Standard Deviation of Balance M-10 = 0.003mg

Uc = -^.00049^ + .00052^ + .00045^

= ^.0000002401 _ .0000002704 + .0000002025

= ^.000000713

Uj, = 0.00084mg

si = .00084 + 3( .003)

= .00084 + .009 = 0.0098mg

For 3mg - Z3mg

Weight Uc (rag)

3mg 0.00052

2mg 0.00045

Img 0.00059

Standard Deviation of Balance M-10 = 0.003mg

Uc = ^.00052^ + .00045^ + .00059^

= Y0000002704 + .0000002025 + .0000003481

= "^.000000821

Uc = 0.00091mg

si = 0.00091 + 3( .003)

= 0.00091 + .009 = 0.0099mg

- 57 -
Buoyancy Corrections

The buoyancy corrections ApAV are computed according to the procedure

set forth in section 5.2 using the formula:

Buoyancy Correction = (p - p ) (V - V )

In this example, only two of the comparisons, 3g - ESg^ and 300mg - Z300mg, are between weights having different densities. A buoyancy

correction need be computed only for these two comparisons. All of

the other comparisons are between weights haAring the same density, so

their volume differences are virtually zero and the buoyancy corrections are also virtually zero.

The buoyancy correction for the comparison 3g - 1.3%^, of series 3,

is

Weights Volumes

1 n 10/C 3 froTM Report of

3g°

0. 3846cm ^ ^ , l- Calxb ration

2g 0.2564cm3

500mg 0.0301cm

300mg 0.0181cm

200mg 0.0120cm

E3g 0.3166cm

p = 1.16mg/cm^ Air density at time of weighing

= 1.20mg/cm^ Normal air density

Buoyancy correction = (1.16 - 1.20) (0.3846 - 0.3166) = -0.0027mg

This is the figure entered on the 3-1 's computation sheet under the

Z3g2 column on the -ApAV line. Sheet 2, Series 3. Note that it is

-ApAV that is called for and the buoyancy correction is -0.0027mg,

therefore, the buoyancy correction is entered as +0.0027mg. (See

section 5.3.2).

The buoyancy correction for the comparison 300mg - Z300mg2»

series 4, is:

- 58 -
Weight Volume

300mg O.OlSlcm 3 From Report of

Calib ration

200mg

50mg

30mg

20mg

0.0120cm

0.0030cm 3

0.0111cm

0.0074cm 3

Z300mg 0.0335cm 3

P

P

n

1. 16mg/ cm ^

1.20mg/cm ^

Air density at time of weighing

Normal air density

Buoyancy Correction = (1.16 - 1.20) (0.0181 - 0.0335) = +0.0006mg

This is the figure entered on the 3-1 's computation sheet under the

J^300mg2 column on the -ApAV line. Sheet 2, Series 4. Note that it

is -ApAv that is called for and that the buoyancy correction is

+0.0006mg, therefore the buoyancy correction is entered as - 0.0006

mg. (See section 5.3.2).

- 59 -
Contputatlon of Predicted or Expected Values

The expected differences are computed from the reported values as

follows: (See report on page 47).

