NATIONAL BUREAU OF STANDARDS REPORT

A TESTING PLAN POE CEMENT

By

W* H» Clatv/orthy, W# S. Connor, and D* N. Evans

(

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
U. S. DEPARTMENT OF COMMERCE

Sinclair Weeks, Secretary

NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director THE NATIONAL BUREAU OF STANDARDS

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NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT mS REPORT

3737-60-0002 15 June 1953 2560

A TESTING- PLAN FOR CEMENT

By

W, H* Clatvror thy

W. S* Connor

Statistical Engineering Laboratory

and

D* N„ Evans

Concreting Materials Section

The publication, reprln

unless permission isobt

25, D. C, Such permlss

cat ly prepared If that

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST) on October 9, 2015

ait, Is prohibited

ards, Washington

has been speclflt for Its own use.

FOREWORD

This report illustrates a statistical approach of wide

applicability, and was prepared in the Statistical Engineering

Laboratory of the National Bureau of Standards, for the

information and use of the Bureau’s Mineral Products Division,

Churchill Eisenhart

Chief, Statistical

Engineering Laboratory

A. V. Astin

Director

National Bureau of Standards

A TESTING PLAN FOR CEMENT

By

W«. H* Clatwortliyyi IaT *' S'. Connor and. Du'. E. Evans;

1, Introduction . This report studies the amount of

testing which is being done by the National Bureau of Standards

of cement produced by the Hermitage plant at Nashville, Tennesse<

The object of the report is to determine whether the present

testing program provides enough testing or too much testing of

Hermitage production, and if too much, to suggest an alternative

program. Such an alternative testing program should be simple

to apply and applicable to the production of any plant®

The data studied were taken from the files of the Concreting Materials section of the Mineral Products division (9.6)

of the National Bureau of Standards. The data are the results

of tests made on grab samples taken from Hermitage production

of Type II cement during the period January, 1952 through May,

1953 » The properties studied are sulphur trl oxide (SO^),

silicon dioxide (SiC^)* aluminum oxide (A1 0 ) , magnesium oxide

(MgO), autoclave expansion, 7“day strength, and air permeability

fineness (A.P.F. )•

Most bins sampled contained l\S 00 barrels, from which 9

samples were taken. Except for fineness, composite samples

were formed from the first and second sets of four samples each.

leaving a single sample to be tested as an Individual, Fineness
2 -

determinations were made of each of the 9 individual samples,,

From these we have chosen the first and fifth,. For the purposes

of this study the data have been split into test results for

composite samples, which are given in Table 1, and those for

Individual samples, which are given In Table 4«> A proposed testing plan Is described in section 3>

applied to tests of composite samples in section anh applied

to tests of individual samples In section 6. The reasoning

underlying the plan Is developed In section 4« The conclusions

are presented in the following section*

2. Conclusions . The testing plan which is described in

section 3 is simple to apply, and can be used either for composite

samples or for Individual samples. If It had been applied to

the Hermitage plant from the middle of October, 1942 to the

middle of May, 1943 > then for SO , Si0 9

, A1 0 , MgO, autoclave

expansion, and 7-hay strength It would have' reduced the number

of tests from 762 to 333 « For SO^ the proposed testing plan

would not have materially reduced the number of tests. However,

for the other properties considered the number of tests would have been

reduced to approximately one- third as many tests as were actually made. This reduction would have been achieved

at no appreciable increase in the risk of falling to detect

violations of the specifications.
- 3 -

The plan is general* Barring some factors or conditions

not found in the cement studied, it can be applied to grab

samples from any plant and to properties other than those

to shi oping studied. It also can be modified to apply/and other samples.

3 * The tes ting plan * We can best describe the testing

plan by applying it to a particular property. So let us trace

the application to SO^ composites. For the sake of realism

we shall suppose that it was decided to put the plan into effect

in October, 1952 , xdien results for bins 1 through 32 were

available, but before bin 33 Wad been tested.

The steps In the application of the plan are as follows:

( 1 ) From the files take the first test result for each

of the last 32 bins, dividing them into groups of 8 each. These

results (from Table l) are as f olloxvs : 12 Group

3 2

i .4 1.5 1.4 1.8

1.6 1.7 1.6 1.7

1.7 1.4 2.1 2.0

1.1 1.6 1.6 1.8

1,6 1.5 1.7 2.0

1.6 1.6 1.8 2.0

1-4 1.5 1.6 1.9

1.2 1.5 1.6 2.0

We emphasize that only the first result from each bin is used
- 4

~

(2)

Determine the range, r, of each group. The range

is the difference between the largest and the smallest number

in the group, so that the ranges are ds follows;

1

Largest 1.7

Smallest 1 .1

Range (r. ) o7£

Group

2

1.7

1 .4

0.3

3

2.1

1.4

0.7

k

2.0

1.7

0.3

(3) Compute the average range, r , thus;

?!

= + r

2 + r^ + r^)/4

= (.6 + .3 + .7 + .3)/4 = 0.475 .

(4) Subtract 0.7025 from 2.0. (If the property has a

minimum specification, add 0.7025 r-^ to the specification

instead of subtracting.) Round off to the same number of

decimal places as are recorded for the test results. Obtain

2.000 - (0.7025) (0.475) = 1.666

and round off to 1.7 • We shall call this value P (Frequent)

to denote the limit for frequent testing.

(5)

Subtract 0.7025 p-^ from 1.666. (If the property has

a minimum specification, add.) Obtain 1.334 and pound to 1.3*

We shall call this value I (infrequent) to denote the limit for

infrequent testing.

,707-r ^±l±l±fO_ _ h,o

d<?

