7. MISCELLEOUS SUBJECTS

7.1 NBS Support for the National Measurement System

Measurements are essential for almost every aspect of human existence.

They are the keystone of our modern civilization. Measurements are always

estimates of the true value of some property and have some degree of uncertainty which ordinarily needs to be known. Moreover. measurements made by

various individuals and/or at various times need to be relatable and compatible. This requires that measurements must be made systematically in what may

be called a national measurement system. The basic operational aspects of the

national measurement system are depicted in Figure 7.1. The upper part of the

figure represents physical measurements while the lower part relates to

chemical measurements. Essentially one can visualize samles of materials that

are measured to obtain data on some physical or chemical property that is

needed for an end use. The measurement is made with respect to some physical

or chemical standard. The basis for all measurements are the seven basic units

shown in the table below. These are interntionally accepted and NBS maintains

national primary standards compatible with the interntional standards foe

fixing the magnitude of the units.

Table -- Units of Measurements

Basic

Length -

Mass -

Time -

Electric Current

Temperature -

Amount of Substance

Luinous Intensity

meter

kilogram

second

amere kelvin

mole

candela

Supplementary

Plane Angle -

Solid Angle -

radian

steradian

A hierarchy of standards can be envisioned. each relatable and hence

traceable to the ones above it as shown in Figue 7.2. It i. possible to use

working standards for applied measurements with calibrations traceable to the

national standards in virtually all areas of physical measurements. The

traceability may be because of NBS calibrations or by measurements by others (a

State weights and measures laboratory. for examle) using higher hierarchy

standards with certified values traceable to NBS. Obviously. the intercomparison measurements that are required need to be made with a high degree of

reliability since the uncertainty of measurement Ilt be added to the

uncertainty of the calibrated value of the standards used.

The propagation of error in a measurement chain is illustrated in Figure

7.2. After several iterations, a lower hierarchy standard (UlS) may have an

intolerable uncertainty for some uses due to the unce~tainties associated with

intervening calibration steps so that a user may need to have a particular

7.1
working standard calibrated closer to the primary standard (see chain C in

Figure 7.2). In such a case, a calibration laboratory higher in the hierarchy

must provide the service (or use of a standard. higher in the hierrchy is

another possibility). Of course, NBS provides clibration services in some

cases.

In consideration of the above, it should be noted that physical standards

may need to meet rigid specifications as to their form, material, workmanship,

and stability to qualify for use as upper hierarchy standards.

Physical measurements may be considered in two general classes. The first

consists of those made to fix the values of measurement standards and can be

called calibration and tolerance testing. The second is applied measurement

and includes all but those in the first. Indeed, one might consider that the

first is really a special class of the second kind. In both cases, measurement

essentially is a comparison of an unown with a standard and the uncertainty

of the result includes that of the standard used together with the uncertainty of the intercomparison. llether for calibration or for application, it

behooves every metrologist and every measurement laboratory to minimize the

uncertainty of its measurements. Improvements can be sought in two directions.

Higher quality standards will reduce the systematic error (heavy lines of

Figure 7.2) while improvements in precision (dotted lines of 7.2) can result

from better quality control and/or increasing the number of replications.

llile replication can make random error uncertainties small, there is a

practical upper limit to which this can be done. In high quality measurement,

the two kinds of uncertainties may equal each other but the systematic should

not exceed the random component. R.eduction of systematic uncertainty to

one-third of the random uncertainty is often practical in which case it does

not contribute appreciable error to a measurement process.

NBS supports the measurement process as shown by Figure 7.3 by maintaining

the basic primry standards and by calibrating or otherwise providing routes to

them for traceability of working standards. NBS conducts fundaental research

to increase understanding of measurement in its broadest interpretation. Along

with others, NBS investigates and develops new and or improved methods of

measurement and provides reference materials to evaluate the measurement

process.

The responsibility for the reliability of any specific measurement is that

of the metrologist/laboratory that reports it. A measured value without limits

of uncertainty (error bars) is virtully useless since such limits are always

needed in any application and are not imlicit in the measurement pro~ess.