Series 1: ZlOOg

Apparent Mass

Weight Value

50g -0.0133mg

30g -0.0134mg

20g 40.0330mg

IlOOg Expected Value +0.0063mg

Series 2: E30gj

20g +0.0330mg

10 g -0.0378mg

E30gj Expected Value -0.0048mg

Series 2: Z30g,

Series 3: I3g^

20g +0 . 0 3 30mg

5g -0.0065mg

3g +0.0191mg

2g +0.0066mg

E30g2 Expected Value +0.0522mg

2g +0.0066mg

Ig -0.0216mg

E3g Expected Value -O.OlSOmg

Series 3: E3g,

2g +0.0066mg

500mg -O.OOOSmg

300mg -0.0041mg

200mR -0.0049mR

Z3g2 Expected Value -0.0029mg

- 60 -
Series 4: Z300mgj

Series 4: ZSOOmg^

Series 5: Z30ing^

Series 5: Z30mg,

Apparent Mass

Weight Value

200mg -0.0049mg

lOOmg +0.0008mg

IBOOmgj Expected Value -0.0041mg

200ing -0.0049mg

SOmg +0.0074mg

SOmg -0.0049ing

20ing -0.0020mg

ZSOOmg^ Expected Value -0.0044mg

20mg -0.0020mg

lOmg +0.0028mg

ZSOmgj Expected Value -K).0008mg

20ing -0.0020mg

5mg +0.0065mg

3mg +0.0030mg

2mg -0.0142mg

Z30mg Expected Value -0.0067mg

- 61 -
Series 6: For weighing 5ing - Z5nig

Weight

5mg

3mg

2mg

Sums

Expected Difference

Apparent Mass Value

5ing Z5mg

+0.0065mg

+0.0030mg

-0.0142mg

+0.0065ing -0.0112mg

-0.0047mg

Series 6: For weighing 3mg - E3mg

3mg I3mg

3mg +0.0030mg

2Tng -0.0142ing

Img -f0.0091mg

Sums +0.0030ing -0.0051mg

Expected Difference -0.0021mg

- 62 -
Tcmpecatur*

HumiiJtty

Baromcicr

Obacrrer

S. KO.

U.S. DEPARTMENT Or COMMCRCC

NATIONAL •UnCAU or BTAMDARO*

SUBSTITUTION WEICHINC

Singi* Pon Dam^»J ftalaiic»t

OBSERVATION SHEET

Dace //-/- 7^

Set

Sheet

Uail fCr. * X>f//.;

NBS Test No.^00 3fa

LomI Dial Settiog Scale Reading Computations

/CO7^ /oo

^

2^

loo

0.oSr

1/00

a,0 /rn.1

/OOJ i-JL

/OO't

11 A.o3<5. yy

0'

a. 97

/JL- S'3

y oo

U^cl :Zo ^vjj^ 73^^,.<^,tx^-.---

^V^r^C<*-«-c

2] /OO^ r i"*? 7

Obs. Ds = M„ =

- 63 -
Std. 1

Std. 1, 1^, I2

Observations

K - A M Cor. Std. 1

Std. 1

^1

'2 - O'^t

£3 - o. y^'

K - 0. orr

Sun =

. d =

Sum/d

0

0

0

3

3 - 00s-^

]^

-1

1

3

12

-1

-2

-1

i-a. Of 9

Check

-3

"3

0

9

Z dovm

E across

-ApAv

Est. True

Mass Cor.

App. ilass vs. Brass Cor.

^2 ~ ^'

3

Sun =

d

Sun/d =

4

1

-1

1

-1

1

-1

-0.01

i- Q. 0/<f

f e>' oof ^

1

-1

1

Check

1

-1

1

T. do\.Ti E across

i-0.00 33

- 6A -
ronM NBS-34S.OA u.s. oeparTmcnT OF COMMEnct

NATIONAL. KUMCAU Or aTANDARO*

SUBSTITUTION WEICHIHG

Singi* Pan Dompvd Balonc**

OBSERVATION SHEET

UniuniQity J: _

Uail (V(a.>

Baromctcf f

Uaic (Cf. * Of//.;

Observer 0

' Balance

5.K0. H-0.OO

Date Set NBS Teat No.

Load Dial Setting Scale Reading Computatiooa

30^-2:3.^,-- -:-

-0. 03

1/

• 33

• /JL 3f

it

m

SI

-0.01 . /C.o*/:r

°Z

• J. 3/

It

II

• /a. 3 2.

•

^^"1- -6;. ^ V> « ^

• J .37

•

1.^0^, it /o •

' m

Q

• •

•

• • 0

n n

•

Obs. D« =

. Ms =

•

- 65 -
Std.

Std. 1

+

+

4

K - A M Cor. Std. 1

Std. 1

32 -Q-

- -o. 07

^3

K ~0. OIJ

Sun =

d =

Suni/d

-ApAV

Est. True

Mass Cor.

App. llass vs. Brass Cor.

a, - O. OX

3 -

Sun

SuKi/cl =

0

0

0

3

~C .039

-O.0I3

~O.0li ,rr^

1

-1

1

^3

(?. Ol

Sheet

1. 1,. I2

1,

Date // - / ' 7°2^

Observations

a,

-1

1

3

~0, 00 3

-0. 003

A.

-1

1

-1

fo. o3

3

•tO-of

-1

-2

-1

3

Check

-3

-3

0

9

1 down

t across

t

+0. o ^1 ^

fO. 06'3

1

-1

1

Check

1

-1

1

-0. a3

-0.01

I do^.Ti

i: across

S- (A,)'' + U.^y + (A3)'

- 66 -
Teoipcrtliu*

;i V. A "cro«M NBS'34S J6 U.S. DEPARTMENT OF COMMENCE

t«-l«*0 NATIONAL BUREAU OP •TANOAROB

SUBSTITUTION WEIGHING

SingI* Pan Dompvd Balance*

OBSERVATION SHEET

Sheet .