' ' i (/ Pj ^

' jiirv-v A * t /i

V 7

O

ou. r f'7 L-O 7

2-dJi/L
(6) (Optional but recommended*) Make up a chart, such

as Figure 1, showing the specification, the 32 test results,

and the numbers F and I. Fne specification line should start

with bin 1 and extend as far into the future as is feasible*

The F and I lines should extend from bin 33 through 64*

The preliminary calculations are complete, so the plan

may now be put into operation. The first new test result, which

in our case occurs for bin 33 will determine the testing rate*

If it Is greater than or equal to F, we shall test frequently

(two tests per bin) but If it Is less than F we shall test

Infrequently (one test per bin)* As it turns out (see Table

1 or Figure 1), the first new test result is 2.1 i^hich e xceeds

F = 1*7, so that we start out testing frequently. Frequent

tests continue until a test result is less than I, which Is

the signal for infrequent testing* The first such result occurs

for bin 38 y when the test result drops to 1.1, less than I = 1

3 , so that we switch to Infrequent testing. This continues until

test result 1*7 is reached for bin Lj.O, which again orders 'frequent

testing. Since no further test result Is as small as I, frequent

tests are run for the remaining bins. Although for SO^ F and

I are unchanged throughout our illustration, we shall see below

that there Is, In general, the possibility that they will change

after each 32 additional bins.
- 6 -

(7) Tliis step is designed to keep a check on the stability

of the range. When the test results for bins 33 through 64

become available, divide the first test results of the bins

into 4 groups of 8 each, and compute the range of each group,

and the average range, 77,. Then form the ratio of the larger

of r-^ and r^ to the smaller. If the ratio is less than 1.5#

continue to use F and I as previously computed through bin

96. If step (6) is in use, we now extend our original P and

I lines through bin 98 . If the ratio is as great as 1.5#

use r^ to recompute F and I according to steps (1) through

(5)

,

and draw new F and 1 lines. After each additional 32

bins, we compare the new r with the r in use to decide whether

we need to recalculate P and I.

For SO^ the calculations are as follows:

Group

1 2 3 k

271 178 176 1.7

1.9 1.7 1.7 1.7

1.9 1.7 1.8 1.6

2.0 1.7 1.8 1.7

1.4 1.9 1.7 1.4

1.1 1 .6 1.8 1.7

1.6 1.8 1.6 1.8

1.7 2.0 1.4 2.0

Larges t 2.1 2.0 1.8 2.0

Smallest

Range (r^ ) 1.1

1.0

1.6

0.4

ih

074

14

0 e O
7

r

2 = lr

$

+ r

6 + r

?

+ r

g

)A

= (i*o + 0.4 + .04 + *o6)/4 = 0*600

r 0/ r_ = .600/. 475 = 1.26

Since 1.26 is less than 1.50, we continue to use F = 1.7 and

I = 1.3. Thus, the F and I lines have been extended through

bin 74 i n Figures 1 and 4# and in practice would be extended

through bin 96. This complete the description of the plan.

It is apparent that with rare exceptions S0^ needs frequent

testing. The testing plan would have reduced the number of

tests by only four tests. We determine this by remembering that

two composite samples and one individual sample actually were

tested on all bins except bin 51 , for* which three compositesi and

one individual were tested. Hence, if when our plan requires frequent

tests we include the individual sample for each bin, we find that

one composite and one individual test would have been saved for

each of bins 38 and 39* This is a reduction of 4 tests out

of 127 tests.

4* Application of the plan to composite samples for

several proper tie s . We have seen that S0^ is running so close

to the specification that frequent testing is almost always

necessary. We now shall consider composite sample test results

for several other properties, SiC^, AlgO^, MgO, 7-day strength,

and autoclave expansion. These results are given in Table 1.
- 8 -

We shall see that the testing plan of section 3 would

have required many fewer tests than actually were made during

the period considered*

Table 2 supplies the necessary calculations for determining

P and I. Perhaps the most striking property for which infrequent

tests would have sufficed throughout the period is autoclave

expansion. Autoclave never came close to specification, nor

for that matter to I • The testing plan for autoclave is

vividly depicted in Figure 2, The first test result for bin

33* » 15>s is much smaller than I = ,38* so from v the beginning

the plan calls for infrequent testing . Since the largest test

result during the period was .33 (bin 67 ) * much less than P = .i|4*

the plan never requires frequent .besting . Let us count the saving in the number of tests which the

testing plan would have provided. As the testing was re ally

done, one individual and two composite tests were run on

every bin but one, and that bin (bin 5>1) had three composites

and one individual, giving a total of 127 tests. The testing

plan, on the other hand, would have required only one test

per bin, or \\Z tests altogether. Thus, the plan itfould have

cut the number of tests to one-third*

The same saving would have been realized for S iOg,

MgO q and 7-day strength* Using only the first sample for each bin

the smallest test result for SiC>2 was 21.9 (bin 73), greater
- 9 -

than P = 21.6; the largest for Al^O^ was 5*3 (bins 62 and 72),

less than F = 5*6; the largest for MgO was 4*4 (bln 72), less

than P = 4*4 > and the smallest for 7 -day strength was i 960

(bin 60) greater than P = 1,870. Hence, for each of these

properties infrequent testing would have sufficed.

To summarize, the testing plan would have reduced the

number of tests for each of autoclave, Si 02 , AlgO^# MgO, and

7-day strength from 127 tests to l\2. tests, or altogether from

635 tests to 210 tests,

5>. Rationale of the testing plan. We consider a testing

plan to be a good one if it prescribes frequent tests when it

is likely that a sample will violate the specification, but

infrequent tests otherwise. The plan which we have described

has these characteristics.

To judge whether or not it is likely that a current sample

will violate the specification for some particular property,

it is necessary to look at the history of that property. Tf

past sample test results were close to the specification, then

there is a good chance that the next sample will violate the

specification, and frequent tests should be made. On the other

hand, if history reveals that the test results were far from

the specification, then there is little danger of a violation,

and infrequent testing is sufficient.
10' -

The problem is to decide what is meant by a test result

being close to or far from the specification. It is apparent

that knowledge of the average value of past results, though

important, is not enough by itself to decide this. To know,

for example, that the last ten test results for autoclave

expansion averaged 0.3k percent does not enable us to judge

whether or not a new sample will exceed 0*50* Further scrutiny

of the data is necessary. If we find that the largest of the

ten was O.Ij.8, it id.ll seem quite possible for the new sample

to violate the specification, but if the largest was only 0.37>

we shall doubt that the new-sample will exceed 0.50* The average,

then, has to be accompanied by a measure of the variation, and

these two measures together form the basis for a sound sampling

plan.

