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Sampling inspection plans and operating characteristics for concrete
Blaut, H.; National Research Council of Canada. Division of Building
Research
FOR SCIENTIFIC AND TECHNICAL
INFORMATION
DE L'INFORMATION SCIENTIFIQlIE
ET TECH NIQlI E
NRC I CNR TT - 1863 TECHNICAL TRANSLATION TRADUCTION TECHNIQUE H. BLAUTSAMPLING INSPECTION PLANS AN D OPERATING
CHARACTERISTICS FOR CONCRETE
DEUTSCHER AUSSCHUSS FOR STAHLBETON (233): 1 - 35. 1973
TRANSLATED BY / TRADUCTION DE ROBERT SERRE
THIS IS THE TWO HUNDRED AND TWENTY-THIRD IN THE SERIES OF TRANSLATIONS PREPARED FOR THE DIVISION OF BUILDING RESEARCH
TRADUCTION NUMERO ZZ3 DE LA SERlE PREPAREE POUR LA DIVISION DES RECHERCHES EN BATIMENT
OTTAWA 1976
1+
National Research Council Canada Conseil national de recherches CanadaStatistical interpretation of tests on concrete is commonplace today and
is explicit or implicit in the requirements of many codes and standards. Some
of these requirements are not fully rational insofar as they do not consider
both the consumer's risk and the producer's risk. The concept of the "operating
characteristic" is not new to statistical theory, but has not generally been
applied to concrete. This translated paper discusses the subject thoroughly and
makes proposals for improved methods of assessing the results of concrete tests.
The Division wishes to record its thanks to Mr. Robert Serre of the
Translation Services, CISTI, who translated this paper and to Mr. W.G. Plewes of DBR for reviewing the manuscript.
Ottawa
June
1976
C.B. Crawford, Director,
TECHNICAL TRANSLATION TRADUCTION TECHNIQUE 1863 Title/Titre: Author/Auteur: Reference/Reference: Trans1ator/Traducteur:
Sampling inspection plans and operating characteristics for concrete
(Stichprobenprufp1ane und Annahmekenn1inien fur Beton)
H. B1aut
Deutscher Ausschuss fur Stah1beton, (233): 1-35, 1973
Robert Serre, Translation Services/Service de traduction
Canada Institute for Scientific and Technical Information Institut canadien de l'information scientifique et technique Ottawa, Canada KlA OS2
Foreword
The new German standards DIN 1045 and DIN 1084 were the first reinforced concrete standards to introduce the statistical approach to describe and
evaluate experimental results and to define concrete strength. The term
"operating characteristic" was also used for the first time in DIN 1084. These
concepts are still unfamiliar to the civil engineer. It was therefore desirable
to report on the subject in the language of civil engineers, and to point out
possible applications. As a result, the present study was carried out on
behalf of the German Committee for Reinforced Concrete.
Sincere thanks are extended to Professor B. Wed1er, chairman of the DAfSt,
for supporting the present study. Thanks are also extended to the members of
the responsible group: Prof. G. Rehm, Dr. -Ing. J. Bonze1 and Dipl. -Ing.
R. Rackwitz have contributed by their criticism and encouragement to the success
of this study. The author also wishes to express his gratitude to Dr. T.
Deut1er of the Aachen Technical University for carrying out the extensive
simulation calculations on an EDP unit to determine the operating characteristics for the test specifications in accordance with the new DIN 1045.
Although the term operating characteristic can readily be explained, its meaningful application to a particular field, such as concrete construction,
involves a learning and rethinking process requiring some time and effort. In
fact, the new terms, aids and procedures do not exempt the civil engineer from
making decisions. They are simply shifted to another, higher level, at which
these decisions hold true for a wider range of phenomena.
It is hoped that the present study will contribute to a better understanding . of the necessary new test specifications in the reinforced concrete standards,
for the process of industrialization in the construction industry can no longer tolerate delays in the application of these inspection and evaluation procedures, which have been used successfully for years in the stationary engineering
industry.
TABLE OF CONTENTS
1. Introduction and General Survey 6
2. The terms "Sampling Inspection Plan" and "Operating Characteristic"
and Their Application 7
2.1 General 7
2.2 Test specification and operating characteristic for inspection
by attributes 9
2.3 Test specification and operating characteristic for inspection
by variables 10
2.4 The double probability paper according to Stange 12
2.5 The nomographs of Wilrich 15
2.6 The producer's risk and the consumer's risk 15
2. 7 Existing inspection plans with accompanying operating
characteristics 17
3. Sampling Inspection Plans and Operating Characteristics for
Concrete 17
29
3.1 General 17
3.2 Operating characteristics for test specifications according to German reinforced concrete standards DIN 1045 and DIN 1048
and DIN 1084 20
3.2.1 Operating characteristics for the test specifications
according to DIN 1045 (old) and DIN 1048 (old) 20
3.2.2 Operating characteristics for the test specifications
according to DIN 1045 (new) and DIN 1084 24
3.2.3 A comparison of the test specifications in the German reinforced concrete standards using their operating
characteristics 28
3.3 Operating characteristics for the test specifications in foreign standards
3.4 The producer's risk and the consumer's risk in the case of concrete
3.5 The use of previous information in assessing concrete 3.5.1 General
3.5.2 A proposal for the use of previous information 3.5.3 Examples 30 33 33 33 34
3.5.4 Critical discussion of the proposed procedure 4. Summary and Outlook
5. References
Appendix 1: Selected Definitions Appendix 2: Notation
Appendix 3: Calculating an operating characteristic for inspection by attributes by means of the binomial distribution Figures 37 38 41 42 48 50 52
1. Introduction and General Survey
The modern methods of statistical quality control are finding their way into the construction industry, because in the midst of ever-increasing specialization they provide an objective description of quality.
As in the mass production industry, it is possible to speak of mass-produced articles in the concrete construction industry, in view of the fact that each concrete structure involves many individual concrete mixtures, which should be identical so as to provide a uniform product whose properties correspond to the assumptions of statistical calculations.
The most important property of concrete, its compressive strength, can
only be determined through destruction. For both economic and technical reasons,
then, it is necessary to work with samples.
During the past three decades methods of statistical quality control have been developed and applied with great success to electrical engineering, textiles and the paper, oil and steel industries, and can therefore also be applied to
the concrete construction industry. They should at least be used in formulating
standards to describe reality, though they are also very appropriate for the practical work of assessing concrete.
The present study deals with the use of the aids "sampling inspection plan" and "operating characteristic" in the field of concrete.
There is at present a need to integrate the research results from various
fields. It is no longer sufficient to provide new knowledge; what is needed
most of all is to make this knowledge accessible to a wider circle of specialists in a form and language which they can understand without too much time and
effort.
