CEN/TR 16369:2012
(Main)Use of control charts in the production of concrete
Use of control charts in the production of concrete
This Technical Report reviews various control systems that are currently used in the concrete industry and, by the use of examples, show how the principles are applied to control the production of concrete. This CEN/TR provides information and examples of the use of method C in Clause 8 of prEN 206:2012.
Anwendung von Qualitätsregelkarten bei der Herstellung von Beton
Utilisation des cartes de contrôle pour la production du béton
Uporaba kontrolnih kart kontrole kakovosti pri proizvodnji betona
To tehnično poročilo zajema pregled različnih kontrolnih sistemov, ki se trenutno uporabljajo v betonski industriji, in z uporabo primerov prikazuje, kako se načela uporabljajo za kontrolo proizvodnje betona. Ta standard CEN/TR podaja informacije in primere uporabe metode C iz točke 8 standarda prEN 206:2012.
General Information
Standards Content (Sample)
SLOVENSKI STANDARD
01-februar-2013
Uporaba kontrolnih kart kontrole kakovosti pri proizvodnji betona
Use of control charts in the production of concrete
Anwendung von Qualitätsregelkarten bei der Herstellung von Beton
Utilisation des chartes de contrôle pour la production du béton
Ta slovenski standard je istoveten z: CEN/TR 16369:2012
ICS:
03.120.30 8SRUDEDVWDWLVWLþQLKPHWRG Application of statistical
methods
91.100.30 Beton in betonski izdelki Concrete and concrete
products
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
TECHNICAL REPORT
CEN/TR 16369
RAPPORT TECHNIQUE
TECHNISCHER BERICHT
October 2012
ICS 91.100.30; 03.120.30
English Version
Use of control charts in the production of concrete
Utilisation des cartes de contrôle pour la production du Anwendung von Qualitätsregelkarten bei der Herstellung
béton von Beton
This Technical Report was approved by CEN on 20 May 2012. It has been drawn up by the Technical Committee CEN/TC 104.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United
Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2012 CEN All rights of exploitation in any form and by any means reserved Ref. No. CEN/TR 16369:2012: E
worldwide for CEN national Members.
Contents Page
Foreword .4
Introduction .5
1 Scope .7
2 Symbols and abbreviations .7
3 Statistics for Concrete .8
3.1 Normal distribution of strength .8
3.2 Characteristic strength and target strength .8
3.3 Standard deviation. 10
3.4 Setting the target strength . 13
4 Simple Data Charts . 14
5 Shewhart Charts . 15
5.1 Introduction . 15
5.2 Shewhart action criteria . 16
5.2.1 Points beyond UCL or LCL . 16
5.2.2 Points beyond UWL or LWL . 16
5.2.3 Patterns within control limits . 16
5.3 Control of standard deviation . 16
5.4 Example Shewhart chart . 16
5.5 Modified application of Shewhart control chart . 17
6 CUSUM . 19
6.1 Introduction . 19
6.2 Controlling mean strength . 22
6.3 Controlling standard deviation . 22
6.4 Controlling correlation . 23
6.5 Design of V-mask . 24
6.6 Action following change . 24
7 Multivariable and Multigrade Analysis . 26
7.1 General . 26
7.2 Multivariable . 26
7.3 Multigrade . 27
8 Speeding the Response of the System . 28
8.1 Early age testing . 28
8.2 Family of mixes concept . 28
9 Guidance on Control Systems . 30
9.1 Abnormal Results . 30
9.2 Handling mixes outside the concrete family . 30
9.3 Handling mixes not controlled by compressive strength requirements . 31
9.4 Test rates . 32
9.5 Action following change . 33
10 EN 206-1 Conformity Rules for Compressive Strength . 33
10.1 Basic requirements for conformity of compressive strength . 33
10.2 Assessment period . 34
10.3 Conformity rules for compressive strength . 34
10.4 Achieving an AOQL of 5 % with CUSUM . 36
10.5 Non-conformity . 37
11 Implementing Control Systems . 38
12 CUSUM Example . 38
12.1 Reference mix and concrete family . 38
12.2 Main relationship . 39
12.3 Applying adjustments . 40
12.4 CUSUM calculation . 41
12.5 CUSUM action following change . 45
12.6 Further data and a change in standard deviation . 47
Bibliography . 51
Foreword
This document (CEN/TR 16369:2012) has been prepared by Technical Committee CEN/TC 104 “Concrete
and related products”, the secretariat of which is held by DIN.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
Introduction
It is safe to assume that ever since manufacturing commenced, attempts have been made to control the
process in order to improve quality and drive down costs. The application of statistical techniques to
manufacturing was first developed by physicist Walter A. Shewhart of the Bell Telephone Laboratories in
1924. Shewhart continued to develop the idea and in 1931 he published a book on statistical quality
control [1].