In the following remarks we shall assume that the test

results are approximately normally distributed* Although we

have not investigated their distribution, there is no reason

to expect any serious departure from normality*

We chose the range as the measure of variation because

(i) it is easy to calculate and (ii) there are long-run shifts

in the average levels of the properties, which suggests that

the data should be divided into groups of consecutive observations

and the variation estimated within each group, a situation
11

in which the range is nearly as efficient an estimator of the

variation as is the theoretically preferred standard deviation

[1 ]*.

Under certain circumstances, theoretical considerations

show that the average of the ranges of groups of 8 tests each

is a better estimator of the variation than the corresponding

average for groups of any other size [2]. For this reason we

have used groups of 8 tests each.

For each bin several samples are available for testing,

whether we test them or not. The problem of how many samples

to test for a bin can be answered by testing the first sample

and judging how close the result is to the specification.

This judgment should be made by consideration of the variation

among samples from the same bin. The ranges which we use,

based as they are on one sample per bin, do not measure this

variation, but rather measure the variation among samples from

different bins. We prefer to use them, however, because they

are convenient, requiring only one test per bin, and they

are conservative, since they tend to overestimate the variation

within bins.

K See reference at end of text.
12 -

That the variation among samples from different bins

exceeds the variation among samples from the same bin is brought

out by Table 4® The numbers ih the table were c omputed from

the results for bins 49 through 74® The last column, Estimated

variance (or variation)”, is of main interest because the first.,

number there (between bins) estimates the variation among samples

from different bins and the second number (within bins) estimates

the variation among samples from the same bin. For every

property the former exceeds the latter, and for some properties

is several times larger.

Tie number F has been chosen such that if the true average

for the property is equal to F, then the chance that a test

result will violate the specification is only about 2£ in 1,000

1 3 3 • This is a conservative choice of F, as we shall see.

Suppose that the history of the property is such that infrequent

tests have been made in the recent past, but the current test

result is equal to F or lies between F and the specification.

We at once switch to frequent testing, taking the dim view that

the true average for the property may be at least as close to

the specification as F, even though the current result could

be due only to sampling fluctuations or testing error when

in reality the true average is not as close to the specification
as P» Thus unless there is a marked trend in the data, the

chance of the next test result violating the specification

is not greater than about 25 in 1,000*

The number I has been chosen similarly. If the true

average for the property is equal to F, then the probability

of obtaining a test result which Is as far from F as I Is

only ,025* Thus, we do not resume Infrequent sampling until

it becomes virtually certain that the true average is not as

close to the specification as F,

These remarks assume that' the true variability does not

change* If there is an increase or decrease in the true variability,

then the probability, * 025 , will Increase or decrease, respectively.

Small changes in the variability will not affect this probability

much, and so may be ignored* However, a sizeable change must

be taken into account, and it is for this reason that step (7)

of the plan (section 3 ) is included*

If r^ Is the average of the ranges from hc groups each

of size 8 and r^ is a similar measure from [|. other groups,

then there Is good reason to believe that the probability that

the larger of r^ and r^will exceed the smaller by as much as

1.5 (when in reality they estimate the same variation) is small.

Hence, we do not recompute F and I unless there is a good chance

that the variation between bins really has changed*
- i4 -

To obtain a graphic picture of the stability of the range

for SO^, autoclave expansion, and 7-day strength, we have

plotted ranges of groups of 4 test results each in Figures

4 and .6. Also given are the average range, R for the

first 8 groups and a control limit which is determined from

R^ # Summary calculations for Figure 4 are given in Table 3,

The control limit in Table 3) is determined such that the

chsjjpce of an individual range exceeding it if were equal to

its expected value is only about 15 in 10 , 000 ® The fact that

no individual ranges exceed the limit for any of the groups 1

through 18 attests to the stability of the process variation®

This is further confirmed by calculation of R^ fnom the ranges

of groups through 16 ® In no case is ver>y different from R^ ft

6® Appli cation of the testing plan to individual samples , The testing plan of section 3 applies to individual samples

equally as well as to composite samples* In Table 6 we have

determined F and I for individuals for all of the properties

already treated for composites, and in addition, A.P. fineness®

Since only one individual sample is available from each

bin, it is impossible to show on a chart all of the test

results which would be required by frequent sampling. However,

Figure 5 gives a plot of the available test results for 7~day

L r. z,//, s - *>? t
- 15 -

strength, together with the minimum specification and the

F and I lines. In practice, when a sample result is as small as F, several samples would be tested for each bin.

As one would expect, the variation among individuals tends

to exceed that among composites. This can be seen by comparison

of the ranges of Table 6 with those of Table 2, For 7-day

strength the difference in ranges is reflected in an increase

in F from 1,870 for composites to 2,080 for individuals, and

an increase in I from 2,250 for composites to 2,650 for individuals.

In the application of the testing plan to 7-day strength,

composite samples never required frequent testing, but Individual

samples oten did. In fact, the available test results for

individuals ordered frequent tests beginning with bins 33, 50, and 61 • For other properties studied, the plan when applied

to Individuals requires about the same number of tests as when

applied to composites.

For autoclave, since r^/ r^ =1.5 (see Table 6), F and

I should be recomputed and the rlew values used for bins 65

through 96. F and I would then be .43 and .37, closer to the

specification.

7.. Acknowledgment . The authors wish to thank Dr. E. P.

King (11.3) for* advice about technical aspects of the use of

the range.
REFERENCES

E. P. King, ’’Estimating the standard deviation of a normal population”, to appear in Industrial Quali ty

Control , July, 195>3»

F. E. Grubbs and C. L. Weaver, ’’The best unbiased estimate

of population standard deviation based on group ranges”.

Journal of the American Statistical Association , Vol. l\.2 f No . 2yo TT947T> pp. 224-24!