The measurement process should follow the procedure outlined in figure

7 . 3 . The measurement laboratory uses existing methodology, appropriate

calibrations and quality control techniques to attain statistical control of

the measurement process. When acceptable precision is attained, the laboratory

can evaluate its bias and set limits of uncertainty for the data. If either

bias or precision are uncceptable, assignable causes should be sought and

appropriate corrective actions should be taken.

7.2
Any laboratory can and should evaluate its own precision of measurement

and its ability to do so is a measure of its competence. Evaluation of bias

can be extremely difficult and facilitated by externally provided calibrations,

reference materials, definitive measurements, and other approaches. Obviously,

biases smaller than the precision of measurement will be difficult to identify.

A laboratory must be capable of evaluating its own precision and

maintaining its measurement system in a state of statistical control. Otherwise, it must be considered as incapable of providing the services it offers.

Furthermore, a laboratory should assign limits of uncertainty and maintain

documented evidence for the basis of such assignent. In on-going measurement

processes, control charts provide the basis for such assignent. In other

cases, the redundant process of repetition is the only means to make such an

assignment.

In addition to the above, NBS provides a limited amount of support for the

measurement system in the form of education and training. Basic metrological

information is contained in a number of papers. Statistical treatment of

measurement data is discussed in a group of papers contained in NBS Special

Publication 300 (l7) and in NBS Handbook 91 (l9). NBS presents a number of

seminars in several areas of metrology. Information about them and the current

schedule can be o~tained from the NBS Office of Measurement Services (l6).

Specialized training for metrologists of State Weights and Measures

laboratories is possible from the NBS Office of weights and Measures.

7.3
TABLE 7.1

OPERTION OF A MEUR PROCESS WITH NBS SUPPORT

l. NBS provides

1.1 Fudaental research to extend frontiers of methodology

l.2 Basic research to develop new methodology

1.3 Applied research to imrove exi.ting methodology

1.4 Reference materials

1.5 Calibration services

1.6 Other approaches for evaluating bias. e.g., definitive methods

2. Measurement laboratory

2.1 Utilizes existing methodology

2.2 Applies appropriate quality control techniques

2 . 3 Demonstrates statistical control of the measurement process

2.4 Evaluates precision

2.4. 1 Precision acceptable

2.4.1.1 Evaluates bias using reference materials, calibration

services, other approaches

2.4.1.1.1 Limits of bi.. acceptable

2.4.1.1.1.1 Reports me..ured value with assigned limts of

accuracy 2.4.1.1.2 Liits of bi.. uncceptale

2.4.1.1.2.1 Assignble cause identified to imrove

methodology or quality control. Material

remeasured

2 . 4 .1.1. 2 . 2 Assignble cause not identified

2.4.1.1.2.2.1 Seek other methods of measurement. or

measurement not possible and maj or research

required

2.4.1.1.2.2.2 Report biased ....ured value with precision,

.m, reported 2.4.2 Precision uncceptable

2.4.2.1 Assignble cauae(s) identified to imrove methodology

and/or quality control: re....ure

2.4.2.2 Assignble cauae(.) not identified: measurement not

possible: seek other methodology or major research

required

7.4
Notes:

l. Measurement laboratories have sole responsibility for evaluating their

precision and can do so with little or no NBS support

NBS can provide education/training/workshops to assist laboratories to

achieve quality control/statistical control

NBS can develop GLP's, GMP' s, SOP's in critical areas of national concern

(including industrial productivity)

2. Measurement laboratories can utilize 1.4, L.S, and l.6, with little or no

NBS assistance, to evaluate bias

3. NBS has responsibility to establish and maintain the National Measurement

System which involves l.l, l.2, l.4, L.S, and l.6

4. NBS engages in state-of-the-art R & D in 1.2 and 1.3 to develop 1.4, L.S,

and l. 6. Much of this is transferable to measurement laboratories.

S. NBS cannot attest for the precision or accuracy of measurement values

reported by others than itself.

6. NBS can make judgments whether a measurement process is or is not

potentially capable of reliable measurements, but the demonstration of

such capability is the responsibility of the measurement laboratory and

must be supported by an adequate quality assurance program.