In Section 2 which follows, the terms "sampling inspection plan" and "operating characteristic" known in other industries making use of statistical quality control are explained to the civil engineer, and illustrated by examples. The main part of the present study, the application of these concepts to concrete, is found in Section 3, in which the quality requirements of the new concrete
standards DIN 1045 and DIN 1084 are discussed.
contains a list of references on this new aspect of civil engineering. The
most important terms and the notation used are described in two appendices. A
third appendix provides, as an example, a detailed calculation of an operating characteristic for inspection by attributes using the binomial distribution.
In view of the mediating role of this study, a generally understandable description of relationships was preferred in most cases to a set of detailed
and abstract mathematical deductions. Readers interested in the underlying
mathematical and statistical principles will find useful references in Section 5.
2. The Terms "Sampling Inspection Plan" and "Operating Characteristic" and Their Application
2.1 General
When purchasing goods, the consumer checks whether they have the agreed
properties. For small lots it is not difficult to check every item. As a rule,
however, lots are so large that it is necessary to make use of samples. Sampling theory makes it possible to draw conclusions, from the results
of one sample, about the expected results for an entire lot. Such conclusions
are not without error, but are only meant as an assignable confidence coefficient.
Example: The unknown mean value of a normally distributed population with
a standard deviation
a
lies, with 90% probability, i.e., in 90% of all caseson the average after many investigations, between the limits
a
x - 1.65 • Vii and x + 1.65 • Viia
where x is the mean of a sample of size n taken at random from the population. In using a sample, then, there is a certain unavoidable, but assignable "uncertainty", which involves of course a risk, namely, the risk that in 10% of all cases the desired mean will not fall within the given boundaries.
The presence of "uncertainties", Le., randomly fluctuating (stochastic) magnitudes as opposed to the clearly defined (determined) magnitudes of classical
of the
statistical approach,
which can no longer be excluded from quality control in all fields of technology.Samples, then, always provide "uncertain" statements, but this "uncertainty"
is assignable. Using operating characteristics, it is possible to compare
objectively the varying "uncertainty" of different samples, and to indicate quantitatively and again compare the risk involved in each case.
The exact description of a sampling, with an evaluation and a comparison
of required values, is called a sampling inspection plan. For each sampling
inspection plan it is possible to determine an operating characteristic
(DC).
The two next sections provide examples of this.
There are basically two types of inspection: inspection by attributes and
inspection by variables.
In the case of
inspection by attributes,
the quality of a specimen isestablished on the basis of which of two mutually exclusive classes it belongs to: "defective" or "not defective" and/or "accepted" or "not accepted".
Example: Flagstones are produced for a concrete structure. Their quality
is partly checked by determining whether their surface corresponds to an existing
standard (sharp edges, no porous spots). Each stone can then be classified as
"defective" or "not defective".
In the case of
inspection by variables,
the result of the inspection ofeach specimen is expressed as a statistic, which is then compared with a required value.
Example: The strength of concrete flagstones is assessed in terms of
bending strength. For each stone tested the bending strength is recorded in. a
breaking test and given in kgf/cm2, for example. The frequency distribution of
the sample values leads to a statement, based on sampling theory, about the distribution of the values for the population, i.e., the lot from which the sample was taken.
If only the admissible load were applied in the test, and if it were determined whether or not the individual stone supported the load, we would have inspection by attributes.
2.2 Test specification and operating characteristic for inspection by attributes Test specifications for inspection by attributes contain the following data: - sample size n;
- admissible number of defective items in the sample (acceptance number c); - method of taking a sample from the lot to be inspected.
Example: A sample of size n
=
50 is taken at random from a supply of 5,000clamp nuts and compared with a prototype for surface texture.
If i = 0, 1 or 2 defective items are found, the supply is accepted.
If i 3 or more defective items are found, the sample is rejected.
If in an individual case two defective items are found in the sample, this
result still s2ys nothing about the quality of the supply. We know only that
4% (2 out of 50) of the sample was defective. This by no means indicates that
4% of the supply is also defective. Further details and definitions are needed
to provide rational conclusions in view of the uncertainty.
We therefore reason as follows: A lot may effectively contain 5% rejects.
A great many samples of size n = 50 are taken at random from this lot. It is
then possible to check how many samples meet the above test specification, i.e.,
how many are accepted or rejected according to the test specification. The
result of this mental experiment can be predetermined using the theory of probability.
It is possible, in fact, to calculate the probability of finding 0, 1 or 2
defective items (the acceptance condition in our example) in samples of size
n = 50 if these samples are taken from a population whose number of rejects is
known (e.g., 5%). If this probability theory calculation is carried out for
various assumed per cent defectives p (see Appendix 3), and the results plotted
graphically, we have curve a shown in Figure 2.01. It is called the operating
characteristic (OC) curve of the test specification. From it can be inferred
how "precise" the test specification is, Le., the probability that lots which effectively contain 5% rejects, for example, will be accepted or rejected by
this test specification. It says, in other words, that lots with 5% rejects or
less are accepted in 53% or more of all cases. Lots with 10% or more rejects
are rejected in 88% or more of all cases.
which would have an operating characteristic in accordance with curve b in
Figure 2.01: all lots having 5% or less rejects would be accepted 100%; lots
having more than 5% rejects would be rejected 100%. If this were to be achieved.
it would be necessary to inspect every lot 100%. which would be economically
unacceptable. The inevitable recourse to sampling inspection is the reason for
a certain "imprecision" in all test specifications based on samples. The slope
of the operating characteristic is a measure of this imprecision: inspection
procedures with steep operating characteristics are "more precise" than those with flat operating characteristics.
Figure 2.02 shows the operating characteristics of various test specifications
using single samples. As the sample size n increases. the operating characteristics
become steeper.
In addition to the single sampling procedures already mentioned. there are
also test specifications based on the results of two consecutive samples. Here
the clearly good or bad lots are determined with little effort for the first
sample, so that a second sample is required only for the doubtful lots. Figure
2.03 is a schematic block diagram showing the test specification of a double plan.
Similarly, multiple plans and sampling systems using successive inspections and decisions (sequential plans) may be set up and used in the inspection of lots.
In the latter case, only one item is taken and inspected at a time. Depending
on the result, the lot is accepted, rejected or further tested. In this case,
the size of the sample needed for a valid decision is itself a random number.
and is not known beforehand. On the whole, however, the number of samples
required is smaller on the average than for the single or double sample. Figure
2.04 illustrates a graphic evaluation using a sequential plan (according to Reference 1).
2.3 Test specification and operating characteristic for inspection by variables
Inspection by variables provides more information than inspection by attributes, as the following example clearly shows.
Checking the diameter of bolts with a snap gauge only indicates how many bolts have a smaller or greater diameter than the required value on the gauge. If, on the other hand, the diameter of each bolt is measured with a vernier
caliper, the distance of each diameter from the required value is also known. In practice, this means that for an equal confidence coefficient, the sample
for inspection by variables can be smaller than that for inspection by attributes. Inspection by variables therefore gains in importance wherever the cost of
specimens is high, as is the case in concrete construction.