E. Lord, ’’The use of range in place of standard deviation

in the t-test,” Biometrlka, Vol. XXXIV, Parts I and II

(1947), PP. 41-67* ...
- 17 - Table 1

TEST RESULTS FOR COMPOSITES

Bin No, Sample

Date

Bin S

°3 Si0

2

M2°3 MgO 7-Day AutoSt]?. clave

1 1/4-5/52 S-l-2 1.4 23.0 4.9 3*1 2000 .15

1.4 23.0 4.8 3*2 2000 .15 2 1/21-22/52 S-4-2 1.6 22.5 4.8 3*1 1850 .12

1.4 22.8 4.9 3.2 1680 .17

3 2/7-8/52 S-l-3 1.7 22.5 5.1 3*6 1790 .20

1.6 22.6 5*3 3*6 1660 .22

4 1/25-26/52 S-5-7 1.1 22.9 5*3 3.4 1480 .15

1.1 23.0 5.1 3.4 1520 .16

5 3/3-4/52 S-4-3 1.6 22.5 5.1 3*4 1910 .18

1.4 23.0 5.2 3.4 1500 .16

6 3/12-13/5.2 S-5-8 1.6 22.4 4.7 3.0 2060 .11

1.4 22.4 4*8 3.0 2220 .11

7 3/25-26/52 s-i-4 1.4 22.4 4*6 3.0 2020 .12

1.4 22.4 4*6 2.9 2010 .13

8 4/2-3/52 s-4-4 1*2 22.4 4.9 3*5 2230 .13

2.0 22.1 4*9 3.4 2210 .11

9 4/11-12/52 s-5-9 1.5 22.2 4.8 3.5 2260 .11

1.2 22.4 5.1 3.'7 1890 .17

10 4/28-29/52 s-1-5 1.7 22.5 4.8 3*1 2220 .11

1.4 22.5 4.8 3.2 2210 .13

11 5/14-15/52 s-2-2 1.4 22.5 4*8 3.3 2090 .16

1.6 22.6 4.5 3.3 2100 .17

12 5/26-28/52 0-1-3 1.6 22.7 4.5 3.1 2510 .12

1.5 22.9 4*3 3.1 2300 .13

13 6/4-5/52 s-4-5 1.5 22.9 4.5 2.9 2480 .13

1.4 22.9 4*4 2.9 2460 .14

14 6/9-10/52 S-l-6 1.6 22.4 4.8 2.9 2350 .13

1.5 22.7 4.9 2.9 2050 .14

15 6A2-13/52 s-5-10 1.5 22.7 4.5 3.1 2350 .12

1.5 22.7 4*6 3.1 2440 .13

16 6/23-25/52 S-2-3 1.5 22.9 4.4 3.2 2340 .12

1.4 23.0 4.4 3.2 24o0 .11

17 6/30/7-1/52 S-3-7 1.4 23.1 4.2 3.2 2000 .14

1.6 23.1 4*3 3.2 2250 .13

18 7/14-15/52 s-4-6 1 .6 22.4 4.6 4.1 i860 .17

1.7 22.6 4*8 4.1 1800 .21

19 7/17-18/52 S-l-7 2.1 21.7 4*6 3.6 204° .15

2.1 21.9 4.6 3.3 1680 .16

20 7/30-31/52 s-5-11 1.6 22.2 4*6 3*8 2410 .18

1.6 22.3 4*6 3.7 2550 .16
- 18 - Table 1 (Continued)

Bin No. Sample

Date

Bin so

3

Si0

2

A12°3 MgO 7 -Day

Str . Autoclave

21 8/4-5/52 s-2-4 1.7 22.4 4.2 3.0 2250 .11

1.5 22.3 4.3 3.1 2080 .12

22 8/6-7/52 S-3-8 1.8 22.1 4.0 3.1 i860 .11

1.6 22.3 3.8 3.3 2010 .09

23 8/13-14/52 S-l -8 1.6 22.7 4.0 2.8 1980 .06

1.6 22.5 4.2 2.7 2160 ,06

24 8/18-19/52 s-4-7 1.6 23.0 4.2 2.8 2170 .06

1.7 23.0 4.3 2.8 2280 .06

25 9/2-3/52 S-5-12 1.8 22.9 4.5 3.2 1980 .10

2.0 22.4 4.5 2.6 2470 .10

26 9/4-5/52 S-2-5 1.7 22.6 4*5 3.1 2120 .10

1.6 22.8 4*7 3*1 2160 ,11

27 9/11-12/52 s-3-9 2,0 22.8 4-9 3*0 1880 .12

1.8 22.9 4.8 3.2 2140 ,12

28 9/15-16/52 s-1-9 1.8 22.7 4.9 3.0 1990 *17

1.8 22,8 5.0 2.9 2000 .18

29 9/18-19/52 s-4-8 2.0 22.6 4.8 2.8 1980 ,14

2,0 22.5 4.8 2.7 2070 .16

30 9/29-30/52 s-5-13 2,0 22,3 4*8 2.9 2190 .18

2.0 22.5 4.8 2.9 2210 .15

31 10/1/52 S-2-6 1.9 22.8 5.0 2.9 2100 .18

1.8 22.5 5.0 2.9 2480 .20

32 10/3-4/52 S-3-10 2.0 22.5 4*8 3*0 2270 .11

1.9 22.3 4.9 3.0 2330 .13

33 10/7-8/52 S-l-10 2.1 22.7 4.8 2.8 1990 .15

1.8 22.6 4.9 2.9 2070 .18

34 10/7-8/52 s-4-9 1.9 22.5 4.8 3.1 2120 .13

1.7 22.5 4.7 3.1 2200 .16

35 IO/22-23/52 s-5-14 1.9 22.5 4.5 2.8 2310 .10

1.8 22.7 4.7 2.9 2170 .13

36 10/23-25/52 S-2-7 2.0 22.8 4.8 2.9 2090 .14

2.0 22.6 4.8 2.9 2120 .12

37 11/1-2/52 S-3-11 1.4 23.2 4.7 2.8 2560 .12

1.5 23.1 4*6 2.6 2500 .11

38 11/3-4/52 S-l-11 1.1 22.7 4.6 2.9 2630 .09

1.5 22.5 4.5 3.0 2620 .09

39 n/5-6/52 S-4-10 1.6 22.3 4.4 2.9 2260 .09

1.4 22.4 4.3 3.0 2210 .08

40 H/ll-12/52 s-5-15 1.7 22,5 4.7 3.3 . 2080 .11

1.7 22.5 4.7 3.4 2090 .12

41 11/13-14/52 S-2-8 1.8 22.6 4.6 3*3 2130 .13

1.7 22.7 4.7 3.3 2170 .11
- 19 - Table 1 (Continued)

Bin No# Sample

Date

Bin S°

3

SiO

2

A12°3 MgO 7-Day

Str.