Shewhart recognised that within a manufacturing process there were not only natural variations inherent in the
process, which affected quality but there were also variations that could not be explained. Shewhart
recognised that it is possible to set limits on the natural variation of any process so that fluctuations within
these limits could be explained by chance causes, but any variation outside of these limits, special variations,
would represent a change in the underlying process.
Shewhart’s concept of natural and special variations is clearly relevant to the production of concrete at a
ready-mixed plant or precast factory and the requirement to achieve a specified compressive strength. Natural
variations exist in the process due to variation in the raw materials (aggregate grading, chemical composition,
etc), batching accuracy, plant performance, sampling and testing, etc. Special causes of variation outside of
the natural variations could be due to changed constituent materials being used, weigh-scales losing
accuracy, a new batcher, problems with testing equipment, etc.
Control charts have found widespread use in the concrete industry in both ready-mixed concrete and precast
concrete sectors as a tool for quality control. Control charts can be applied to monitor a range of product
characteristics (e.g. cube/cylinder strength, consistence, w/c ratio), constituent materials (aggregate grading,
cement strengths, etc.) or production (batching accuracy).
Their most common application of control charts is as a means of continuously assessing compressive
strength results in order to:
check whether target strengths are being achieved;
measure the variations from target (all products vary);
identify magnitude of any variation;
objectively define action required (e.g. change w/c ratio) to get the process back on target;
identify periods and concretes where the strength was less than specified so that investigations can be
carried out and corrective action taken.
The use of control charts should not be treated in isolation from the rest of production control. For example
routine checking and maintenance of weigh equipment will minimise the risk of a weigh-scale failure. Control
charts provide information about the process, but the interpretation of the information is not a mechanical
process. All the information available to the concrete producer should be used to interpret the information and
make informed decisions. Did a change in quality occur when a new batch of constituent was first used? Is all
the family showing the same trend? Are other plants using similar materials showing a similar trend? Such
information leads to the cause of the change in quality being identified and appropriate action being taken. For
example a loss of accuracy in the weigh-scales should lead to repair, maintenance and re-calibration and not
a change in mix proportions. Where a change in mix proportions is required, the use of control charts can lead
to objectively defined changes in proportions.
Effective control of concrete production is more easily achieved when there are good relationships with the
constituent material suppliers, particularly the suppliers of cementitious materials. Early warning of a change
in performance from the constituent material supplier should be part of the supply agreement, e.g. that stock
clinker is being used during the maintenance period, and on the basis of this warning, the producer will decide
the appropriate action.
Some producers use changes in cement chemistry to predict changes in concrete strength. Effective
production control is about using all this information to produce concrete conforming to its specification.
Effective production control, which includes the use of control charts, significantly reduces the risk of non-
conformity benefiting both users and producers of concrete.
There are drawbacks to the existing method of assessment of conformity of mean strength adopted in
EN 206-1 [3] including not following the CEN Guidance on the evaluation of conformity [2]. It is believed that
control charts (already widely used as a quality assurance tool in factory production control) would provide an
alternative and better means of ensuring the characteristic strength is achieved and it is a method that follows
the CEN Guidance.