The test specification for an inspection by variables may read as follows:
1. Take a sample of size n from the lot to be inspected.
2. Determine the test size z = x - k • 0.
3. Compare the test size with the required value SwN.
If z ｾ SwN ｾ accept the lot.
If z < SwN ｾ reject the lot.
In the above, x is the mean value of the sample and 0 is the standard
deviation of the population; k is the acceptance factor, which is taken from the accompanying operating characteristic as a function of the admissible per cent defective p and of the sample size n.
Of course it is also possible, for this test specification, to determine
and plot an accompanying operating characteristic. Here too it can be asked
how great the probability is that a lot will be accepted according to the above
specification (item 3), if it contains 5% rejects, for example. If these
probabilities of acceptance are plotted over the accompanying per cent defectives, the result is an operating characteristic as in Figure 2.06.
An example of the determination of an operating characteristic for inspection by variables
It is assumed that the features x to be checked are normally distributed
with a mean ｾ and a standard deviation 0. Then the test size zi = xi - k • 0
determined from a large number of lots is also normally distributed with the
mean ｾ
=
ｾ-
k • 0 and the standard deviation 02=
0/1n.
Figure 2.05 showsthe distribution of features x and below them (on the same abscissa scale) the
distribution of the test size z. The tolerance limit T =
S
N is also plottedun w
in such a way that p% of the x values fall below T •
un
Figure 2.05 indicates the following: a lot with p% rejects "provides" in
W% of all cases a test size z which is greater than SwN' so that this lot,
in 1 - W% of all cases.
For a different per cent defective, Figure 2.05 gives a correspondingly
different probability of acceptance W. If the probabilities of acceptance
determined in this way are plotted over the per cent defective p for different values of p, the result is the entire operating characteristic.
Figure 2.06 shows three operating characteristics calculated in this way
for k
=
1.65 and n=
10, 15 and 30.2.4 The double probability paper according to Stange
Determining and plotting operating characteristics for inspection by variables can be simplified significantly using the double probability paper
according to Stange(2). According to his notation, both the abscissa and the
ordinate represent a division in accordance with the summation curve of the normal distribution (Figure 2.07).
The probability of acceptance Wis plotted in % along the ordinate, and
the per cent defective p along the abscissa, the latter being related to the At the upper edge of the grid a second scale was plotted tolerance limit T
un
for the abscissa, the acceptance constant k. It corresponds to the standardized
value u = (T - ｾＩＯ｡ associated to the lower scale.
un
A division of functions for n
=
u2 was plotted as a second scale along thew
ordinate, where u is the standardized value corresponding to the W scale.
w
Finally, the division of functions n
=
(2u )2 was plotted on the right side tow provide a large domain for n.
In the form described, the double probability paper is suitable to represent
operating characteristics when the standard deviation of the lot is known. For
operating characteristics where the standard deviation is not known, the upper section of the double probability paper contains an auxiliary curve related to k for the value
The details concerning the mathematical derivation and foundation of the double probability paper will not be dealt with here; the reader is referred to
the work done by Stange(2). The following example illustrates the application of the double probability paper to concrete construction.
Example:
Concerning a supply of concrete, it was agreed that it would be acceptable if the portion of the compressive strength results below the nominal quality
B
WN = 350 kgf/cm 2, the "rejects", were p < PI = 1.9% (even 2%). The lot is no
longer acceptable if the rejects are p > P2 = 11%. The probability of acceptance
WI for good lots should have a value of at least WI = 1 - a = 95%, and the
probability of acceptance W2 for bad lots should have a value of W2 =
B
= 5% atthe most. It is known from previous experience that the standard deviation of
the concrete producer is a = 50 kgf/cm 2, and that the strength values are normally
distributed.
With the above data, the inspection plan and the operating characteristic can be determined graphically as follows (Figure 2.07):
Through points PI (PI
=
1.9%; WI=
1 - a=
95%) and P2 (P2=
11%; W2= B =
5%)can be drawn a straight line which intersects the abscissa at point A. This
straight line is the operating characteristic.
Along the operating characteristic we have for W
=
50% the acceptancefactor k = 1.65 at the upper edge. At the lower edge the line segment 1 (unit
of the upper k division) is drawn leftwards from A. This gives us point C.
The ordinate of intersection point B of the operating characteristic with the
vertical in C yields n = 15 on the left side. We thus find the parameters of the
inspection plan. The test specification now reads:
1. Take n = 15 samples (cube specimens) at random from the concrete lot.
2. Determine the compressive strength of the n = 15 cube specimens, and
calculate the mean
x
of the samples (e.g., 452, 390,419,440, 346, 395,460, 438, 478, 377, 462, 431, 518, 496, 451; x 437 kgf/cm 2).
3. Calculate the test size z
=
x - k •a
(e.g., z=
437 - 1.65 • 50=
354 kgf/cm 2).4. If the test size z ｾ
B
wN' accept the lot; z <
B
wN' reject the lot.(For example: z = 354 >
B
WN = 350 ｾ accept.)
The sample does contain 1 reject (6.7%). However, the "additional information"
about the pattern and about the standard deviation of the strength distribution makes it possible to accept the lot on the basis of this inspection.
It is of course possible for given nand k, i.e., for an existing inspection plan, to determine the accompanying operating characteristic graphically as
follows:
The point of intersection W= 50% and k yields one point of the operating
characteristic. Its slope is obtained from triangle C'A'B' plotted in Figure
2.07 with the base "1" and the height n
=
15. The parallel line through thepoint (W = 50%; k) yields the desired operating characteristic, from which the
required probabilities of acceptance can be read.
If the standard deviation is not known from previous experience, the
standard deviation s of the sample can be used as an estimated value for 0.
This lack of "additional information" must be compensated for by a larger sample
size. We then proceed as follows:
The base of the reading triangle in the double probability paper is no longer "1" but b (b > 1). The line segment b/2 is read from the auxiliary
curve with the help of k (Figure 2.07). The larger reading triangle AFE
necessarily yields a greater n (in the example: n = 35).
s
If the left division is not sufficient for n, n can be read from the right division, using the reading triangle AGH with the base b/2.
Determining the operating characteristic from given nand k is done in a similar way with the larger reading triangle D'F'E' in the lower left corner of the double probability paper.
If, in the above example, the sample size were
not
increased for an unknownstandard deviation of the population, but remained n
=
15, the result would bes
a more level operating characteristic through the point W
=
50%; k=
1.65(Figure 2.08). Its direction is parallel to the side KL of the reading triangle
KML in the lower left corner of Figure 2.08. The right side of the operating
characteristic then shows reject levels. To avoid this, it is necessary to
shift the operating characteristic, kept parallel, to the left until it again
goes through P2. However, this increases the acceptance constant k to k'
=
1.89,and this adds precision to the inspection plan. Moreover, as k increases, the
base of the reading triangle also increases from b to b'. As a result the sample
size is increased to n
=
18. Consequently, by further turning the operatings
and "sighting". This can be avoided by using the nomographs of Wilrich (Section 2.5).