Autoclave

42 11/25-26/52 3-3-12 1.7 22.7 4*5 3.0 2360 .10

1.6 22.7 4*6 3.0 2370 .20

43 11/28-29/52 S-l-12 1.7 22.7 4*6 3.0 2080 .09

1.5 22.7 4.9 3.0 2050 .10

44 12/2-4/52 s-4-11 1.7 23.0 4.8 2.7 2210 .07

1.7 22.9 4.8 2.6 2260 .08

45 12/15-16/52 s- 5-16 1.9 22.9 4*4 2.9 2640 .07

1.7 22.6 Il.6 2.9 2400 .08

46 12/18-19/52 s-2-9 1.6 22.6 4.7 2.9 2700 .10

1.6 22.5 4-7 2.9 2690 .09

47 12/26-27/52 s-3-13 1.8 22.4 4.7 3.3 2550 .11

1.8 22.5 4.8 3.3 2530 .11

48 12/29-30/52 s-1-13 2.0 22.6 4.8 3.3 2430 .12

1.6 22.7 4*7 3.3 2360 .13

49 1/5-6/53 S-4-12 1.6 22.6 4.5 3.2 2510 .10

1.8 22.7 4.5 3.2 2350 .10

50 1/21-22/53 S-2-10 1.7 22.7 4.9 3.3 2160 .12

1.9 22.7 4.9 3.2 2160 .13

51 1/26-28/53 0-5-4 1.8 22.3 5.2 3.9 2080 .20

1.8 22.2 5.2 3.9 2490 .19

52 1/19-20/53 s-5-17 1.8 22.8 4.8 3.0 2120 .09

2.0 22.9 4.8 3.1 2080 .10

53 1/30-31/53 s-3-14 1.7 22.4 4.9 3.5 2550 .08

1.8 22.3 4.8 3.6 2550 .17

54 2A-5/53 s-1-14 1.8 22.9 5.0 3.2 2100 .13

1.7 22.8 4.9 3.1 2090 .15

55 2/26-27/53 S-2-11 1.6 22.6 4.9 3.4 2210 .11

1.5 22.6 4.7 3.4 2390 .13

56 2/28-3/1/33 s-3-15 1.4 22.7 4.9 3.6 2230 .14

1.4 22.7 5.0 3.9 2180 .15

57 3/2-3/53 s-4-13 1.7 22.5 4.9 4.0 2100 .17

1.5 22.6 4.9 4.1 1940 .19

58 3/6-7/53 S-l-15 1.7 22.5 4.7 3.3 2380 .12

1.5 22.1 4*6 3*2 2540 .12

59 3/4-5/53 S-5-18 1.6 22.3 4.9 3.4 2230 .16

1.8 22.2 4.9 3.6 2190 .17

60 3/18-19/53 S-2-12 1.7 22.9 4.8 3.4 I960 .12

1.9 23,0 4.8 3.3 2000 .12

61 3/23-24/53 S-3-16 1 *> 22.8 5.1 3.9 2060 .18

1.6 22.7 5.2 3.9 2000 .18

62 3/25-26/53 S-4-14 1.7 22.3 5.3 4.0 2340 .22

1.4 22.5 5.0 4.2 2100 .23

63 3/27-28/53 s-5-19 1.8 22.5 5.1 3.9 2060 .18

1.7 22.6 5.0 3*9 1820 .20
- 20 - Table 1 (Continued)

Bin No* Sample

Date

Bin SO

3

Si0„

2

Al^O^ MgO 7 -Day AutoStr. clave

64 3/30-31/53 S-l-16 2.0 22.1 5.1 4.1 2060 • 26

1.5 22.5 5.2 4.1 1840 .22

65 4/8-9/53 S-3-17 1.7 22.4 5.2 4.2 2100 .20

1.8 22.5 5.2 4.1 1980 .19

66 4/2-3/53 S-2-13 1.7 22.5 5.2 3.9 2340 .19

1.7 22.5 5.3 4.1 2220 .21

67 4/13-14/53 's-4-15 2.0 22.0 4-9 4.0 2540

.

.33

1.7 22.1 4.8 4.6 2350 .31

68 4/15-16/53 s-5-20 1.8 22.0 4-9 4.1 2260 .32

2.2 21.8 5.0 4.2 2380 .27

69 4/17-18/53 S-l-17 2.0 22.0 5.0 4.1 2480 .21

1.7 22.4 5.1 4.1 2170 .25

70 4/27-28/53 s-2-14 1.8 22.2 5.1 4.1 2470 .23

1.7 22.3 5.1 4.o 2360 • 26

71 5/1-2/53 s-4-16 2.0 22.1 4.8 4.o 2530 .22

1.8 21.9 5.0 4.1 2640 .20

72 5/5-6/53 s-5-21 1.7 22.1 5.3 4*4 2460 .29

1.7 22.1 5.2 4.3 2480 .27

73 4/29-30/53 S- 3-18 2.1 21.9 4-9 4.0 2610 .20

2.0 21.9 5.2 4.o 2430 .21 • 74 5/8-9/53 S-l-18 1.6 22.2 4-9 4.3 2600 .28

1.5 22.2 5.1 4.2 2740 .30
21

Table 2

CALCULATION OP P AND I FOR COMPOSITES

Auto- 7-Day

so

3

Si0

2 ai 2o

3

MgO clave Strength

IS 0.6 0.6 0.7 0,6 .09 770

r

2 0.3 0.7 0.4 0.6 .05 420

0.7 1.4 0.6 1.3 .12 550

r, 4 h

2 r

0.3 0.6 0.5 0.4 .08 390

1.9 3.3 2.2 2.9 .34 2130

1=1 1

r

l 0.475 0.825 0.550 0.725 0.085 532.5

0,7025^ 0.334 0.580 0.386 0.509 0.0597 374.1

Max* Spec.

Min. Spec.