1 Scope
This Technical Report reviews various control systems that are currently used in the concrete industry and, by
the use of examples, show how the principles are applied to control the production of concrete. This CEN/TR
provides information and examples of the use of method C in Clause 8 of prEN 206:2012.
2 Symbols and abbreviations
AOQ Average outgoing quality
AOQL Average outgoing quality limit
Constant giving the cement content increase required to produce a
C
mra
1N/mm increase in strength
dc Change in cement content
Dl Decision interval
G Gradient
f
Individual test result for compressive strength of concrete
ci
f
Specified characteristic compressive strength
ck
f
Mean compressive strength of concrete
cm
k Statistical constant
L
Lower limit
l
LCL Lower control limit
LWL Lower warning limit
n Number of samples
q
Statistical constant that depends upon n and the selected AOQL
n
s Sample standard deviation
UCL Upper control limit
UWL Upper warning limit
Test result
x
NOTE According to EN 206-1 [3], a test result may be the mean value of two
i
or more specimens taken from one sample and tested at one age.
Mean value of ’n’ test results
x
Estimate for the standard deviation of a population
σ
3 Statistics for Concrete
3.1 Normal distribution of strength
Compressive strength test results tend to follow a normal distribution as illustrated in Figure 1. A normal
distribution is defined by two parameters, the mean value of the distribution and the standard deviation (σ ),
which is the measure of the spread of results around the mean value. A low standard deviation means that
most strength results will be close to the mean value; a high standard deviation means that the strength of
significant proportions of the results will be well below (and above) the mean value. The area under the
normal distribution between two values of ‘x’ represents the probability that a result will fall within this range of
values. The term ‘tail’ is used to mean the area under the normal distribution between a value, e.g. a
compressive strength, and where the frequency is effectively zero. For strength it is the lower tail, i.e. low
strength results, that is important but for other properties, e.g. consistence, both the lower and upper tails are
important.
Key
X cube strength, N/mm²
Y frequency
1 target mean strength
2 specified Characteristic strength, f
ck
3 minimum strength (f – 4)
ck
4 tail
Figure 1 — Illustration of concrete strength distribution
At the extremes of the strength range for a given set of constituent materials, the assumption of a normally
distributed set of data may not be valid. It is not possible to have strengths less than zero and most concretes
have a ceiling strength beyond which they cannot go. In these situations the data set is skewed. However as
low strengths are of concern to specifiers, an assumption of normally distributed data does not lead to
problems in practice.
3.2 Characteristic strength and target strength
EN 206-1 [3] specifies the characteristic compressive strength of concrete in terms of a standard cylinder test
or a standard cube test carried out at 28 days. The characteristic strength is defined in EN 206-1 [3] as the
“value of strength below which 5 % of the population of all possible strength determinations of the volume of
concrete under consideration, are expected to fall”. Put simply this means that if every single batch was
tested, 5 % of the results would fall within the lower ‘tail’ of the normal distribution that starts 1,64σ below the
actual mean strength. However the actual mean strength will not be known until the concrete has been
produced and tested and therefore the target mean strength (TMS) is usually set at some higher value to
ensure the concrete achieves at least the specified characteristic strength.
The target mean strength is given in Equation (1):
TMS = f + k × σ (1)
ck
where
TMS = target mean strength
f = characteristic compressive strength
ck
σ = estimate for standard deviation of population
k = statistical constant
k × σ = the margin
The fixed point in the distribution is the specified characteristic strength and as the margin increases and/or
the standard deviation increases, the target mean strength increases, see the following Example.
EXAMPLE The target mean strength for a specified characteristic strength of C25/30 is given in Table 1. A standard
2 2
deviation (σ ) of 3 N/mm is typical of a concrete with low variability and a value of 6 N/mm represents high variability.