This example has made it clear that the inspection plan and operating characteristic can be adapted, in the double probability paper, to definite demands with respect to the probabilities of acceptance and/or the constants nand k.
2.5 The nomographs of Wilrich
Another tool for easier handling of the sampling inspection plan and
operating characteristic was recently published by Wilrich(4). His paper deals
with nomographs, which provide an outline of the relations between n, k, WI,
W2, PI, P2 for
(x;
a) sampling plans and for(x;
s) sampling plans; i.e., forknown and unknown standard deviations of the population. The nomographs make
it possible to plot point by point in a normal grid the operating characteristic given by 4 parameters.
Figure 2.09 illustrates, as an example, the nomograph used to determine
(x;
a) sampling plans and the accompanying operating characteristics. Theoperating characteristic for the
(x;
a) sampling plan according to Section 2.4was determined and plotted point by point using the nomograph with n = 15 and
a
k
=
1.65 in Figure 2.06.It is possible, of course, to combine the nomograph with the double prob-ability paper and, using two points of the operating characteristic taken from
the nomograph, to plot this DC curve as a straight line in the double probability
paper.
2.6 The producer's risk and the consumer's risk
In Section 2.2 and in Figure 2.01 it was seen that the transition from 100% inspection to sampling inspection introduces a degree of "uncertainty" in
all test specifications. This "uncertainty" has a particular meaning for the
producer and for the consumer of a lot. According to Figure 2.07, for example,
the producer runs the risk that lots with a proper per cent defective of PI = 2%,
i.e., "good" lots, will be rejected in 5% of all cases. His risk is therefore
sampling plan lots having a per cent defective of P2 = 11%, which is no longer
suitable, will nevertheless be accepted in 5% of all cases. The consumer's
risk is therefore
S
= 5%. Values of 1 - 10% have been recorded for a andS.
The two risks can be determined as follows:
By means of suitable facilities and measures, the producer tries to ensure
that his output only contains p = 2% defectives. In the case of an inspection
using the above sampling plan, it is possible that in a% of all cases a good
lot will nevertheless be rejected. The same occurs for the consumer who,
because of the "uncertainty" of the sampling inspection plan, must accept lots
having too high a per cent defective. Since, as a rule, the consumer determines
what he wants, the producer finds it necessary to offset the uncertainty of the inspection plan by means of a definite production policy, or to bear the risk of rejection.
The significance of these relationships for the concrete construction industry is described in greater detail in Section 3.4.
There is yet another very practical interpretation of the relationship between the "uncertainty" of the inspection plan, as expressed in the slope
of the operating characteristic, and the risks for the producer and the consumer. It is possible to choose as reference point a per cent defective which is
accepted or rejected in 50% of all cases. This is called the point of control
Po (Figure 2.07).
Lots with defectives exceeding the point of control p are rejected to an
o
"increasing degree", whereas lots with less defectives than p are accepted to
o an i1increasing degree".
The point of control Po is a compromise, so to speak, between the wishes
of producer and consumer. Both partners agree about a definite per cent defective
and also about the "uncertainty", which is revealed through verification using a sample, and which is expressed in the slope of the OC curve.
As a rule, such an agreement assumes that the producer maintains good factory control, so that only accidental dispersions occur with no large systematic shifts in the mean value.
2. 7 Existing inspection plans with accompanying operating characteristics Only during and since World War II have sampling inspection plans been used in Anglo-Saxon countries, especially by the military administration of the
United States, for the inspection of supply lots. In the process, plans were
developed for
inspeotion by attributes;
these were published. together withinstructions for their use and the corresponding operating characteristics, and
during the next two decades they were expanded and revised(6,7). Large industrial
. (5 8) (6)
fi rms (e.g., Philips) also developed sampling systems ' • ABC Standard 105
is the inspection plan best known internationally, and is used very often; it was developed in 1963 by specialists from the United States, Great Britain and
Canada as a substitute for MIL-STD 105, used in the U.S. since 1950. In Germany
there are the ASQ sampling tables for attributes inspection(9); these were
adapted to the ABC Standard. Figure 2.10 shows an excerpt from the ASQ sampling
tables.
The best known plans for
variables inspeotion
are Military Standard 414,issued by the U.S. Defense Department in 1957(10). In this field, large
industrial firms in the Anglo-Saxon countries and in Holland have also prepared (5 11)
their own inspection plans ' • In Germany there appeared in 1960 a publication
by K. Stange entitled "Aufstellung und Handhabung von Stichprobenplanen fur
messende Prufung mit Hilfe des doppelten Wahrscheinlichkeitsnetzes" (3) • This
work was later issued as ASQ/AWF publication No. 5 entitled "Stichprobenplane
.. .. (2)
fur messende Prufung" . Contrary to all other references on the subject, this
work can be used to set up sampling inspection plans in a simple way and "made
to order" (cf. Section 2.4). Wilrich(4) achieved the same goal by means of
nomographs (cf. Section 2.5).
3. Sampling Inspection Plans and Operating Characteristics for Concrete
3.1 General
Quality control conditions in the concrete construction industry are not as simple as those in other industries such as the steel industry, machine
building and the mass production industry. Concrete construction, as a rule,
large quantities and can be inspected as a part or lot. Only in the figurative sense can the concepts of quality control used in the industries mentioned be applied to concrete construction.
Concrete is produced as small, fresh batches in a mixer, placed in forms
on the site or in prefabricated units, and compacted. Following the chemical
process of hardening, which is a function of time, temperature and humidity, the concrete has the desired properties, particularly in terms of compressive strength. If the latter is to be determined for the completed structure, this structure
or parts of it must be destroyed. Compressive strength has been determined and
continues to be determined in terms of a standard test specimen, e.g., a cube
with an edge length of 20 cm. Such a cube is kept 28 days at 18 - 22°C, i.e.,
7 days damp and the rest exposed to air.
There are also nondestructive testing procedures, such as those using
ultrasonics or recoil hammers. These procedures, however, do not measure
compressive strength directly, but through other properties of the concrete more or less related to compressive strength.
Test specimens are therefore the principal means of quality control. Their
number is not large since they are too expensive to produce. There is also a
disadvantage in that they are tested only after 28 days, so that the results
only serve to confirm the planned strength. A more constant control of
compres-sive strength in the production of concrete can be achieved with cube results only for mass concrete at long-term construction sites.
The methods of statistical quality control would therefore be used above
all for the results of cube testing. If useful conclusions are to be drawn,
the number of samples must be of the order of 30, making it possible to calculate the mean and standard deviation of an unknown strength distribution with sufficient accuracy for concrete construction(12,13).