Humitiicy Unit pi'UO

Bsrancicr ^

Obierrer ^ Balaoce D.te Set NBS Test No.

Load ' Dial Secttog Scale Readiog Computatioo3 — 0 .390

^Jdp m 0. 3ol

tt

•

9

%

It

i\

m t 0, 01^ —• V

if

• a, BOS'

<

«

•

• 6'. 310

It £'.32.7

n 0 .hoi

II

•

•

f 1 s.3xy

•

• •

• •

a

• •

*

•

• •

• •

•

a

3

n

•

Obs. Ds =- Ms =

- 67 -
Std. 1. 1^. I2

SCd. 1

Sheet *2 -<^A-<.-<Lo -3

Date //- / - 7^

Observations

a.

"2

^3

K - A M Cor. Std. 1

std. 1

»2 O- <^ 1^

^3 " 0- Q/*/

K -f O. 0/9/

Sura »

d =

Sum/d

-ApAV

Est. True

Hass Cor.

App. llass vs. Brass Cor.

a

^2 0- 01 ^

^3 r_o^Ll.

Sum =

d

Sum/d =

0

0

0

3

3_

f 0.0 1^1

•f 0. 019 I <yyr.J

1

-1

1

4 O. OOU

f 0.001-

—*-

1

3

-0. oSC)

-O. 0/3 ^

-1

1

-1 - o. 00 y

-O. 00 i

I2 Check

-1

-2

-1

3

-3

-3

0

9

Z down

I across

^0.00 0^

t 0.00X1

i O. pots' - o. 0021

1

-1

i__

t 0.00(0

3

-0.000^

Check

1

-1

1

1 do\.'n I across

S= /"(A,V + (A 2')^ + (A,')'

68 -

I
Tcapctatitf*

Humidity

Barem«tct HQ y>

U.S. DC ARTM£NT OF COMMEFlCC

NATIONAL BUKCAU Or aTANOARO*

SUBSTITUTION WEIGHING

SingI* Pan Damped Bolancas

OBSERVATION SHEET

Sheet

Upit (Wt;)

Uoii (Ct, h Din.)

Obaarret

3. 1/: o

BaUacc Date Set NBS Test No.

Load Dial Settiag Seal* Reading Computatioos

3oo /y>» 0.30 0 . 2-9/ .oh

^

1 3oo , f 0.001

1^ 5-/

•I

3^0 f ^^^^

2 doo^^x

It 0, ^^(,

- o.ool

O, 00 O O.'J^QS cr^^

5^

5;

300 ^'^^

-t 0. o(

S'OOi^'

2 •f O. oo5

=r OV

/ sv t 0.0

Obs. D.

- 69 -
Std. 1

+

+

K - A K Cor. Std. 1

Std. 1

'

t O. no /

^2 0. OOP

^3 "^O.

Sunt =

d =

Sum/d

-ApAV

ts t . True

Mass Cor.

App. I lass vs,

Brass Cor.

Cot •

i-0. OO I

0 . OOP

Sun =

d

Su,- /d ^

0

0

3

-0. 0/^2.0

3 - 0. oo'io

- 0. vojo

Sheet 6^ .yXt/iA-J^ Y

Date //- p. -

Std. 1, 1^, I2

1

-1

1

f- 0. O 03

Observations

a.

}

-1

1

3

-1

-2

-1

Check

-3

"3

0

'0.012.0

-a. ooio

-O. o/'S'O

Y. down

1 across

- O- 0006

- o. 00 '/Q - a. oc> s-(> 7

o. o D i I 'yr^cf -0.0° yy

-1

1

-I

- o. 00

1

-1

^1 j-o. 003

^3 / 0.00 I

Check

1

-1

1

r across

/O'^ - O. 00/7

- 70
Teapctaiuta

Humidity

1H1 : \ rr*^-:r^ /> I.Jd, nry^^ Jc^

U.S. OcPARTMEMT OF COMMEFICC

NATIONAL BUREAU OF aT*NOAHO>

SUBSTITUTION WEIGHING

Singl* Pan Dompvd Balances

OBSERVATION SHEET

Unit (Via.;

Obacnr«r

S.Y. 0.

Balaace Date//- /- 7;l

Set NBS Teat No.

Loa4 Dial Setting Scale Reading Computatioos

30

30 1^ /

^^^J^

3o^c^- :^5o^, - I

5".