Table 1 — Target mean strength for specified characteristic strength of 30 N/mm (cube)
Area in lower tail
Target mean strength (cube), N/mm
Margin
(i.e. percentage below
2 2
σσσσ = 3 N/mm σσσσ = 6 N/mm
characteristic strength)
1,64σ 5 % 35 40
1,96σ 2,5 % 36 42
2,00σ 2,28 % 36 42
2,33σ 1,0 % 37 44
3,0σ 0,13 % 39 48
The numbers in this table have been rounded.
A concrete strength below the characteristic strength is not a failure as statistically 5 % of the results are
expected and accepted as to fall below this value. However for structural safety reasons, a batch with a
concrete strength significantly below the characteristic strength is excluded, even though it forms part of the
expected population. Consequently EN 206-1 [3] specifies a minimum strength requirement for individual
results (f ) of (f – 4). Any batch below this strength is a non-conforming batch.
ci ck
The risk of non-conformity decreases as the margin increases. Statistics are used to quantify that risk. For a
given margin the probability of a test result falling below the specified characteristic strength or failing the
individual strength criterion is given in Table 2. Table 2 shows that the probability of having a result below the
specified characteristic strength is independent of the standard deviation (as the margin is based on the
standard deviation) but the risk of failing the criterion for individual batches increases as the standard
deviation increases.
Table 2 — Effect of margin on proportion of concrete below characteristic strength; and risk of failing
the strength criterion for individual batches
Risk of failing the strength criterion for
Probability of a test
individual batches
Margin result being below the
characteristic strength
2 2
σσσσ = 3 N/mm σσσσ = 6 N/mm
1 %
1,64σ 1 in 20 (5 %) 0,1 %
1 in 40 (2,5 %) 0,05 % 0,4 %
1,96σ
1 in 100 (1 %) 0,01 % 0,1 %
2,33σ
1 in 1 000 (0,1 %) 0,000 5 % 0,01 %
3,08σσσσ
The definition of ‘characteristic strength’ in EN 206-1:2000 [3] has its complications. For a structural engineer
the phrase ‘the volume of concrete under consideration’ may be applied to all the concrete in their structure
and to the concrete in a single element of that structure even if this comprises a single batch. For conformity
to EN 206-1 [3], the ‘volume under consideration’ is all the concrete in an assessment period. Neither of these
interpretations of this phrase is suitable for use in control systems as the process is continual. Caspeele and
1)
Taerwe [5] have proposed that if the production achieves an average outgoing quality limit (AOQL) of 5 %,
the production can be accepted as having achieved the characteristic strength.
3.3 Standard deviation
The standard deviation of a population will only be truly known if every batch of concrete is tested. However if
35 or more results are available, the estimated standard deviation is likely to be very close to the true standard
deviation. This is the reason why EN 206-1 [3] requires 35 results to calculate the initial standard deviation.
When n ≥ 35, the standard deviation may be estimated using the equation:
Standard deviation,
(x − x)
i
∑
σ =
(n − 1)
Alternatively it can be determined through a range of pairs approach where:
Mean range of successive pairs = 1,128 × standard deviation (2)
or,
Standard deviation = 0,886 × mean range of successive pairs of results
The range is the numerical difference between successive results and the difference is always taken as a
positive number, e.g. |2 – 3| = 1. The range of pairs method of calculating the standard deviation is particularly
suited for populations where there are step changes in mean strength in the data set, e.g. concrete, as the
effect of the step change will be limited to a single pair of results. With concrete production, step changes in
mean strength (usually due to a change in a constituent) are more common than drifts in mean strength.
EXAMPLE 1
1) From the operating-characteristic curve for the selected sampling plan, the average outgoing quality (AOQ) curve is
determined by multiplying each percentage of all possible results below the required characteristic strength in the
production by the corresponding acceptance probability.