In concrete construction as in other industries, the standard deviation for a given lot can be assumed to be known and practically constant; in any case,
an upper bound can be specified for it (e.g., the 95% fractile). About 10
samples would then be enough to determine with sufficient accuracy the unknown mean of the distribution.
be so chosen that the operating characteristic would meet the needs of the
consumer in terms of safety. Such an operating characteristic was used as the
basis of the statistical evaluation in DIN 1084, Sheets 1 - 3, Section 2.2.6.
The producer would rightfully object that this inspection plan is only based on cube testing information which is expensive and/or obtained late, and that it does not take into consideration the large, inexpensive amount of
existing information such as cement strength, w/c ratio, consistency and grading curve.
The use of statistical quality control on the basis of operating charac-teristics would therefore be greatly promoted if it were possible to include, for the required number of samples, not only the expensive results of cube testing, but also the more easily obtained previous information.
Current findings in concrete technology, together with numerous tests and observations, make it possible to estimate the expected strength from the
composition of the fresh concrete. The cement and aggregate components can be
monitored by controlling the scales. The water admixture, on the other hand,
is a function of the grading curve, the required consistency and the dampness
of the aggregates. It can only be determined by measuring aggregate moisture
and the extra water, or by directly measuring the water/cement ratio.
Measuring techniques already exist for this purpose (e.g., the Thaulow technique and the test for aggregate moisture).
The goal, then, is to evaluate the previous information in such a way that it provides, alone or with the results of cube testing, a sample which is
sufficiently large to produce, with the help of the operating characteristic, a reliable estimate of strength.
In the following sections the quality requirements set down in the reinforced concrete standards are presented and discussed in the form of operating
charac-teristics. Particular attention is given to the producer's risk and the
con-sumer's risk which can be derived from the operating characteristic, since this approach is completely new in the concrete construction industry, and requires
new agreements. Finally, a procedure is proposed whereby previous information
3.2 Operating characteristics for test specifications according to German reinforced concrete standards DIN 1045 and DIN 1048 and DIN 1084
Although a completely new edition of the German reinforced concrete
standards was published recently, it would be useful, first of all, to explain and discuss the operating characteristics for the test specifications and/or
quality requirements of the standard which was used previously. For engineers
working in concrete construction, it will be easier to make a first transition from the long familiar requirements to the new mode of representation, and then to make a further transition to the requirements of the new versions of standards DIN 1045 and DIN 1084.
3.2.1 Operating characteristics for the test specifications according to
DIN 1045 (old) and DIN 1048 (old)
The following excerpts from the old versions contain information about a test specification.
DIN 1045, Section 6, item 3 b)
"Testing during construction. When using concrete B 100, B 225 and B 300,
quality inspections as described in Part D must be carried out at all
times on the construction site. Rigidity must be determined simultaneously.
For this purpose the concrete shall be taken from its point of use. If a
suitability test is carried out (cf. item 3 a), the results of the quality test, including the rigidity test, shall be compared with the results of the suitability test.
"The inspections must be repeated whenever the conditions prevailing during
previous inspections have changed. As a rule, three test cubes must be
prepared for each 200 m3 of concrete. If concreting is done on a larger
scale and without interruption, three test cubes per 500 m3 of concrete
are sufficient. However, a minimum of three cubes must be tested for each
structure. Individual cubes having low strength values shall not be
re-jected if they are no more than 15 per cent below the required strength, and if the average compressive strength of the three test cubes of the same batch lies above the required strength.
means that the prescribed minimum strength is adhered to.
"See Section 13, item 1 for the investigations to be carried out prior to form stripping."
DIN 1048, Section 1, paragraph 3
"Concrete for tests during building construction (Part A, 6/3b and 5;
Part C, 6/3), must be sampled at the point of use. The sample shall
appear to correspond to the average condition of the concrete." Section 4, item 2
"Number. For the Suitability Test at least 3 cubes with 20 or 30 cm
edge-length shall be made for each age and each different composition of the concrete.
"The same number of cubes is recommended for each Quality Test. See Part
A 6/3b, paragraph 2 for repetition of the Quality Test.
"It is useful to make 4 or 6 cubes for the Hardening Test so that the Compression Test, should it prove unsatisfactory, may be repeated after further hardening of the concrete."
Section 8, item 6, paragraph 1
"The maximum load achieved is the ultimate load. The ultimate stress shall
be recorded to the nearest kg/cm2• The standard is the mean value of the
ultimate stress for cubes of the same batch."
A critical analysis of these test specifications from the point of view and using the concepts of statistical quality control, yields the following:
1. The concrete in a lot of at most 500 m3 is evaluated by means of a sample
of size n = 1, in fact, "the mean value of the ultimate stresses of the cubes
of the same batch" provides only one result for the strength of the concrete
in the mixture from which the usual three cubes were taken. Finding the
mean value simply decreases the effect of the dispersion of the testing procedure, and the effect of the inhomogeneity within the mixture.
2. Since "the sample shall appear to correspond to the average condition of the
concrete", the sample n = 1 does provide a sample mean value, which can be
considered as an estimated value for the mean strength of the concrete in the lot.
3. To find a mean value by examination, it is possible to imagine a fictitious sample of size nt, from which the observed "mean value" could have been determined, if the sample had been drawn at random from the lot according to statistical principles.
The fictitious sample size n t would thus be a measure of the precision with which the mean value of the population is estimated from the sample mean. The "better" the mean value is found by examination, the greater n t should be.
An operating characteristic for the quality requirements of DIN 1045 (old) can only be established indirectly, since the old standard mentions no per cent
defective, and the samples need not be drawn at random. Items 2 and 3 of the
foregoing analysis provide a starting point. This is illustrated below by an
example.
A few years ago, the author had the opportunity to carry out, at a large-scale construction site involving structural engineering, an extensive statistical
investigation of construction concrete. A test cube was to be prepared at
random, throughout the construction period, after each series of approximately
50 mixtures. This cube was to be stored according to standards, and subjected
to a pressure test after 28 days. Figure 3.01 shows the resulting distribution
of the number of mixtures between two samplings. The average span between two
samplings was about 78 mixtures, the most frequent value being 50 mixtures.
For the concrete of class B 300 in the reinforced concrete frame (about
20,000 m3 of concrete), there were n ; 353 individual strength results. In
terms of the precision requirements of the concrete construction industry, a
sample of this size can be considered as a population. Figure 3.02 shows the
frequency distribution, with a mean of ｾ ; 369 kgf/cm2; the standard deviation
was
a
;
48.6 kgf/cm2; the 5% fracti1e was 288 kgf/cm2• Since the statisticalevaluation of the strength results was stipulated by contract, it also replaced
the quality test according to the old standard. From the strength distribution
in question, however, it is possible to simulate the samplings according to the old standard, so as to provide a link between the old quality test and the statistical evaluation.
the mean value of a fictitious sample of size nl
=
6. This would mean that,
according to the old standard, a set of sample cubes from one mixture had been
prepared and tested, on the average, for each of 78 • 6 = 468 mixtures
(corresponding to about 350 m3 of concrete).