7. The development and maintenance of an adequate quality assurance program

is the sole responsibility of the measurement laboratory. This is a

prerequisite for offering and providing measurement services. NBS can

assist by conducting research in quality assurance techniques, development

of reliable methodology and conducting seminars or workshops, all intended

to make measurement assurance self-sustaining.

8. If a measurement assurance program requires extensive NBS direct

involvement, it needs to be redesigned to eliminate such involvement and

or to remove the reason why such involvement is necessary.

7.S
Modlfl.

C8tlon

Ad.pt.tlon.

Nat.1 Prm.ry

PhyalC81

St.nd.rds

M.nu.

f.cturer Con.truc.

tlon

NBS

r1flC8tlon

ChmlC81

St.nd.rd.

Prr.tlon

M.nuf.c.

tum of

ChIC8ls

SRM's

(N.tlon.1

Prm.ry

Chmical

St.nd.rds)

I

Sythe.is I

I

I

I

- ..

NATIONAL MEASUREMENT SYSTEM

O.ta

Int.r.

n.llon.1

Std.. Bol..

..

End

U..

N.tl.1

Int.m.1I

Stdi.

Orgs.

Scl.ntlfc

Technlc.1

R....rch

FIGU 7. 1 NATIONAL MESUR SYSTEM

7.6
A

NATIONAL

PRIMARY

STANDARD

Secondary

Standard

Tertiary

Standard

Lower

Hierarchy

Standard

,/ ,

~r.tory~ Ýr-L.-i

I Working I Standard L__--

B

/

I

_I

/

I

_I

,

\

\-

C

,r :',

.

/

I

,

\

\-

/

I

_I

,

\

\-

r _.. - -i I I L___-.

FIGU 7.2 PROPAGATION OF CALIBRATION UNCERTAINT

~

_I U IJ \__1 f II 11 \

i-----L----1

I Sum of Uncertainties of all laboratoris . I L____~~____

A. Calibration Chain

B. Prpagation of Uncertainty

C. Altemate Calibration of Chain Uncr1lnty

7.7
Measurement

Precision

Evaluated

Methodology

Unsuitable

Material

Measurement

Methodology

Quality

Control

Techniques

Statistical

Control

Has

,.

Measurement

Accuracy

Evaluated

Other

Approach

Reference

Material

Calibration

Service

FIGU 7. 3 NBS SUPPORT FOR TH MEUR PROCESS

7.8
7.2 Tolerance

Tolerances for weighing and measuring devices are established on the

following basis: tolerance values are so fixed that the permissible errors are

sufficiently small that there is no serious injury to either the buyer or

seller of commodities, yet not so small as to make manufacturing or maintenance

cost of equipment disproportionately high. With respect to the standards used

to test weighing and measuring devices, the error in the standard should be

less than 2S percent of the smallest tolerance to be applied to .the device when

the standard is used, otherwise, a correction factor must be applied to the

standard so used.

:

Whenever a customer's standard is tested in the laboratory and returned to

the user, the standard should be expected to remain within tolerance until the

time it is scheduled to be recertified. Whenever a standard is out of tolerance or near the tolerance limit such that it is likely to go out of tolerance

before it is expected to be retested, the standard should be adjusted as

closely as practical to zero error. The rate with which the standard changes

its value depends upon the material of which it is made, the frequency of use,

the care" it receives, and the environment to which it is subjected. Any

standard that is daaged or is subject to an incident that may have changed its

value significantly, resulting in a question of its validity, should be removed

from use until it can be tested in the laboratory.

The tolerance applicable to the device for which the standard is to be

used is not the only consideration for establishing the tolerance for the

standard. An additional factor is that the tolerance on the standard should

not be an excessively large fraction of the value of the standard. The

standard should be a reasonably accurate representation of its nominal value. A

determination of what is "reasonably accurate" depends upon the type of

standard, its nominal value, its use, and the accuracy required in the

measurement process in which the measuring device (under test) will be used.

Tolerances for Commercial Equipment

AcceDtance and Maintenance Tolerances - The official tolerances prescribed

by a weights and measures jurisdiction for commercial equipment are the limits

of inaccuracy officially permissible within that jurisdiction. It is recognized

that an errorless value or performance of mechanical equipment is unattainable.