Table 3 — Calculation of the standard deviation using mean range
Transposed
Range,
cube strength,
Result Calculation of standard deviation
N/mm
N/mm
1 54,5
2 52,5 2,0
3 49,5 3,0
Estimation of the standard deviation
4 47,5 2,0
= 0,886 × 51/14
5 49,0 1,5
6 43,5 5,5
= 0,886 × 3,64 = 3,0 N/mm
7 54,5 11,0
(rounded to the nearest 0,5 N/mm )
8 46,5 8,0
9 50,0 3,5
10 50,5 0,5
11 47,0 3,5
12 48,5 1,5
13 53,0 4,5
14 51,5 1,5
15 48,5 3,0
Sum of ranges 51,0
Mean of ranges 3,64
EXAMPLE 2 (copied from Reference [4])
2 2
15 random data have been generated assuming a mean strength of 37,0 N/mm and a standard deviation of 3,5 N/mm .
These have been repeated to give a total of 30 data, see Figure 2a. The standard deviation of the 30 data given in
Figure 2a) is:
3,6 N/mm when determined by the standard method;
3,7 N/mm when determined from 0,886 × mean range.
To illustrate the effect of a change in mean strength on the standard deviation, an extreme reduction in mean strength of
2 2
5,0 N/mm is introduced at result 16 i.e. data 16 to 30 are all 5,0 N/mm less than in Figure 2a). The dispersion of the data
around these mean strengths is unchanged. The standard deviation of the 30 data given in Figure 2b) is:
4,4 N/mm when determined by the standard method;
3,8 N/mm when determined from 0,886 × mean range.
This shows that the standard deviation calculated from the mean range has been less affected by the change
in mean strength.
Figure 2a) — Fifteen random data generated assuming a mean strength of 37,0 N/mm2 and a standard
deviation of 3,5 N/mm (the first group of 15 results are the same as the second group of 15 results)
Figure 2b) — The same data as in Figure 6a), but with a reduction in mean strength of 5,0 N/mm
introduced at result 16
Key
X result number
Y compressive strength – N/mm²
1 reduction of 5 N/mm² in the mean strength
Figure 2 Example of the impact of a step change in mean strength on the calculated standard
deviation
The true standard deviation of a population, σ , can only be determined if all the population were to be tested,
which is impractical. In practice the population standard deviation is estimated by testing samples. The more
samples that are tested, the more reliable the estimated population standard deviation will be. EN 206-1 [3]
requires at least 35 results to initially estimate the population standard deviation. Prior to obtaining the
estimated population standard deviation, concrete is controlled by more conservative initial testing rules.
Without an estimated population standard deviation, it is not possible to use control charts to control the
concrete production.
Once the initial population standard deviation has been estimated, EN 206-1 [3] permits two methods for
verifying the initial estimate. The first method involves checking that the standard deviation of the most recent
15 results does not deviate significantly from the adopted value. The second method involves the use of
continuous control systems.
The standard deviation for strength tends to be constant for medium and high strength mixes but for lower
strengths it tends to increase proportionally with mean strength [6] and the relationship illustrated in Figure 3
may be assumed. In practice this means that the standard deviation for concretes that have a characteristic
strength of 20 N/mm or more is determined by testing and calculation, while the standard deviation for
concrete with a lower strength is interpolated.
Key
X strength (N/mm²)
Y standard Deviation (N/mm²)
Figure 3 — Simplified standard deviation to mean strength relationship
3.4 Setting the target strength
The target strength is set to achieve a balance between the following requirements:
high probability of achieving a population with at least the specified characteristic strength;
low risk of failing the minimum strength criterion;
low consumers risk;
low producers risk;
competitive and economic.
The target strength is selected by the producer, but the producer may have to comply with certain minimum
values. The target strength should never be lower than (f + 1,64σ ), but it is normally higher than this value.
ck
National requirements, the requirements of a certification body or other requirements (see 10.4) may impose
minimum target strengths.
UK experience is that a minimum target strength of (f +1,96σ ) at a test rate of at least 16 results per month
ck
is a good balance between these conflicting demands. With a concrete family this gives about a 3σ margin,
i.e. a 1:1 000 risk of failing the minimum strength requirement (f – 4). Data collected by a UK certification
ck
body on individual batch non-conformities shows that the actual rate of non-conformity is an order of
magnitude lower and this is due to the active control of the production.