This process can be carried out for the distribution shown in Figure 3.02.
The distribution of the mean values from samples of size n = 6 from this
dis-tribution has a mean value ｾ
=
369, and a standard deviation a-=
48.6/16=
19.8.x From the equation
300 369 - u •
a-p x
we have for the statistical value u of the standardized normal distribution
p
u
p =
369 - 300
a-
x =..:..::.---=-
69 •48.616
= 3. 5From a normal distribution table we read for this a per cent defective
p
=
0.02%, i.e., the sample means will fall below the required value 300 inonly 0.02% of all cases, which is practically never. This means that this
concrete is distinctly a B 300 in terms of the old standard. This is also
shown by the mean value of 369 kgf/cm2, which is quite common for a well
super-vised B 300.
For an assumed fictitious sample size of nl
=
3, we have a below-par percent defective of p
=
0.7%; for nl=
2 we would have p
=
2.2%. This means,then, that in the present case (Figure 3.02), practically no shortcoming would be expected even if "finding a mean value by examination" were carried out so "poorly" that it would only correspond to a fictitious sample of size nl
= 2.
On the basis of the new standard, the old B 300 corresponds to a Bn 250.
The operating characteristic for the test specification of the old standard is
. therefore obtained, for a known standard deviation
a,
by approximation asshown in Figure 3.03 with n
=
6 and k=
1.65 from the double probability paper.A further argument for the accuracy of this approximation solution is
provided by the observation that for a target mean value of 360 kgf/cm2 the
standard deviation would be 67 kgf/cm2, which corresponds to normal accuracy in
3.2.2 Operating characteristics for the test specifications according to DIN 1045 (new)(17) and DIN 1084(18)
In defining concrete quality, the new standard introduced for the first
time the statistical approach: the nominal strength B
WN of a class of concrete
strength corresponds to the 5% fracti1e of the population of compressive
strengths. Thus the path is cleared for a simple application of the very
effective procedures of statistical quality control. This is especially true
of the statistical evaluation of test results provided in DIN 1084.
As for the quality requirements in DIN 1045 (new), Section 7.4.3.5.2, a traditional form was chosen, which is not easily grasped with the concepts and
notions of statistical quality control. This would be necessary, however, to
compare objectively the various quality requirements.
Section 7.4.3.5.2 reads as follows:
"The strength requirements are to be regarded as fulfilled if the average compressive strength of each series, each comprising three consecutive cubes, attains at least the values stated in Table 1, column 4, and the compressive strength of each individual cube attains at least the values stated in column 3.
"However, for concrete of the same composition and made in the same way,
one out of every 9 consecutive cubes may fall not more than 20% below
the values in Table 1, column 3; at the same time, the average value of any three consecutive cubes must at least attain the values in Table 1, column 4."
Using the concepts of statistical quality control, we have the following test specification A and B:
Test specification A (as per paragraph 1 of the standards)
1. Draw a sample of size
n
=
3(x!; X2; X3)3. Decision:
I f Z1
,
SwNand also Z2 ｾ SwN
and also Z3 ｾ SwN
and also Zit ｾ S + 50 (kgf / cm2)
wN then accept the lot. I f either Z1 < S wN or Z2 < S wN or Z3 < S wN or Zit < B + 50 (kgf/ cm2) wN then reject the lot.
Test specification B (as per paragraph 2 of the standards)
1. Draw from the test results occurring in temporal sequence a sample of 9
consecutive values;
2. Determine the following test sizes:
Zl
=
(Xl + X2 + x3)/3 Z2 (X2 + X3 + xIt)/3 Z3 (X3 + XIt + xs)/3 Zit=
(XIt + Xs + x6)/3 Zs (x , + X6 + x7)/3 Z6 (X6 + X7 + X8) / 3 Z7=
(X7 + X8 + x9)/3Z8 X (1, (the smallest of 9 values of the sample)
Z9 x (2) (the second smallest of 9 values of the sample)
3. Decision: If Zl ｾ S + 50 wN and also Z2 ｾ SwN + 50
...
and also Z7 ｾB
WN + 50 and also Z8 ｾ 0.8.
B
WN and also Z9 ｾB
WN then accept the lot.If either Zl < SwN + 50
or Z2 < SwN + 50
or Z7 < SwN + 50
or Zs < 0.8
.
SwNor Z9 < SwN
then reject the lot.
Deutler and Nowak(l9) have calculated the operating characteristics
corresponding to test specifications A and B. They started from the assumption
applicable to concrete that concrete strengths are normally distributed and
that the standard deviation of the population is known from previous observations. In the case of test specification A, the exact, theoretical solution yields an integration in three-dimensional space, and therefore a great deal of mathematical
calculations. In the case of test specification B, the exact solution meets
with practical, mathematical difficulties because of integration in the
multi-dimensional range. By means of electronic data processing, however, it is
possible to determine the operating characteristic for both test specifications
A and B with good approximation. The operating characteristics thus obtained
are given in Reference 19, where the compressive strength was chosen as abscissa,
and the corresponding probability of acceptance was chased as ordinate. The
ordinate is evenly subdivided from 0% to 100%. The operating characteristics
from Reference 19 were transferred to the double probability paper (Figures
3.04 and 3.05) for the standard deviations 0 = 40 - 50 - 70 (kgf/cm2) , and the
per cent defective p of the compressive strengths was plotted along the abscissa
(that part which lies below the nominal strength). Each of the points plotted
in Figures 3.04 and 3.05 was determined through 2,000 simulations. An equalizing
straight line can be drawn with the eye through these points. The operating
characteristics in Figures 3.04 and 3.05 hold true for all nominal strengths.
They are nevertheless a function of the standard deviation a of the population.
A deeper interpretation for this is that when test specifications A and B were
formulated, the difference SwS - SwN = 50 kgf/cm2 for all nominal strengths was
chosen as a constant and not as a function of the standard deviation
a
of thepopulation.
The determination of these operating characteristics brings out a basic
Z
B35
=
sB
15=
0
which an operating characteristic can only be determined through excessive
effort. Unfortunately, this was not kept in mind in the draft of DIN 1045.