Tolerances are established, therefore, to fix the range of inaccuracy within

which equipment will be officially approved for commercial use. In the case of

classes of equipment on which the magnitude of the errors of value or performance may be expected to change as a result of use, two sets of tolerances are

established: acceptance tolerances and maintenance tolerances. Acceptance

tolerances are applied to new or newly reconditioned or adjusted equipment, and

are smaller than (usually one-half of) the maintenance tolerances. Maintenance

tolerances thus provide an additional range of inaccuracy within which equipment will be approved on subsequent tests, permitting a limited amount of

deterioration before the equipment will be officially rejected for inaccuracy

and before reconditioning or adjustment will be required. In effect, there is

assured a reasonable period of use for equipment after it is placed in service

before reconditioning will be officially required. The foregoing comments do

not apply, .' of course, when only a single set of tolerance values is

established, as is the case with equipment such as glass milk bottles and

7.9
graduates, which maintain their original accuracy regardless of use, and single

service measure-containers, which are used only once.

Tolerances and Adjustments - 'l'olerances are primarily accuracy criteria

for use by the regulatory official. However, when equipment is being adjusted

for accuracy, either initially or following repair or official rejection, the

effect should be to adjust as closely as practicable to zero error. Equipment

owners should not take advantage of tolerances by deliberately adjusting their

equipment to have a value or to give performance at or close to the tolerance

limit. Nor should the repairman or serviceman bring equipment merely within

tolerance range when it is possible to adjust closer to zero error.

Tolerances for Standards A general principle that has long been

recognized by the National Bureau of Standards is that the error in a standard

used by a weights and measures official should be known and corrected for when

the standard is used; or if the standard is to be used without correction, its

error should not be greater than l/3 of the smallest tolerance to be applied

when the standard is used. The reason for this is to keep at a minimum the

proportion of the tolerance on the item tested that will be used up by the

error of the standard. Expressed differently, the reason is to give the item

being tested as nearly as practicable the full benefit of its own tolerance.

Field testing operations are complicated to some degree when corrections

to standards are applied. Except for work of relatively high precision, it is

recommended that the accuracy of standards used in testing commercial weighing

and measuring equipment be so established and maintained that the use of

corrections is not necessary. Also, whenever it can readily be done, it will

be desirable to reduce the error on a standard below the 1/3 of the smaller

tolerance' previously mentioned.

The numerical values of the tolerances recommended by the National Bureau

of Standards for the standards of length, mass, and capacity used by weights

and measures officials may be obtained upon request from the Office of Weights

and Measures of the National Bureau of Standards.

When Corrections Should Be Made - llen testing a measuring device the

weights and measures official has expressly only one official duty, and that is

merely to determine whether equipment. is or is not suitable for commercial use.

If a device conforms to all of the official requirements, the official seals it

to indicate approval. If it does not conform to all official requirements, he

is required only to reject it and prohibit its use until the device is brought

into proper conformance.

Some officials contend that it is 'justifiable for the official to make

minor corrections and adjustments in order to correct faulty equipment if there

is no service agency nearby or if the owner or operator depends on this single

device and would be "out of business. during the repair of the device.

Adjustments should be made, with the permission of the owner or his

representative, only when the official is thoroughly competent to make such an

adjustment and when he is certain that the real cause of the inaccuracy will be

corrected thereby and is not due to faulty installation or a defective part.

He should never undertake maj or repairs, or even minor corrections if the

services of c~mmercial agencies are readily available.

7.10
Gaudni - In the majority of cases, when the weights and measures official

tests commercial equipment, he is verifying the accuracy of a value or the

accuracy of the performance as previously established either by himself or by

someone else. There are times, however, when the test of the official is the

initial test on the basis of which the calibration of the device is first

determined or its performance first established. The most common example of

such gauging is in connection with vehicle tanks, the compartments of which are

used as measures. Frequently the official makes the first determination on the

capacities of the compartments of a vehicle tank, and his test results are used

to determine the proper settings of the compartment indicators for the exact

compartment capacities desired. Adjustments of the position of an indicator

under these circumstances are clearly not the kind of adjustments discussed in

the preceding paragraph.

lnsnection versus TestinJ A distinction may be made between the

inspection and the testing of commercial equipment that should be useful in

differentiating between the two principal groups of official

requirements - - specifications and performnce requirements. Al though frequently

the term inspection is loosely used to include everything that the official has

to do in connection with commercial equipment, it is useful to limit the scope

of that" term primarily to examinations made to determine compliance with

design, maintenance, and use requirements. The term testing may then be

limi ted to those operations carried out to determine the accuracy of value or

performance of the equipment under examination by comparison with the actul

physical standards of the official.