4 Simple Data Charts
Simple data control charts are used to routinely monitor quality. There are two basic types of control charts:
Univariate — a control chart of one quality characteristic (e.g. mean strength);
Multivariate — control chart of a statistic that summarises or represents more than one quality
characteristic (e.g. coefficient of variation).
If a single quality characteristic has been measured or computed from a sample, the control chart shows the
value of the quality characteristic versus the sample number or versus time.
Simple data charts are useful in providing a visual image of production and unusual results. Simple charts
may also give an indication of trends but the general scatter of the data may also mask trends that can be
identified only by more in-depth analysis of the data.
Consider the data in Table 4 and illustrated in Figure 4. A review of the data shows that all the results are
within +/- 8 N/mm of the target. The results are fairly evenly distributed around the target (2 on target,
9 results above and 7 below) so it is not immediately obvious what conclusions can be drawn from the data.
Table 4 — Example data for mean strength with a target strength of 40 N/mm
28-day strength, 28-day strength,
Result Result
2 2
N/mm N/mm
1 37 10 40
2 42 11 34
3 36 12 44
4 35 13 46,5
5 42 14 42
6 38 15 44,5
7 39,5 16
8 40 17 44
9 35 18 48
Key
X sample number
Y strength, N/mm²
Figure 4 — Simple univariate control chart for strength
5 Shewhart Charts
5.1 Introduction
While graphical plots can give useful information about the pattern of a production process, the control chart
becomes a much more powerful tool if statistical rules are also applied to the data. Shewhart control systems
measure variables in the production processes (e.g. target mean strength). They make use of calculated
control limits and apply warning limits based on the measured variation in the production process.
ISO 8258 [7] gives general information on Shewhart control charts and ISO 7966 [8] gives general information
on Shewhart control charts for acceptance control.
The Shewhart chart will have a horizontal central line which represents the expected mean value of the test
results on the samples taken from production; in the case of concrete, the Target Mean Strength for a chart
controlling compressive strength. Lines representing the upper control limit (UCL) lower control limit (LCL),
upper warning limit (UWL) and lower warning limit (LWL) may also be added. Generally action is required if a
result is beyond either of the control limits.
The UWL and LWL are set at a level so that most of the results will fall between the lines when a system is
running in control. These are not specification limits but ‘warning’ limits based on the variability of the
production process. Given that concrete strengths follow a normal distribution (Figure 1), it follows that there is
a 50 % chance that a result will be above the TMS and a 50 % chance that it is below the TMS. In Clause 3, it
was shown that a margin of 1,96 × σ will lead to 2,5 % of results being below the characteristic strength.
Some variables, e.g. consistence, have both upper and lower limits and in these cases it is essential to have
both an UWL and a LWL. While for conformity to a specified characteristic strength a high value is not
significant, from the viewpoint of economic production it does matter. Therefore in practice, both upper and
lower warning limits are used even for a variable that has a single limit value, e.g. concrete strength. Setting
upper and lower warning limits at 1,96σ leads to the expectation that 95 % of the results will fall within these
limits and 2,5 % in each of the ‘tails’ of the normal distribution. If a margin of 3,0 × σ is adopted, there is very
little chance of a result falling outside this limit due to natural variation (0,3 % for two-tailed test). A Shewhart
control chart can be constructed with:
UCL = TMS + 3 × σ
LCL = TMS – 3 × σ
UWL = TMS + 2 × σ
LWL = TMS – 2 × σ
The probability of a single result falling outside of either the UWL or LWL is 4,56 %, i. e. 2,28 % above the
UWL and 2,28 % below the LWL (see Table 1).
The probability of two consecutive results falling outside the limits purely by chance is:
= 0,045 6 × 0,045 6 = 0,002 079 or 0,21 %.