2.0

0

1

*

•

11—

1

C\J

1 6.0 5.0 0.5

1500

P 1.7 21.6 5.6 4.5 0.44 1870

I 1.3 22.2 5.2 4.0 0.38 2250

r

r5

6

r

7

1.0 0.9 0.4 0.5 .06 640

0.4 0,6 0.4 0.6 .06 620

0.4 0.6 0.7 0.9 .12 470

To

8

8 0.6 0.8 0.6 0.8 .14 420

2 r

i i=5 1 2,4 2.9 2.1 2.8 co . 2150

r

2 0.600 0.725 0.525 0.700 .095 537.5

Ratio of r f s 1.26 1.14 1.05 1.04 1.12 1.01
22 - Table 3

CALCULATION OP Rp L, AND R2 FOR RANGE CONTROL CHARTS

FOR COMPOSITES

Auto- 7 -Day

S°

3

sio

2 A1

2°3 MgO clave Strength

R

1r|

0 ;6 0.5 0.5 o;5 ;08 520

0;4 0.1 0.5 0.5 ;07 340

R7 0.3 0.5 0.3 0.4 .05 420

%

0.1 0.5 0.4 0.3 ;oi 140

0.7 l;4 0.4 1,0 .04 550

0.2 0.9 0,2 0.3 ,05 390

R

7 0.3 0.3 0.4 0,2 ;07 240

r!

8

8

2 R,

i=l 1

0.1 0.7 0.2 0.2 ,07 290

2.7 4.9 2.9 3.4 0 . 44 2890

R

i 0.3375 0.6125 0,3625 0.4250 0.0550 361.25

L=2.2f2R1 0,77 1.40 0.83 0.97 0.126 824

Ro R? n

0.2 0.3 0.3 0;3 .05 320

0.6 0.5 0.3 o»5 .03 550 plO n 0.1 0.4 0,3 0 ,6 .06 280

oil R12

R13

S14 R

15

16

16

o .4 0.5 0 .4 0.4 ,05 270

0.2 0,5 0.7 1.0 ,11 430

o.4 0,3 0.1 04 ,‘06 450

0.1 0 ,6 0,2 0,7 .05 420

0 *6 0,7 0,2 0,2 .08 280

2 R 2.6 4.0 2,5 4.1 0.49 3000

1=9 1 - " R

2 0.3250 0,5000 0.3125 0.5125 0,0^125 375.00
- 23 - Table 4

\

COMPARISON OP BETWEEN AND WITHIN

BIN VARIATION FOR INDIVIDUALS

Source of Degrees Sum of Estimated Variance

Property Variation of Freedom Squares (or variation)

SOo Between Bins 25 1.15 0.0460

3 Within Bins 26 0.56 0.0215

Total 51 1.71

SiOQ Between Bins 25 4.423 0.17692 d. Within Bins 26 0.365 0.01404

Total 51 4.788

A1 0 , Between Bins 25 1.71 0.684

2 3 Within Bins 26 0.21 0.00807

Total 51 1.92

MgO Between Bins 25 8.07 0.3228

Wi thin Bins 26 0.35 0.01348

Total 51 8.42

Auto- Between Bins 25 0.20155 0.008062

clave Within Bins 26 0.00955 0,000367

Total 51 0.21110 V- "

?

7 -Day

Strength Between Bins 25 2,221,133 88,845.32

Within Bins 26 351,950 13,536.53

Total 51 2,573,083
- 24 - Table 5

TEST RESULTS FOR INDIVIDUALS

Bin Sample Bin SO SiOp Ai 0 MgO 7 -Day Auto- A.P.F

No, Date Str . clave

1 V4-5/52 S-l-2 1.4 22.9 4.9 3.4 1980 .15 3730

3900

2 1/21-22/52 S-4-2 1.1 23.0 5.0 3.3 1540 .20 3640

3940

4330

3790

3410

3 2/7-8/52 S-l-3 1.6 22.6 5.2 3.6 1560 .25

4 1/25-26/52 s-5-7 1.2 23.0 5.1 3.4 1500 .18

» 3630

5 3/3-4/52 s-4-3 1.2 23.0 5.2 3.5 1540 .19 3340

3380

6 3/12-13/52 s-5-8 1.8 22.3 4-7 3.0 2140 .10 3640

3510

3480

3520

3860

7 3/25-26/52 s-1-4 1.4 22.3 4.6 3.0 I960 .13

8 4/2-3/52 s-4-4 1.6 22.2 5.0 3.4 2050 .12

3610

9 4/11-12/52 s-5-9 1.2 22.2 5.0 3.8 1950 .17 3970

3630

10 4/28-29/52 s-1-5 1.5 22.5 5.0 3.2 2260 .10 3760

3570

11 5/14-15/52 s-2-2 1.4 22.7 4*5 3.3 2000 .16 3850

3380

12 5/26-28/52 0-1-3 1.7 22.8 4.2 3.1 2430 .11 3590

3740

13 6/4-5/52 s-4-5 1.3 22.9 4.6 2.9 2700 -3" 1

• 1— 3730

3630

14 6/9-10/52 S-l-6 1.5 22.8 4.8 2.9 2150 .13 3860

3570

15 6/12-13/52 s-5-10 1.4 22.7 4.6 3.0 2270 .13 3610

3500

16 6/23-24/52 S-2-3 1.6 23.1 4.3 3.2 2630 .11 3740

3590

17 6/30/7-1/52 S-3-7 1.6 23.1 4.3 3.2 2150 .15 3610

3470

3800

3480

4250

18 7/14-15/52 S- 4-6 1.9 22.3 4.8 3.9 1850 .14

19 7/17-18/52 S-1-7 1.7 22.6 4.8 4.2 1320 .26

3940

w A.P.F. means A. P. Fineness
Bin

No.

