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THE USE OF THE CONTROL CHARTS TO CONTROL THE
DIMENSION OF THE CLAY BRICK UNITS
lecturer Sada A. Hasan, Dr.Tumadhir M., Borhan
Civil Engineering Department, University of Al-Qadissiyah ,Iraq
e-mail: sada.hasan@qadissuni.edu.iq . tumadhir_borhan@qadissuni.edu.iq
Received 3 December 2013 Accepted 27 March 2014
ABSTRACT
Some manufactured material properties are expected to have unavoidable shifting in its average
value for many reasons, however, they are still able to meet the established specifications. This case
occurs when the standard deviation of the process at the various average values is very small compared
to the difference between the upper and lower specification limits. On the other hand, any results out of
these limits indicates that the efficiency of the process changes and the reasons have to be investigated
and corrected .In this study, Al-Qadissiyah brick factory was adopted to examine the acceptance of the
produced brick, in terms of its dimensions, according to Iraqi specifications. Control charts were
plotted for this purpose. Two types of charts were used, the mean and the standard deviation charts.
The upper and the lower limits (UCL andLCL) of each brick dimension were plotted and discussed.
The results showed that the lower, the upper limits and the mean value for all dimensions are within
the IQ specifications limits and the process is under control. However, the results of the length show
that there is one point outside the LCL at the mean chart and one point outside the UCL at the standard
deviation chart. This due to the chance causes, as it is only one point from thirteen patches .These
charts can be adopted by the factory to show the production process and can be used in the future to
investigate the mean of any measured patch.
Keywords: quality control, control charts, mean chart, standard deviation chart, brick dimensions.
استخدام لوحات السيطرة للسيطرة على إبعاد الطابوق الطيني
الخالصة
من المتوقع ان تتغير خواص بعض المواد المصنعة وتتحول في متوسط قيمتها ألسباب كثيرة ,ومع ذلك فأنها ماتزال قادرة على تلبية
ف المعياري للعملية عند المتوسط الحسابي لمختلف القيم صغير جدا عندما يكون االنحراالمواصفات المعمول بها . تحدث هذه الحالة
مقارنه بالفرق بين حدود المواصفة العليا والدنيا . من ناحية أخرى فان أي نتيجة خارج هذه الحدود تعطي مؤشر بان كفاءة العملية
دراسة اعتمد معمل طابوق القادسية لفحص قبول إنتاجه من الطابوق من تتغير ويجب البدا بالتحقق عن األسباب وتصحيحها. في هذه ال
mailto:sada.hasan@qadissuni.edu.iq
mailto:tumadhir_borhan@qadissuni.edu.iq
Al-Qadisiya Journal For Engineering Sciences, Vol. 7……No. 2 ….2014
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حيث اإلبعاد وفقا للمواصفة العراقية . وقد رسمت لهذا الغرض خرائط السيطرة وقد استخدمت نوعين من خرائط السيطرة ,خريطة
رسمها ومناقشتها . المتوسط وخريطة االنحراف المعياري , الحدود العليا والدنيا لكل أبعاد الطابوق قد تم
مخططات السيطرة للمتوسط واالنحراف المعياري لكل من الطول والعرض والسمك للطابوق قد رسمت وبينت ان الحدود العليا
والدنيا والمتوسط الحسابي لكل اإلبعاد ضمن المواصفات العراقية والعملية اإلنتاجية تحت السيطرة .
لوحة المتوسط للطول بينت بان هناك نقطة واحدة خارج الحدود الدنيا للمخطط بينما بينت لوحة االنحراف المعياري بان هناك نقطة
03واحدة اعلى من الحدود العليا وبعد إجراء التحقق ألموقعي تبين ان هذه النتائج تعود ألسباب صدفية كونها نقطة واحدة من اصل
يطرة على العرض قد رسمت والنتائج تشير بان النقاط كلها ضمن الحدود وتتوزع بشكل عشوائي حول الخط خرائط الس .عينة
المركزي واتجاه النقاط هذا يعطي مؤشر بان العملية اإلنتاجية ضمن السيطرة ونفس النتيجة قد تم تحصيلها لخرائط السيطرة على
لتبين نتائج عمليات اإلنتاج ويمكن ان تستخدم في المستقبل لتصحيح معدل نتائج السمك . هذه الخرائط من الممكن اعتمادها في المعمل
أي وجبة مقاسه كما تساعد على مقارنة النتائج الجديدة للفحوصات بالحدود المرسومة في خرائط هذا البحث .