Only with DIN 1084 was this requirement complied with. The wording of section
2.2.6 in DIN 1084(18) does take the form of an unambiguous test specification:
"2.2.6. It is permissible to depart from the provisions of DIN 1045,
section 7.4.3.5.2, with respect to the number of samples and the determin-ation of the results, if it was shown by statistical evaludetermin-ation, and if it is shown regularly for futher inspections, that the 5% fractile of the population of compressive strength results for concrete of approximately the same composition and preparation does not fall below the nominal
strength. Such proof, to be established through random samples, is deemed
valid if the following conditions are met on the basis of an operating characteristic2) :
a) when the standard deviation 0 of the population is not known
z
=
B35 -
1.64 • s ｾB
WN
b) when the standard deviation 0 of the population is known
z
=
B15 -
1.64 • 0 ｾB
wN' "In these equations,
test size;
mean of a random sample of size n
=
35;s
standard deviation of the sample, but at least 30 kgf/cm2;
mean of a random sample of size no = 15;
standard deviation of the population, which is known from at least
35 previous strength results; if this is not the case, 0
=
70 kgf/cm2can be used as an empirical value for the upper bound of the standard deviation;
B
WN=
nominal strength according to DIN 1045, Table 1, column 3."The strength values determined from water/cement ratios (cf. DIN 1045, Section 7.4.3.5.1) may be included in the statistical evaluation, whereby the mean value from two water/cement ratio determinations of the same batch are to be used in each case for the determination of a strength value3).
"Footnotes:
Hilfe von Annahmekennlinien. "beton", H. 7/8, Betonverlag, Dusseldorf 1969; in that paper the operating characteristic is determined as follows:
For a per cent defective of p
=
5% (k=
1.64), let the probability ofacceptance be W
=
50%; for p=
11% let W=
5%. In this manner the operatingcharacteristics for n = 35 and n = 15 are identical.
s c
3) K. Walz: Herstellung von Beton nach DIN 1045, Seite 53/54, Betonverlag,
Dusseldorf 1971."
The operating characteristic corresponding to the test specification in DIN 1084 is determined quickly and unambiguously with the acceptance factor k = 1.64, the sample size TIs 3S or ncr = 15 and the point of control p = 5%
(2) 0
in the double probability paper according to K. Stange (Figure 2.07).
3.2.3 A comparison of the test specifications in the German reinforced
concrete standards using their operating characteristics
For the sake of comparison, Figure 3.06 brings together the operating characteristics of the test specifications in the German reinforced concrete
standards in the double probability paper. In the case of test specifications
A and B according to DIN 1045 (new), the operating characteristics determined
for cr = 50 kgf/cm2 were plotted in each case with a continuous line, and the
two others with a broken line.
Such a comparison is an essential objective of this paper; it provides the following results:
1. As expected, DIN 1084 yields the most precise test specification.
2. The operating characteristics of DIN 1045 (old), determined by approximation,
and that of the test specification B according to DIN 1045 (new) come in second place.
3. Test specification A according to DIN 1045 (new) shows the least test
precision. The point of control Po lies at 12%. Lots with 20% rejects are
3.3 Operating characteristics for the test specifications in foreign standards
The methods of statistics and the statistical approach are already being used in the concrete standards of a few countries(20,2l,22) with respect to
definitions, and in test specifications as evidence of concrete strength. So
far, the OC curve used as a means of objectively representing and comparing test specifications has only been suggested and discussed in a few publications; it has not as yet been included in a standard.
As was revealed in an international inquiry by the CEB/CIB/FIP/RILEM Joint Committee in 1969-70, there is a great deal of diversity among the test specifi-cations of various countries with respect to
- classes of concrete, - types of sampling,
- methods of inspection, and - conditions of inspection.
The differences are still so great that it is at present impossible to establish operating characteristics for the test specifications of various
countries on a unified basis so that comparisons could be made. It would be
necessary to apply new methods here, and to formulate anew the test specifications in various countries on a common basis, in line with the recommendations of the
Joint Committee. This common basis would include
- the definition of concrete strength as a 5% fractile (characteristic strength) (20);
- the choice of a sampling inspection plan whose operating characteristic could be determined with reasonably little effort (for economic reasons, this will generally mean choosing a sampling plan for inspection by variables - variables inspection);
- the assessment of the sampling inspection plan by means of the operating characteristic.
The common basis by no means implies the adoption of uniform test
specifi-cations. It leaves much room for the individual formulation of test specifications
3.4 The producer's risk and the consumer's risk in the case of concrete
When using inspection by means of samples, producers and consumers run the risk of obtaining false information about the lots to be supplied or purchased. The producer runs the risk that good lots will be rejected under the sampling inspection plan; the consumer runs the risk that bad lots will be accepted under the sampling inspection plan.
The choice of these risks when establishing the operating characteristic or the sampling inspection plan is not a matter of statistics, but one of
agreement within the field concerned. It is here that the specific experience
of specialists enters the picture. At this point the objective technique of
statistical quality control can be adapted to the particular requirements of
a given situation. This shows once more that modern techniques, while they
make decisions easier for the engineer, by no means exempt him from the
decision-making process itself. The question is to come to grips with the possibilities
which the new "working" operating characteristic represents for the concrete construction industry.
In concrete construction, the consumer's risk is determined through the
required safety during measurement. On the basis of extensive theoretical
. . . R k ' (23) h d h I ' h . f 30% .
lnvestlgatlons, ac Wltz s owe t at ots Wlt a maXlmum 0 0 reJects
should be accepted in 2% of all cases at the most. This establishes one point
of the operating characteristic. By choosing as a second point, on formal
grounds, p
=
5% forW
=
50%, we obtain the operating characteristic "R" aso
shown in Figure 3.07, whose lower half represents the boundary for the operating
characteristics of concrete as taken from the safety theory. If, for example,
we were to choose the operating characteristic "RB" on the significant side in
Figure 3.07, with n = 12 and k
=
1.65, this would mean that lots having, fors
example, one per cent defectives would only be rejected in 5% of all cases. The
producer will therefore take a "conservative stand", that is, he will only produce, i f at all possible, lots having 1% rejects, so that "almost all" his lots will
be accepted under the test specification. In his production, he will aim for
a mean value of
8
= SwN + 2.33 •a
good inspection), he would therefore have to work with a conservative target
value of 2.33 • 40
=
93 kgf/cm2• If he wanted to ensure that a Bn 350 concretewith a sample of only 12 cubes was accepted in a majority of cases, he wouid
have to aim for a production mean of 443 kgf/cm2 (450 in round figures). This
corresponds quite well to traditional conditions.
There is one more point to be made. To determine the conservative target
value for the mean to be aimed for when calculating concrete mixtures, the equation used until now has been
B
WN + 1.65 • a
B
wN + k •a
The increase in the theoretical target value, which, according to the foregoing, becomes necessary as a result of the "uncertainty of samples", can also be
represented as an addition ｾｳ to the conservative target value. The above
equation then reads as follows:
S
=
B
+ 1.65 •a
+ ｾｳwN
where ｾｂ
=
(2.33 - 1.65) • a=
0.68 • aThis addition to the target value can be offset by the applicable cement strength.