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

- 25 - Table 5 (Continued)

Sample

Date

Bin S0

3

sio

2

Al^O^ MgO 7 -Day

Str

AutoclaveA.P.P

7/30-31/52 s-5-ii 1.3 22.5 4.7 3.6 2270 .15 3780

3410

3870

3850

iil80

3840

3800

3980

8/4-5/52 s-2-4 2.0 22.1 4.4 3*1 2110 .11

8/6-7/52 S-3-8 2.0 22.2 3.6 3.2 2290 .09

8/1.3-14/52 S-l-8 1.8 22.7 4.2 2.7 2530 . 06

8/18-19/52 s-4-7 1.7 23.0 4.3 2.9 2240 .09 3540

3670

3730

3570

9/2-3/52 S-5-12 1.6 22.4 4.6 3.3 2470. .11

9/4-5/52 S-2-5 2.0 22.3 4.5 3*0 2260 .08 3680

3530

9/11-12/52 S-3-9 1.9 22.9 4.8 3.2 2010 .12 3210

3840

9/15-16/52 s-1-9 1.9 22.9 5.1 2.9 2010 .17 3290

3490

9/18-19/52 s-4-8 1.9 22.4 4.8 2.7 2290 .17 3830

3790

3660

4oio

9/29-30/52 s-5-13 2.0 22.5 4.8 2.9 2330 .05

10/1/52 s-2-6 1.8 22.2 4.8 2.9 2690 .20 3630

3890

3640

3640

10/3-4/52 s-3-10 1.4 22.7 4.9 3.0 2010 .14

10/7-8/52 s-1-10 1.7 22.6 4.9 3.0 2060 .17 3710

3830

10/7-8/52 s-4-9 1.7 22.5 4.8 3.1 2230 .14 3520

3530

10/22-23/52 s-5-14 2.0 22.7 4.8 2.5 1830 .12 4070

3960

3670

3990

3550

3500

4090

4300

10/23-25/52 s-2-7 1.8 22.7 4*6 2.6 2020 .11

11/1-2/52 s-3-11 1.7 22.9 4.5 2.8 2500 .10

n/3-4/52 s-1-11 1.6 22.4 4*5 3.0 2530 .09

n/5-6/52 s-4-10 1.8 22.2 4*3 3.1 2550 .07 4220

3820

3790

3730

H/ll-12/52 s-5-15 1.6 22.3 4.7 3.5 1930 .12
Bin

No,

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

- 26

Table 5 (Continued)

Sample

Date

Bin so

3

S10

2 A12°3 MgO 7-Day AutoStr. clave

11/13-14/52 s.-2--8 2.1 22.5 4-7 3.2 2270 .10

11/25-26/52 s--3--12 1.6 22.7 4.6 2.9 2560 .09

11/28-29/52 S'-1--12 1.6 22.8 4.8 3.0 2220 .10

12/2-4/52 s.-4--11 1.6 22.9 4.8 2.5 2310 .08

12/15-16/52 S'-5.-16 1.8 22.6 4.5 2.9 2820 .08

12/18-19/52 S'-2.-9 1.7 22.5 4.8 2.9 2430 .08

12/26-27/52 S'-3--13 1.8 22.5 4.8 3.3 2280 .13

12/29-30/52 S'-1--13 1.4 22.6 4.7 3.2 2620 .14

1/5-6/53 S'-4*-12 1.5 23.1 4-5 3.2 2420 .11

1/21-22/53 S'-2.-10 1.5 22.9 5*2 3.5 1990 .18

1/26-23/53 0--5--4 — ---- — --- — —

1/19-20/53 S'-5--17 1.8 22.9 4.6 3.0 2140 .09

1/30-31/53 S'-3--14 1.9 22.3 4.8 3.4 2650 .19

2/4-5/53 S'-1--14 2.3 22.5 4.9 3.3 2550 .11

2/26-27/53 S'-2.-11 1.5 22.6 4.8 3.3 2360 .12

2/28-3/1/53 S'-3.-15 1 .6 22.6 4.8 3.8 2480 .13

3/2-3/53 S'-4--13 1 «

4

22.6 4.9 4.1 2210 .18

3/6-7/53 S'-1--15 1.7 22.3 4.5 3.4 2660 .12

3/4-5/53 S'-5.-18 1.6 22.2 4.5 3.4 2640 .13

3/18-19/53 S'-2--12 2.0 22.8 4.8 3.4 I960 .13

3/23-24/53 S'-3--16 1.8 22.2 5.2 3.8 2080 .18

A.P.F.

3500

3570

3940

3640

2600

3530

3590

3660

3800

3730

3790

3650

3980

3730

3640

3760

3610

3550

3600

3710

3450

3750

3480

3350

3450

3720

3370

3730

3300

3670

3200

3640

3440

3300

3550

3790

344° 3440

3390

3350

3460

33io
Bin

Wo,

62

63

64

65

66

67

68

69

70

71

72

73

74

r 27 -

Table 5 (Continued)

Sample

Date

Bin so

3

Si0_

2

a1 2°

3

MgO 7 -Day AutoStr. clave

A.P.F

3/25-26/53 S-4-14 . 1,3 22.8 5.4 4.2 1850 .24 3530

3560

3/27-28/53 s-5-19 1.4 22.7 5.1 3.9 2020 .21 3440

3360

3/30-31/53 S-l-16 1.7 22.4 5.2 4.1 I960 .20 3330

3440

364°

3270

4/8-9/53 S-3-17 1.7 22.5 5.2 4.0 1970 .20

4/2-3/53 S-2-13 1.7 22.4 5.2 3.9 2090 .21 3460

3420

3570

3590

3670

3380

4/13-14/53 s-4-15 1.4 22.3 5.0 4.3 2160 .34

4/15-16/53 S-5-20 2.3 21.9 5.1 4.1 2370 .25

4/17-18/53 s-1-17 2,0 22.2 5.2 4.1 2310 .27 4030

3410

4/27-28/53 Sr2-14 1.9 22.2 5.0 4.0 2390 .21 3280

3510

5/1-2/53 S-4-16 1.7 22.1 5.0 3.9 2630 .20 3520

3530

5/5-6/53 s -5,-21 1.6 22,3 5-2 4.3 2480 .29 3690

3720

4/29-30/53 s-3-18 1.3 21.9 5.0 4.1 2240 .23 3650

3750

3480

3820

5/8-9/53 s-1-18 1.5 22.2 5.0 4.2 2770 .28
- 28 -

Table 6

CALCULATION OF F AND I FOR INDIVIDUALS

so

3

SiO^ AI2O3 MgO

Autoclave7-Day

Strength

A.P.P.