INTRODUCTION
The quality control is one of the main functions in all organizations as a tool that is responsible for
the accomplished work in each stage of production process in order to make sure that the final results
and the estimated results are identical. This will help to detect the deviation early so remedies can be
deployed quickly. The quality of the product is a result of the quality of the process of production and
the statistical quality control is necessary to detect changes in the behavior of these processes. The
factories of different materials produce a large amount of products. This may causes shifting in their
specifications. To control the quality of their products and testing the quality characteristics, many of
laboratories are established inside the factory.
Since one of the basic tools in the control processes are the charts to monitor the quality of the
products, as if the output acceptable, it allows for the manufacturing process to continue. However, if
the output is unacceptable, it means that the process is out of control, which requires corrections. These
charts are considered one of the important functions of the control in management of the structures in
general and the construction industry factories in particular. The most widely used control charts are
the Shewhart control charts[ Gibra,1975],[ Box,2011] that developed to distinguish between common
and special-cause variation. The special cause variation was measured by a change in the mean of
process. These Shewhart charts are known as the ̅-chart (Average-chart or Mean–chart), the R-chart
(Range–chart) and the σ-chart (Standard deviation chart) [Leavenworth,2000],[ Montgomery,2007] .
The brick unites produced in Iraqi factories are mostly varies in its dimensions and may not meet the
standard specification. In this case, it is very helpful to apply the control charts in these factories to
eliminate this problem.
To control the upper and the lower limits of the brick dimensions in a specific factory in Iraq (Al-
Qadissiyah Factory), these charts were used in this study. The charts used are the mean ( ̅-chart) and
standard deviation(σ-chart) charts. This will help to reduce or eliminate the variation outside the limits
in the brick dimensions if it is caused by common causes not by chance causes[ Heizer,2008] .
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COLLECTING DATA
The collected data for quality control purposes is obtained directly from the factory. Thirteenth
patches of brick units that produced during one month were taken from the factory. Each of them has
twenty-four brick units as recommended by the Iraqi specifications No. 24. The dimensions of the
units were measured according to method stated by Iraqi specifications [IQSNO.24 , 1988] .Tables 1-
3show the length, width and the thickness of the selected brick units for these patches.
CONTROL CHARTS
The ̅-chart plots the process averages of each patch from the production against three horizontal
lines. The central line represents the average value of the mean of each patch. While the σ-chart plots
the process standard deviation of each patch from the production against three horizontal lines. The
central line represents the average value of the standard deviation of each patch. The other two lines
are known as Upper and Lower Control Limits (UCL & LCL). The mean and the standard deviation
are calculated as shown in Table 4.The Eqs.(1-3) and (4-6) represent the limits for the ̅-chart and σ-
chart respectively [ Altaai,2008] .
UCL= ̿+A1 ̅ ………………………………………………………………………………………………(1)
CL= ̿ ………………………………………………………………………………………………(2)
LCL= ̿A1 ̅ ……………………………………………………………………………………………….(3)
UCL=B1. ̅ ……………………………………………………………………………………………….(4)
CL= ̅ ……………………………………………………………………………………………….(5)
LCL=B2. ̅ ………………………………………………………………………………………………(6)
Where:
A1, B1, B2 is a constant and predetermined values [7] .
̿is the average value of the mean
̅is the average value of the standard deviation
RESULTS AND DISCUSSION
Figures (1 -3) show the control charts for the mean and the standard deviation of the length, width
and the thickness respectively. It can be seen that the lower, the upper limits and the mean value for all
dimensions are within the IQ specifications limits and the process is under control.
Figure (1a) shows the control chart for the mean of the length . It can be seen that there is one point
outside the LCL. Figure (1b) shows the control chart of the standard deviation and there is one point
outside the UCL. After the site investigation, these results can be attributed to the chance causes, as it
is only one point from thirteen patches.
The control charts for the width, using the mean and the standard deviation charts, are shown in
Figure 2 (a and b) respectively. The results indicated that all points are within the limits and
distributed randomly around the centerline. The trend of the points indicates that the production
process is under control. The same results are obtained for the thickness as shown in Fig. 3 (a and b).
Al-Qadisiya Journal For Engineering Sciences, Vol. 7……No. 2 ….2014
168
These charts can be adopted by the factory to show the production process and can be used in the
future to investigate the mean of any measured patch. This will help to compare the new results with
the charts limits stated in this study.
If the results of the new patch are outside the limits, we have to study the cause and again we have to
measure a second patch and compare it with the limits. If the results obtained from the second patches
are similar to the previous one (the mean is outside the limits), then the production process is out of
control and should be corrected. However, the number of the brick unites in the patch, specified by the
IQ specifications, for measuring the dimensions of the brick unites (24 unites)is relatively high as
shown in Fig.4(a and b). This increase the chance for the patch to pass the test successfully. As a
result, it can be concluded that changing the specifications of the brick dimensions is urgent to give an
accurate indication about the quality of the process of the production in the brick unites factories.