The probability that the two results are either both above or below the line (i.e. in the same direction) is only
0,05 %. Such an outcome is very strong evidence that the expected outcome is not being achieved.
5.2 Shewhart action criteria
5.2.1 Points beyond UCL or LCL
The presence of one or more points lying outside of the UCL or LCL is primary evidence that the system is out
of control at that point. Since there is only a 0,3 % chance that this result is due to natural variation, it is
probable that special variation will account for the extreme value and an immediate investigation into the
cause should be undertaken.
5.2.2 Points beyond UWL or LWL
The presence of two consecutive, or more than 1 in 40, points beyond either warning line is evidence that the
process is out of control and an investigation of the data should be undertaken.
5.2.3 Patterns within control limits
It is also possible to analyse data that does not breach either the control or warning limits to evaluate whether
any trends are significant. Runs analysis can give the first warning of a system going out of control before
points are seen beyond the warning limits.
The following simple rules of thumb have been proposed for sequences of results that remain within the
warning limits [9]:
1) Seven or more consecutive results on the same side of the target mean strength;
2) At least 10 out of 11 results on the same side of the target mean strength;
3) At least 12 out of 14 results on the same side of the target mean strength;
4) At least 14 out of 17 results on the same side of the target mean strength.
5.3 Control of standard deviation
The control and warning limits are determined by the standard deviation of the process; it is therefore
important to monitor the standard deviation. As the calculation to determine standard deviation is relatively
complex, the alternative calculation in Equation (2) is used linking standard deviation to the range of pairs of
results. Plot the running mean range of the last n successive results where n ≥ 15 against test result number.
Select the change in standard deviation that will prompt action (∆σ) and set action lines at:
1,128*current standard deviation ± 1,128* ∆σ
5.4 Example Shewhart chart
Consider again the strength data in Table 4 and subject it to a Shewhart analysis using the rules stated in 5.2.
Figure 5 shows the data with a UCL, LCL, UWL and LWL applied. Immediately it is apparent that point 18 has
exceeded the UWL This does not breach the rule defined in 5.2 (requiring 2 consecutive points above UWL)
but also at this point there is a sequence of 7 points on the same side of the target mean strength (see 5.2.3).
The Shewhart chart is showing that the process is out of control, i.e. the actual mean strength is higher than
the mean strength required.
Key
X sample number
Y strength, N/mm²
1 upper control limit
2 upper warning limit
3 target strength
4 lower warning limit
5 lower control limit
Figure 5 — Control levels applied to data
5.5 Modified application of Shewhart control chart
If the aim is to assess whether the level of production is higher than a specified characteristic value, a
modified application of Shewhart control charts can be used, with the use of specific modified variables. This
application comprises checking that the average of n measured strength results is greater than a lower line L
l
situated at a given distance from f with the following variables:
ck
L ≥ f + (q × s)
l ck n
where
q depends on n and on the AOQL chosen,
n
s is an updated evaluation of the standard deviation of the relevant production.
In the case where n ≥ 15 and q ≥ 1,48, the Shewhart charts will satisfy the requirement for an AOQL of 5 %.
n
This criterion also satisfies the conformity criteria for mean strength in EN 206-1 [3]. A warning line at some
higher value may also be appropriate.
EXAMPLE A precast concrete factory intends using a Shewhart chart system to show conformity to the mean
strength criterion in EN 206-1 [3]. Due to process requirements the strengths tend to exceed the characteristic strength
within a few days and therefore they opt to test at a real age of 7 days to verify that the specified 28-day strength is
already being achieved at 7 days. As the compressive strengths are expected to be well above the specified strength, they
opt not to have a warning line.