*1 0.7 0.8 0.6 0.6 0.15 640 990 Jo r2

o.5 o,9 0.7 0.9 0.07 750 380

r

3

o.7 1.0 1.2 1.5 0.20 1210 710

4

r

h

0.6 0.7 0.6 0*6 0.15 680 620

2 r i=l** 2.5 3.4 3*1 3,6 0.57 3280 2700

?

1 0,625 0.850 0.775 0.900 0.1425 820 675

0.7025? 0.439 0.597 0.544 0.632 0.100 576.0 474.2

Max , Spec* . 2.0 6.0 5*0 0.5

Min. Spec. — 21.0 1500 3000

F . 1.6 21.6 5*5 4*4 0.40 2080 3470

I 1.1 22.2 4.9 3*7 0.30 2650 3950

0.4 0.7 0.6 1.0 0.10 720 700

A 0.7 0.4 0.3 0.8 0.06 600 1380

r

7 0.9 0.8 0.7 1.1 0.10 660 410

r L 8

d

2 r. i=5 1

0.7 0.6 0.9 0.8 0.12 810 320

2.7 2.5

* 2.5 3*7 0,38 2790 2710

r

2 0.675 0.625 0.625 0.925 0.095 697.5 677.5

Ratio of r's

F

I

1.08 1.36 1.24 I.03 1.50

0.43

0*37

1.18 1.00
TEST

RESULTS

FOR

S0o

COMPOSITES

A

cireied

dot, @,

Indicates a

sampling

order,

TEST

RESULTS

FOR

AUTOCLAVE

COMPOSITES

—r~nn

i T^

i

|

1

1 |

1 1 1

1 |

1 1 1 1 |1 1 1 9

i

1

1

i 9

l i

1

1 9

1

1

l

i 9 _

l

1

i

i 9 _

i i i 9 _

i

1

1 9

i

1

1 9 _

1

1

i

i 9 _

1

1

1

J

• _

i

i 1 • _

1

1

1

1

1

1

i

i •

1 1

| •

i i 9 _

i

l •

i

1

1 ©

_

l

i • _

i

l •

i

i

!

9 ©

1

i

i ©

1

1

i

i •

m

;

1

1 i 9 _

1

1

1

|

a>

1

1

! *

1

1 i © „

1 ! 9

_

i 1 6 _

1 1 e

i

i

i

i

© A

1

1

] ©

1

|

! © _

1 t « _

i

i

1

1 © —

i

i

1

|

0

1 i

1

i ©

-J Lu i L-i_i

i i.i j. B I 1 i.t; t 1 . 8

81

<_ .._t

$

A

circled

dot, @

,

indicates

a

sampling

order.

Bin

Humber

RESULTS

FOR

SEVEN

DAT

COMPRESSIVE

STRENGTH —

COMPOSITES

A

circled

dot, ©,

indicates a

sampling

order.

Figure h

RANGE CHARTS — COMPOSITES

Percent SO^ 1.0

0.77

(Ranges for groups of 1* tests each)

control limit

•

• ®

• 0

« « © •

© • ©

© ® • ®

0.5

0.0 1 5

R-^ = 0.3375

Percent autoclave expansion

1.5

Group 13 K

2 = 0.3250

17

1.26

1.0

0.5

0.0

_ • control limit

- •

© • •

• • •

- © •

• « «> « •

»

' •

9 _l 1 L__J J O 1 1 Ill'll J __l .J 1 5

Rj = 0.0550

7-day strength (pounds) 1000 r- 02^ co^:ro]^liait_

500 _ • *

Group 13 Rg= 0.06125

17

® 0

1 5 £j= 361 Group 13 R

2= 375

17

TEST

RESULTS

FOR

SEVEN

DAT

COMPRESSIVE

STRENGTH

-

INDIVIDUALS

8mCM 8

O

CM 8

in o

oo

8 8O

CM 8

in

8

Om

o

-=r

A

circled

dot,

®

,

indicates

a

sampling

order.

Bin

Number

No

sample

was

available

for

Bin

No.

51.

Figure 6

RANQE CHART FOR 7-DAT STRENGTH-INDIVIDUALS

(Ranges for groups of U tests each )

R

2 = L71.25

THE NATIONAL BUREAU OF STANDARDS

Functions and Activities

The functions of the National Bureau of Standards are set forth in the Act of Congress, March

3, 1901, as amended by Congress in Public Law 619, 1950. These include the development and

maintenance of the national standards of measurement and the provision of means and methods

for making measurements consistent with these standards; the determination of physical constants and properties of materials; the development of methods and instruments for testing materials,

devices, and structures; advisory services to Government Agencies on scientific and technical

problems; invention and development of devices to serve special needs of the Government; and the

development of standard practices, codes, and specifications. The work includes basic and applied

research, development, engineering, instrumentation, testing, evaluation, calibration services, and

various consultation and information services. A major portion of the Bureau’s work is performed

for other Government Agencies, particularly the Department of Defense and the Atomic Energy

Commission. The scope of activities is suggested by the listing of divisions and sections on the

inside of the front cover.

Reports and Publications

The results of the Bureau’s work take the form of either actual equipment and devices or published papers and reports. Reports are issued to the sponsoring agency of a particular project or program. Published papers appear either in the Bureau’s own series of publications or in the

journals of professional and scientific societies. The Bureau itself publishes three monthly periodicals, available from the Government Printing Office: The Journal of Research, which presents

complete papers reporting technical investigations; the Technical News Bulletin, which presents

summary and preliminary reports on work in progress; and Basic Radio Propagation Predictions,

which provides data for determining the best frequencies to use for radio communications throughout

the world. There are also five series of nonperiodical publications: The Applied Mathematics

Series, Circulars, Handbooks, Building Materials and Structures Reports, and Miscellaneous

Publications.

Information on the Bureau’s publications can be found in NBS Circular 460, Publications of

the National Bureau of Standards ($1.00). Information on calibration services and fees can be

found in NBS Circular 483, Testing by the National Bureau of Standards (25 cents). Both are

available from the Government Printing Office. Inquiries regarding the Bureau’s reports and

publications should be addressed to the Office of Scientific Publications, National Bureau of Standards, Washington 25, D. C.