CONCLUSION
On the basis of the results obtained from the analysis of the real data of the brick dimensions, we can
conclude that the mean value for all dimensions is within the IQ specifications limits and the process is
under control.The control charts presented in this study can be used to help the factoryto investigate
the mean of any measured patch in the future.
- It can be concluded that there is a need to change the IQ specifications regarding the number of the
brick unites that have to be examined for its dimensions, as the current number is relatively high and
give more realistic results.
References
[1] Altaai, y. h. and m. a. alajily (2008). Quality management systems in the productivity organization. Iraq.
[2] Box, G. E. P. and W. H. Woodall (2011). "Innovation, Quality Engineering, and Statistics." Quality
Engineering 24(1): 20-29.
[3] Gibra, I. N. (1975). "Recent developments in control chart techniques." Journal of Quality Technology 7(4):
183-192.
[4] Heizer, J. H. and B. Render (2008). Operations management, Pearson Education India.
[5] IQSNO.24 (1988). standard methods for physical and chemical tests and sampling of building bricks in
Iraq.
[6] Leavenworth, R. S. and E. L. Grant (2000). Statistical Quality Control 7/E, Tata McGraw-Hill Education.
[7] Montgomery, D. C. (2007). Introduction to statistical quality control, Wiley. com.
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Table 1: The measured length of the selected unites
Table 2: The measured width of the selected unites
1 24.13 23.75 24.2 24.15 23.8 24.3 24.4 24.08 23.4 24.13 24.01 23.97 23.75 23.95 23.4 24.07 24.4 23.8 24.15 24.13 24.07 24 24.13 24.14
2 24.01 24.13 23.97 23.95 24.13 23.75 24.2 24.15 23.8 23.4 24.13 23.95 24.97 24.13 23.75 23.8 24.07 24.13 23.95 24.13 24.15 23.75 24.01 23.8
3 23.97 24.13 24.13 23.75 24.3 24.16 23.75 24.3 24.4 24.1 23.5 24.2 24.15 23.85 23.95 24.25 24.15 23.9 24.18 24.5 23.8 24.18 24.4 23.9
4 24.25 24.23 24.4 24.1 23.95 24.2 24.15 24.34 24.3 24.1 24.01 24.07 24.02 24.15 24.01 24.2 24.15 23.8 23.98 24.2 23.99 23.8 24.01 23.85
5 23.9 23.85 23.95 23.8 24.12 24.13 23.65 23.85 23.65 23.98 24.15 24.1 23.75 23.85 24 24.1 23.82 24.01 23.98 23.95 23.85 24.1 24.2 24.15
6 23.75 24.08 24.06 23.9 23.85 24.02 24.08 24.13 23.95 24.1 24.01 23.85 23.9 23.95 24.1 24.12 24.1 24.08 23.95 23.8 23.78 23.95 24.1 24.12
7 24.12 24.07 23.85 24 23.75 24.3 24.4 24 23.6 24.12 23.653 24.03 24.2 24.123 23.85 24.035 24.13 24.21 24.2 24.12 24.1 24.11 23.85 23.8
8 24.1 23.8 23.95 23.75 24.2 23.98 23.75 24.07 23.85 23.9 23.8 23.95 24.08 24.12 23.8 23.9 24.13 24.06 24.13 24.12 24.12 24.07 24.05 24.13
9 23.85 23.65 24.08 23.95 23.8 23.4 24.13 23.85 24.15 24.04 23.8 23.85 23.95 23.9 23.85 23.85 23.95 24.12 24.1 23.75 23.8 23.5 23.65 23.7
10 23.97 24.12 24.14 24.08 23.85 24.15 24.04 23.97 24.25 23.9 23.5 24.2 23.95 23.75 23.95 23.9 23.9 24.15 23.85 24.4 23.9 24.13 23.95 24.12