To do this task the running average strength of the last ‘n’ consecutive results, where ‘n’ is a predetermined number that is
at least 15 are plotted on a Shewhart chart with one limit line with a value of (f + 1,48s). If the running mean strength
ck
below this line this indicates that an AOQL of 5 % is not being achieved. A warning line at some value higher than
(f + 1,48s) may be added.
ck
The specified compressive strength class is C25/30 and they use cubes for assessing the production and conformity. The
current standard deviation is 2,5 N/mm . The limit value Ll is:
30 + 1,48*2,5 = 33,7 N/mm
For control purposes, rather than using non-overlapping groups of results, they opt to use the running mean of the last 15
results. This is shown in Figure 6a), which shows that the mean strength is consistently above the limit value.
Figure 6a) — Control of conformity of mean strength using a running mean of 15 results
The sample standard deviation is also checked to ensure that it has not changed significantly. Though 8.2.1.3 of
EN 206-1:2000 [3] states that the present value is still applicable if the calculated value based on the last 15 results is
within about ± current value/3, this is not a very sensitive indicator of change and most producers would regard a
2 2
0,5 N/mm change in standard deviation as significant and the precast company uses this value of 0,5 N/mm , which is
controlled with another modified Shewhart chart. On this chart a horizontal line is drawn at the current mean range value
(1,128σ ) and action lines ± 1,128 × 0,5 from this value.
Again a running mean range of the last 15 consecutive and overlapping pairs of results is used. When the running mean
value crosses one of these action lines, this indicates that the standard deviation has changed by 0,5 N/mm and a new
value should be applied.
In this example the current standard deviation is 2,5 N/mm and this equates to a mean range of
2 2 2
1,128 × 2,5 = 2,82 N/mm and upper and lower action lines at 3,38 N/mm and 2,26 N/mm (2,82 ± 1,128 × 0,5). These
are shown in Figure 6b). At test result 26, the mean range crosses the upper action line indicating that the standard
deviation has increased by 0,5 N/mm . The limit value is increased in Figure 6a) to 34,4 N/mm2 and in Figure 6b) a new
2 2 2
mean range is set at 3,38 N/mm with upper and lower action lines set at 3,94 N/mm and 2,82 N/mm respectively. As
the running mean strength is still well above the limit line, the mix proportions are not changed, i. e. the appropriate action
is to take no action other than change the values on the control charts.
Figure 6b) — Control of standard deviation using the running mean range of the last 15 ranges
Key
X test result number
Y mean range of last 15 results
1 line showing when σ has increased by 0,5 N/mm²
2 current mean range, i.e. 1,128x current standard deviation
Figure 6 Example of the application of the modified Shewhart control chart system
6 CUSUM
6.1 Introduction
CUSUM control systems (short for cumulative sum) were developed in the 1950s, initially for quality control of
continuous manufacturing processes. They have found widespread use in the concrete industry. In CUSUM
charts, the central line does not represent a constant mean value but is a zero line for the assessment of the
trend in the results. In concrete production three CUSUMs are used:
CUSUM M, for the control of mean strength;
CUSUM R (range), for the control of standard deviation;
CUSUM C, for the control of correlation.
The CUSUM method, described in more detail in BS 5703 [10] and Concrete Society Digest No. 6 [11] and
ISO/TR 7871 [12], involves subtracting the test result from a target value then producing an ongoing running
sum (the CUSUM) of the differences. If the process is in control, the points on the CUSUM plot are distributed
randomly (positive and negative differences cancelling each other out) to give an accumulative sum that is
close to zero, but if the process slips out of control, this will be quickly illustrated by the CUSUM plot moving
towards the UCL or LCL.
BS 5700 [13] describes the following advantages of the CUSUM system:
a) for same sample size it gives a more vivid illustration of any changes;
b) uses data more effectively therefore produces cost savings;
c) gives clear indication of location and magnitude of change.
CUSUM charts have been found to be more sensitive at detecting small shifts in the mean of a process than
Shewhart, whereas Shewhart charts are superior at detecting large shifts [14]. When the CUSUM reaches the
UCL or LCL, it is possible to use the plot to determine at what point the process went out of control and what
scale of corrective action is required.
Historically, CUSUM control charts were plotted manually and to determine whether a trend in the plot was
significan
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