Accura~y of Standards The accuracy of testing apparatu should

invariably be verified prior to the official use of the apparatu. Standards

should be reverified as often as circumtances require. By their natue, metal

volumetric standards are more susceptible to dage in handling than are

standards of some other tyes. llenever dage to a standard is known or

suspected to have occurred, and Whenever repairs that might affect the accuracy

of a standard have been made, the standard should be recalibrated. Routine

recalibration of standards, particularly volumetric standards, even when a

change of value is not anticipated, should be made with sufficient frequency to

affirm their continued accuracy, so that the official may never be in an

indefensible position with respect to the accuracy of his testing apparatu .

If use is made of secondary standards, such as special fabric testing tapes,

these should be verified much more frequently than such basic standards as

steel tapes or volumetric provers to demonstrate their constancy of value or

performnce.

Accurate and dependable results cannot be obtained with faulty or

inadequate standards. If either serviceman or official is poorly equipped, it

cannot be expected that their results will check consistently. Disagreements

between servicemen and officials can be avoided, and the servicing of commercial equipment can be indefensible improved if servicemen and officials will

give equal attention to the adequacy and maintenance of their testing

apparatus .

7.11
7.3 Distinction Between Mass and Apparent Mass

The mass of an object can be simply defined as the quantity of matter that

comprises the object. The mass of an object remains constant regardless of its

location. Thus, the mass does not vary as the obj ect is moved from one part of

the country to another although the forces acting on the mass may change. In

mass measurement, the term "true mass" is frequently used to mean the mass of

an object. The adjective "true" is redundant and will not be used in the

remainder of this paper.

The purpose of mass measurement is to determine the mass of an unown

object; Le., the unown object is calibrated by comparing its mass to that of

a known mass standard. A mass calibration is performed in air as are virtually

all mass measurements. Thus, when two objects are compared, each object is

being subj ected to a lifting force equal to the mass of air displaced by the

object times the force of gravity in addition to the downward force on each

object resulting from the earth's gravity. The mass of air displaced by an

object depends on the density of the air and the volume of the object. Since

all mass measurements are made in air and mass calibrations are performed by

comparing an unknown standard to a known standard, the mass of a s~andard is

frequently reported as the apparent mass of the standard. The appare:nt. mass of

an object is the mass of a (hypothetical) reference standard of a specified

density. that will 'produce a balance reading equal to that produced by the

object if the measurements are made at 20 .C in air with a density of 1.2

mglcm3. llenever the term "apparent mass" is used, it is necessary to specify \

the density of the (normally hypothetical) reference standard against which the

unown standard is being compared. This statement of the density of the

reference standard, called the reference density, is necessary because the

apparent mass value depends in part upon the volume of the hypothetical

reference standard. The reference density of 8.0 g/cm3 is normlly used to

report the apparent mass of a standard or object. This is called the apparent

mass versus 8.0 g/cm3. In' the past, the apparent mass was reported against the

density of brass at 20 .C. This density is 8.3909 g/cm3. This apparent mass

value is referred to as the apparent mass versus brass.

The definition of apparent mass versus a reference density specifies the

conditions under which the apparent mass of a standard or object is to be

determined. To compute apparent mass, it is necessary to know:

1.' the density of the hypothetical reference standard;

2. the mass of the hypothetical reference standard which is the mass of

a reference standard that will give the same balance reading as the

'unown standard under specified conditions;

3. the temperatue (20 .C) at which the .comparison. of the masses is

made;

4. the density of the air (1.2 mg/cm3) in which the .comparison" is

made; and

5. the density of the standard being calibrated.