When calculating mixtures it is customary to apply the 5% fractile of the
cement strength. The gap between N
5
%
and N is ｾｎ=
1.65 - 25 = 40 kgf/cm2
• The
compressive strength of the concrete increases by about the same amount as the
cement strength Ｈｾｂ ｾ ｾｎＩＮ The cement dispersion is already contained in the
standard deviation a of the population. It is therefore also contained in the
conservative target value k •
a.
The popu Labion mean to be aimed for is
S=s
+ k - awN
The required water/cement ratio is taken from the w/c diagram (cf. Figure 3.10) by using the 5% fractile N
5% on the significant side as the available cement
strength. During concreting operations, however, the
actual
cement strengths66 ｾ 6N = 40 kgf/cm2
i.e., the conservative target value is also greater by 66.
6 + 66 = 6wN + k
• a
+ 66B
+ 0" (k + 6k) wN6 +
a
• k 'wN
The result is that the nominal value 6
wN does not correspond to the 5%
fractile of the strength distribution, but, because of the higher mean of the
population, to a smaller fractile, perhaps the 1% fractile. A more precise
assessment with the usual values for the standard deviation(16) of the population
(a
=
50 ./. 67 kgf/cm2) yields:6k
=
66=
40=
0" 50 ./. 67 0.6
.r,
0.8Thus the standardized statistical value for the normal distribution becomes
k'
=
k + 6k=
1.65 + (0.6 ./. 0.8)= 2.25
.t .
2.45This corresponds to the (1.2 ./. 0.7) % fractile, or about the 1% fractile on the average.
For the selected operating characteristic "RB" (Figure 3.07), then, the producer's risk drops to less than 5%, since his lots only show small per cent defectives as a result of the higher conservative target value.
In cases where the producer, for some reason, supplies lots having a greater number of rejects, the proposed operating characteristic "RB" makes it possible to reject with 95% probability lots with per cent defectives of 18%, or to accept them in only 5% of all cases, so that the consumer's risk comes to 5%.
For the sake of comparison, the operating characteristic "BM" proposed by
Bonzel/Manns(24) is also presented in Figure 3.07. In view of the greater number
of samples (ns
=
35), it is on the significant side.In conclusion, it can be said that the starting point for establishing the operating characteristic, and thus for determining the sampling inspection plan
and the risks of both producer and consumer, is the largest per cent defective
P2 defined by the significance of the measurement. We then have a practically
realizable sampling specification with nand k. Finally, a producer's risk of
PI
=
5%, which is still reasonable, yields the conservative target value forthe mean of the population. Since the total dispersion is taken into account
in the conservative target value, it is possible to start from the mean of the cement strength when evaluating the mixture, and this offsets the higher target value in comparison with earlier calculations.
3.5 The use of previous information in assessing concrete
3.5.1 General
It is obvious from the foregoing that either a larger number of samples or a high target value is needed if the producer's risk and the consumer's risk
inherent to sampling inspection are to be kept within reasonable limits. It
would therefore be desirable to include in the sample, in addition to the usual strength results, some "previous information" about concrete strength, which can
also be obtained objectively, but more quickly and at a lower cost. The resulting
increased sample size provides a more suitable operating characteristic, that is, a smaller risk for both producer and consumer, and therefore a more reliable assessment of the quality of the concrete.
The proposal outlined below was prepared by the author while working for the CEB/CIB/FIP/RILEM Joint Committee on Statistical Control of Concrete Quality,
and published in greater detail (25). The following considerations are largely
based on that publication.
3.5.2 A proposal for the use of previous information
The knowledge now available in concrete technology makes it possible to assess concrete strength with the help of previous information obtained before 'and during the preparation of the concrete, and of diagrams or formulas resulting
from several tests and subject to further tests at any time. The diagram used
below for evaluation (Figure 3.10) was compiled by the author from data provided by K. Walz(26) and G. Rothfuchs(27).
- the standard strength of the cement,
- the measured water/cement ratio of the fresh concrete,
- the cement content of the concrete per m3
,
- the water content of the fresh concrete per m3 from the measurement of aggregate
moisture and the added water,
- the consistency of the fresh concrete,
- the grading curve of the aggregates, expressed in terms of the sum of the siftings as a measure of the water demand of the aggregates,
the standard deviation of the concrete strength population from previous results.
The most important condition for the use of sampling theory in the inspection
of concrete lots is that samples be drawn at random. This also holds true when
gathering previous information. It is important that the total number of samples
(cubes and previous information) be distributed as much as possible over the entire concreting period.
The suggestion that previous information be considered in the inspection of concrete lots is illustrated below in the compact form of a checklist
(Figure 3.08) with four appendices (Figures 3.09 to 3.12). The checklist and
its appendices contain all the information and processing instructions needed for the decision to "accept" or "reject". Practical examples are given in section 3.5.3.
The compact form of the checklist was chosen intentionally to illustrate how the civil engineer can master the flow of information which he must face in his work.
3.5.3 Examples
3.5.3.1
The building of a reinforced concrete frame construction required a B 300
concrete whose 5% fractile would be above 300 kgf/cm2• Six cubes were prepared
from six different mixtures. Apart from this, there were seven recordings of
the water/cement ratio and two of the consistency of the fresh concrete at different times during the concreting operations.
All 15 items of information, together with the accompanying mixture data,
are brought together in "Appendix
e"
(Figure 3.11). Using the diagram ininto estimated values for the cube strength
B
W28• As mean value we obtain
397 kgf/cm2
The operating characteristic for n = 15 given in Appendix A (Figure 3.09) is
a
taken as standard. The acceptance factor is then k = 1.645.
The standard deviation of the population can be entered as
a
on the basis of previous findings.
55 kgf/cm2
According to the checklist and the decision tree in Appendix D (Figure 3.12), we then proceed as follows:
Test size: z = z
=
Note:S
-
k • a = 397 W28 306 ｾ 300 kgf/cm2 1.645 • 55 -; accept. = 397 - 91If, for this construction site, there was no previous information about the expected standard deviation of the population, some general information about
the standard deviation would have to be used, e.g., the results of an international
.. / / . (16)
enquiry on concrete strength at building sites by Rusch Sell Rackwltz .
Figure 3.13 is a proposal, based on this enquiry, for an evaluation of the
quality of concrete production using the standard deviation value. In the
present case, we would accordingly enter
a
=
70 kgf/cm2• We would then have:Test size:
z = 397 1.645· 70 = 397 - 115
z
=
282 ｾ 300 kgf/cm2 ｾ reject.Another resort in the present case would be to use the standard deviation of the sample as an estimated value for the standard deviation of the population.
(12)
It can be determined graphically or computationally using known methods .
We obtain s = 42 kgf/cm2•
The acceptance factor must now be taken from an operating characteristic
for n 15. On the basis of the Bonzel/Manns proposal (24), the latter was
s
entered in Figure 3.09 in such a way that 11% rejects (below par) are still