3o

136

ii

£30 Qyt^

0. jz-r

f O. GO 5' 5' X ^

= tii-_o.4:-

1 30 f-L^^^ I

Obs. Dj,

Ms

-7
Date

Std. 1, 1^, 1^

Std. 1 Observations

+

+ -

+

^2

03

K - A M Core sud. 1

std. r ^ Check

a

J - 0.0 0 5" 0

1 -I -3

&2 "O. O 03 0 -1 -2 -3

+ O. 0 05" 0 1 -1 0

3_ 3 3 9

Sun =» c» \J 1 g f O. CO 33

1 down

K across

d = 3 3 3

Sua/d

-o.ooij -t 0. 00/ /

-Ap&V

Est. True

ilasS Cor.

App. ilass vii.

Brass Cor,

7

O-0OH9 O. (50 6 7

Ai A3 Check

1 -1 1 1

- O. 0 03 -1 1 -1 -3

1 \_

+ 0. O <D 3 - 0. C5 0 3 +0.003

Sun = 5 clo\.'n

3 across

d ^3^ -1-6. ooi -6. oo 1 4 0.00'

bum /d =

S= /"(aV)'^+ (Aj)' + (A 3")"

- 72 -
Tc .p«i*tiw«

B*rem«iM

U.S. OEPAKTMENT COM».:enCE

NATIONAL BUNCAU Of aTANOANOa

SUBSTITUTION WEIGHING

Single Pan Oatnpmi Bolancss

OBSERVATION SHEET

Uaii (Wi;)

Oba«f«M

^v<o. M - /o

Date S«i NBS Teat No.

Lon4 Dial Settiog Scale Reading Computatioos

isII

A39

O,

3:-

57 ootp

Obs. D,

- 73
NBS-1)4A (REV 7-7S)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. iniMI.K A HON OR Ki;PORT NO.

NBSIR 76-999

2. Gov't Accc-s.sion No.

3. Ri c ipicnt'.s Acces.sion No.

4. T.Ti.K AND suRTm.K

SURVEILLANCE TESTS

PROCEDURES

5. Publication Date

February 1976

6. Performing Organization C'ode

7. AUTHOR(S)

H. E. AlmPr FHi tpri by. ^^rry KpII Pr

8. Performing Organ. Report

NBSIR 76-qqq

No.

9. PEKFORMING ORGANIZATION NAMF AND ADORKSS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

10. Project/Ta.sk/Work Unit No.

11. Contract/Grant No.

12. .Spon.soring Organization Name and ('omplctc Addrcs.s (Streel, City, State, ZIP)

Same as No. 9

13. Type of Report & Period

( . ov e r e d Final

14. Spon,soring Agency Code

15. SUPPI.KMENTARY NOTES

16. AHSTRA(;T (A 200-word or less (actual summary of most si^ilicant information. If document includes a significant

bibliography or literature survey, mention it here.)

Surveillance tests are designed to monitor the values of

mass standards between calibrations. Two types are

described; both consist of comparisons of the weights of an

ordered set of mass standards with each other. The

differences found are compared with those computed from the

reported mass values. Surveillance limits based on the

precision of both the calibration and the surveillance test

processes are computed. These limits are estimates of the

departure of the measured differences from the expected, or

predicted, differences as computed from the reported values.

A larger change is considered significant. Additional

measurements to identify individual weights which have

changed are required when a given comparison indicates that

the mass of one or more of the weights involved has changed.

Buoyancy corrections are used to correct for. the difference

in the buoyant effect on weights of differing densities.

Records document the surveillance test results, and control

charts help detect trends. Judgments concerning

recal ibration can be made based on the constancy of the

wpight<; anH thp ii<;p rpqni romontc

17. KHY WORDS (six to twelve entries; alphabetical order, capitalize only the fir.'il letter of the first key word unless a proper name, .separared by .sem,co/on.s> Apparent mass; buoyancy; buoyancy correction; change;

comparison; difference; mass; records; set; surveillance limits; surveillance

test; test interval; true mass; value; weighing design; weights.

18. AVAII.AHII.n Y X Unlimited

I- or Official Di.siribution. Do Not Release to N I I.S

Onlei I rorn Sup. of Doc, U.S. (loverrimciu I'rmimj; Office

Washin^-toM, D.( . ?i)U)2, SD ( at. No. < I )

JjJ Order I roni Naiional Icchnical liilormai ion Seivirt (NIISi

Spr Innf !<• Id , Virj^inia 2.?I'SI

19. SEf.llRlTY Cl.A.SS

( rmS REPORT)

UN( I.ASSII II D

20. sl ( UKI I Y ( I. ASS

' nils I'AGK)

lINf I ASSII II I)

21. NO. OF PAGES

77

22. Prue

USCOMM.OC i904<'-P74