The density of the object being calibrated must be known since its volume

is involved in the apparent mass determination. It is the difference in the

volumes between the object being calibrated and the hypothetical reference

standard that determines the apparent mass of an obj ect versus a specified

reference densi ty .

7.12
The apparent mass versus 8.0 g/cm3 of an obj ect can be defined as the mass

the object would app'ear to have if it was compared against a standard which has

density of 8.0 g/cm3 and a mass giving the same balance reading as the object

when the comparison is made at 20 .C in air having a density of 1.2 mg/cm3.

The definition for apparent mass versus brass is exactly the same except

that the density of brass at 20 .C (8.3909 g/cm3) is substituted for 8.0 g/cm3.

An example will be given to illustrate the apparent mass concept.

Suppose that we have three weights made of aluminum (Al) , brass, and

stainless steel (SS). Assume that the densities of these weights are 2.7

g/cm3, 8.3909 g/cm3, and 8.0 g/cm3; respectively, and that all three weights

have a mass of exactly 1 kg. The weights then have volumes of 370.37 cm3,

ll9.l8 cm3 and l2S. 00 cm3, respectively. When the weights are in air, there

will be a lifting force due to the effect of the displaced air and a downward

force due to the mass (m) of the weight.

l Fup=PalrV Aig

Aluminum

PAl =2.7 g/cm3

VAl =370.37 cm3

t Fup~alrVBrassg

l F up = PairV ssg

Brass '

D =8.3909 g/cm3

. Brass

VBrass =119.18 cm3

Stainless Steel

Pss =8.0 g/cm3

V ss =125.00 cm3

, F down=mg

l F down=mg l Fdown=mg

It can be seen that the larger the volume, the greater the upward force.

Since gravity appears in all terms when the weights are intercompared, the

gravity factor (g) cancels.

Suppose now that a perfect equal-arm balance exists and is used to compare

the weights in both a vacuum and in air. Suppose that the aluminum weight is

placed on one pan of the balance and the stainless steel weight is placed on

the other pan and the balance and weights are placed in a vacuum. Because there

is no air present, there is no lifting force so the weights will appear to have

equal masses since only the downward force is acting on the weights. If the

aluminum weight was compared in a vacuum against the brass weight, the two

weights would also appear .to have equal masses. The same would be true if the

brass weight was compared to the stainless steel weight. Thus, the mass of an

object can be visualized as the mass an object would appear to have when it is

compared in a vacuum against a known standard.

Now suppose that the .aluminum and stainless steel weights are compared on

the balance in air that has a density of 1.2 mg/cm3. The air will exert a

lifting force on each weight as described earlier. This can be illustrated in

mass units (since gravity cancels out) as

7.13
l PalrVA1=1.2(370.37) uA =4.4 mg lPalr

55 AI

v ss =1.2(125)=150 mg

l.m= 1 kg

l m= 1 kg

The . aluminum weight experiences a much larger lifting effect than the

stainless steel weight, naely, 44.4 mg versus 150 mg. Thus, the aluminum

weight appears to be 294.4 mg lighter th the stainless steel weight. This is

simly the air density times the difference in weight volumes. Hence, the

apparent mass of the aluminum weight versus 8.0 g/cm3 is approximately

1 kg - 294.4 mg - 999.7056 g

If the aluminum weight was compared in air against the brass weight, the

sitution is illustrated as

l PalrVAI=4.4 mg

A

lPa

Brass

AI

l m=1 kg

Ir V Bra.. =1.2(119)

=143.0 mg

l m=1 kg

This mean the aluminum weight appears to be 301.4 mg lighter than the

brass weight. Hence the apparent mass of the aluminum weight versus brass is

approximtely

1 kg - 301.4 mg - 999.6986 g

7.14
To carry the example further, suppose the brass weight and the stainless

steel weight were compared in air with a density of l. 2 mg/cm3. The effect can

be illustrated as

/'

lPairVBrass=143.0 mg lPa:ir

Brass

55

=

Vss=150 mg

l m 1 kg

l m=1 kg

Using the stainless steel weight as the reference standard, the brass

weight appears to be 7 mg heavier than the stainless steel weight. This is due

to the difference in the lifing effect of air on the weights. The lifting

effect is less on the brass weight because its volume is less than that of the

stainless steel weight. This condition can also be reported using the brass

weight as the reference standard. In this case, the stainless steel weight

appears to be 7 mg lighter than the brass weight. Hence, we can say that the

apparent mass of the brass weight versus 8.0 g/cm3 is 1 kg + 7 mg or LOOO. 007

g. Similarly, the apparent mass of the stainless steel weight versus brass is

i kg - 7 mg or 999.993 g. Thus, the apparent mass of a weight depends upon the

density chosen for the reference density. This is particularly clear for the

results for the aluminum weight. Thus, the apparent mass versus a reference

density is the mass an object would appear to have if it was compared against a

standard of a specified density and having a mass that would give the same

reading as the object when the comparison is made at 20°C in air with a

density of 1.2 mg/cm3.

The equations recommended for use to compute the apparent mass of an

object are given in SOP No.2.

7.1S
7 .4 Control Charts

Control charts provide a gl aphical means to decide whether a measurement

system has attained and is maintaining a state of statistical cm:'crol. They

can'indicate drifts warn of the initiation of potential problems and reveal the

need for corrective actions.

Control charts were first proposed in 1934 by Walter Shewhart for use in

statistical process control. Since that time, various modifications of his

original formt have been proposed and used. Cameron and co-workers at NBS (7)

were among the first to use control charts for monitoring measurement

processes, using essentially the Shewhart format. A general discussion of

control charts and extensive tables useful for calculating control limits will

be found in ASTM Manual for Presentation of Data and control Chart Analysis

( 3 ) . Croarkin discusses control charts as they are used in measurement

assurance programs (11). The following discussion reviews the kinds of control

charts considered to be most useful for laboratory use.

Several kinds of control charts will be found to be useful. The simplest

is based on the repetitive measurement of a stable test object and either the

results of single measurements (X chart) or the means of several (X chart) are

plotted with respect to sequence or time of measurement. The results should be

randomly distributed about the mean (X) in the case of an X chart and about the

mean of means (I) in the case of an X chart when the measurement system is in a

state of statistical control. Furthermore, the results should lie within

defined limits, based on statistical considerations.

, There is nothing really wrong in maintaining a simle X chart. However,

an X chart is preferable to an X chart because average values will indicate a

change in performnce more conclusively than individual values. This advantage

must be evaluated against the increased effort required to maintain the former.

An X chart based on the average of two measurements is a good compromise when

possible.

In addition to the above, there are precision control charts in which

either the standard deviation, estimated at various times, or the range, I., of

a set of measurements is plotted and interpreted similarly. Because of the

economy of effort, an I. chart is l)referable to an s chart. inen a propertyvalue control chart (X chart or T ~hart) and a precision chart are maintained

in parallel. diagnosis of out-o: ~ontrol situations as due to imprecision or

bias and the identification of assignable causes for such are facilitated.

X Control Chart

Single measurements are made of a stable test object, at least once on

each test day or at least monthly (if a measurement system is to be maintained

in statistical control over a period of time). The results are plotted

sequentially and the process is considered to be in control when they are

ranr~:mly distributed within limits as defined below.

7.16
Initial Control Limits, X Chart

Central Line, X

Measure the test object on at least 12 occasions (recommended) but no more

frequently than daily, i. e . never twice on the same day. The initial central

line is the mean of the n measurements, Xi for i-l,..., n.

_ 1:i

Central line, X - --

n

Calculate Sx the estimate of the standard deviation of X in the usual manner.

Note that this is an estimate of the long-term standard deviation. Calculate

the upper and lower control and warning limits as:

UCL - X + 3sx

UW - X + 2sx

LWL - X - 2sx

LCL - X - 3sx

When so set, approximately 95' of the plotted points should fall between

the warning limits (LWL and UW) and rarely should any fall outside of the

control limits (LCL and UCL) if the system is in a state of statistical

control. The control limits are conservative.

X Control Chart

A stable test object is measured in replicate, periodically. It is

recommended that these should be duplicate measurements made at least once on

each test-day or at least monthly, whichever is the more frequent. The means

of the measurements, X, are plotted sequentially. Statistical control is

judged when the plotted points are randomly distributed within the control

limi ts, determined as outlined below.

Initial Control Limits, X Chart

Central Line X

Measure the test object, in duplicate on at least l2 occasions

(recommended) and no more frequently than daily, i. e. never twice on the same

day. The initial central line is the mean of the means of n duplicate

measurements, Xi for i-l,..., n.

i:i

central line, X - --

n

Calculate si, the estimate of the standard deviation of X in the usual manner.

Note that this is a long-term standard deviation of the mean of n

measurements. and will ordinarily be larger than the short-term (within day)

stadard deviation which may be calculated from the value of i (see later).

7.l7
However, if the long-term exceeds the short-term standard deviation by more

than a factor of 2, the quality control should be improved to decrease the

former to more acceptable values.

Control Limits

UCL - X + 3si

WL - X + 2si

LWL - X - 2si

-

UCL - X - 3si

The limits are set so that approximately 9S% of the points should fall

within the warning limits (LWL and WL) and rarely should any fall outside of

the control limits (LCL and UCL) if the system is in a state of statistical

control. The limits are conservative.

i. Control Chart

The absolute differences (I.) of duplicate measurements of the test object,

and also of similar test specimens may be plotted sequentially to evaluate the

precision of the measurement process. This constitutes an i. (range) control

chart. Note that the range is related to the short-term standard deviation,

i.e. the repeatability of measurements over a relatively short period of time.

Initial Control Liits, i. Chart

Central Line i

, The observed ranges Ri (absolute values) for k sets 'at least l2 is

recommended) of duplicate measurements are averaged to obtain c: '"alue for i.

_ i:i i. --k

The control limits for duplicate measurements are as follows:

UCL - 3.267 i

WL - 2.512 i

LWL-O

LCL - 0

The control limits have the same significance as in the case of an X or X

chart.

For triplicate measurements, the control l1mi ts are:

UCL - 2.Sl2 i

WL - 2.050 i

LW-O

LCL-O

7.18
Updating Control Charts

After additional control data are accumulated (at least as much as

originally used) the control limits may be updated. A t test is made to see - -

whether the second set of data for X or X is significantly different from the

first set (see Chapter 8.11). .!f not. all data may be combined to obtain a new

and more robust estimate of X or X. If the second set is significantly

different from the first, only the latter should be used in revising the

control chart.

The value for the standard deviation s for the second set of

determinations should likewise be compared with the first estimate using the F

test (see Chapter 8.9) to decide whether to pool it with the first (see Chapter

7.4) or to use it separately in setting new control limits. A smaller value

for s, may result from improvement of the precision as the result of a learning

experience, for examle. A larger value for s could be due to an original poor

estimate of the standard deviation of the measurement process, or to a decrease

of precision resulting from an assignable cause(s). In either case, the reason

should be ascertained.

If the values of R show no systematic trends, and if i has not changed

significantly, all of the values of i. may be combined to obtain an updated

estimate of R, from which updated control limits can be computed. Judgment of

the significance of apparent changes in i can be made by computing the

corresponding values of s (see Table 9.1) and conducting an F test (see Chapter

8.9) .

Interpretation of Control Chart Data

Plotted points should be randomly distributed within the warning limits

when i the system is in a state of statistical control. If a plotted point lies

outside of the warning limits, a second set of measurements should be made. If

this point lies outside of the warning limits, corrective action is required

and demonstrated attainment of control is necessary before measurements may be

reported with confidence. Barring blunders, one point outside of the control

limits is reason for corrective action. The nature of the corrective action to

be taken, in either case, will depend on the kind of measurement made. If the

X or X point is outside the limits but the i. point is not, a source of bias

should be sought and eliminated. If the i. point is outside of limits, X or X

will probably but not necessarily be outside, as well (note that compensating

fluctuations could cancel one another). Sources of extraordinary rando~ error

should be sought and eliminated, before any possible bias can be detected.

Control charts may be used to evaluate the uncertainty of measurement in

some cases. When an appropriate control chart is maintained, an X or X chart

may be used to evaluate bias and to document the standard deviation of the

measurement process. Then the values for s on which the control limits are

based may be used in calculations of confidence limits for measurement values

(see Chapter 8.6).

7.19