11 24.25 24.1 24.08 23.98 23.95 24.1 24.12 24.25 24.2 23.8 24.01 24.07 24.18 24.15 24.08 23.95 23.85 24.02 24.15 24.01 23.85 23.9 24.18 23.85
12 23.95 24.13 23.75 24.14 24.12 23.8 23.68 23.95 24.04 24.12 24.15 24.1 23.95 24.12 24.12 24.07 24.15 23.75 23.85 24.2 24.15 23.8 23.98 24.2
13 24.1 24.01 24.07 23.75 23.85 24.15 24.04 23.85 23.95 23.8 23.85 23.85 24.3 24.31 24 24.016 24.3 24.18 23.86 23.9 24.12 24.125 23.95 24.01
2418 19 20 21 22 2312 13 14 15 16 176 7 8 9 10 11unit no
batch no
1 2 3 4 5
1 11.55 11.5 11.65 11.5 11.5 11.16 11.42 11.52 11.53 11.5 11.35 11.75 11.61 11.16 11.6 11.6 11.53 11.52 11.42 11.61 11.75 11.35 11.42 11.51
2 11.35 11.3 11.52 11.14 11.75 11.5 11.35 11.75 11.6 11.17 11.5 11.65 11.5 11.5 11.16 11.6 11.45 11.55 11.35 11.41 11.16 11.5 11.35 11.65
3 11.5 11.45 11.7 11.55 11.43 11.18 11.71 11.62 11.65 11.75 11.62 11.16 11.35 11.5 11.57 11.42 11.6 11.65 11.55 11.45 11.5 11.63 11.65 11.4
4 11.75 11.62 11.55 11.16 11.35 11.28 11.16 11.6 11.5 11.42 11.65 11.5 11.6 11.5 11.35 11.53 11.45 11.5 11.16 11.4 11.45 11.65 11.5 11.6
5 11.5 11.35 11.45 11.5 11.13 11.6 11.4 11.45 11.35 11.16 11.25 11.45 11.5 11.35 11.65 11.35 11.4 11.55 11.3 11.14 11.16 11.4 11.5 11.65
6 11.56 11.6 11.66 11.5 11.75 11.45 11.35 11.4 11.55 11.6 11.45 11.14 11.6 11.16 11.55 11.75 11.45 11.35 11.4 11.54 11.23 11.35 11.53 11.54
7 11.75 11.5 11.76 11.6 11.5 11.42 11.65 11.6 11.35 11.53 11.55 11.43 11.18 11.71 11.6 11.65 11.55 11.65 11.34 11.45 11.45 11.55 11.43 11.5
8 11.65 11.55 11.54 11.45 11.35 11.16 11.25 11.54 11.65 11.54 11.3 11.12 11.16 11.54 11.55 11.45 11.5 11.16 11.65 11.35 11.35 11.3 11.45 11.6
9 11.55 11.16 11.35 11.16 11.25 11.45 11.43 11.18 11.43 11.54 11.65 11.34 11.43 11.16 11.4 11.45 11.45 11.45 11.5 11.65 11.45 11.24 11.45 11.4
10 11.45 11.5 11.55 11.6 11.45 11.14 11.16 11.54 11.35 11.16 11.23 11.24 11.22 11.3 11.14 11.16 11.4 11.45 11.5 11.34 11.54 11.35 11.4 11.16
11 11.34 11.36 11.5 11.35 11.53 11.55 11.54 11.5 11.65 11.12 11.23 11.3 11.34 11.45 11.45 11.55 11.45 11.35 11.53 11.25 11.4 11.55 11.45 11.26
12 11.45 11.35 11.16 11.25 11.5 11.5 11.34 11.16 11.55 11.43 11.18 11.71 11.35 11.35 11.3 11.45 11.35 11.16 11.55 11.45 11.5 11.63 11.8 11.26
13 11.4 11.55 11.6 11.16 11.25 11.6 11.27 11.16 11.12 11.16 11.54 11.55 11.45 11.24 11.23 11.26 11.34 11.18 11.23 11.4 11.45 11.65 11.5 11.17
5unit no
batch no
1 2 3 4 176 7 8 9 10 11 12 13 14 15 16 2418 19 20 21 22 23
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Table 3: The measured thickness of the selected unites
1 7.65 7.5 7.56 7.7 7.5 7.6 7.57 7.55 7.45 7.47 7.6 7.6 7.6 7.65 7.5 7.5 7.6 7.57 7.54 7.57 7.56 7.6 7.6 7.5
2 7.5 7.75 7.57 7.65 7.58 7.7 7.56 7.56 7.62 7.45 7.67 7.5 7.45 7.63 7.59 7.38 7.45 7.6 7.43 7.65 7.54 7.55 7.54 7.47
3 7.65 7.54 7.47 7.57 7.56 7.6 7.36 7.59 7.38 7.56 7.45 7.5 7.68 7.5 7.55 7.58 7.57 7.63 7.65 7.54 7.65 7.63 7.5 7.5
4 7.65 7.5 7.55 7.58 7.55 7.56 7.62 7.64 7.55 7.68 7.5 7.56 7.65 7.6 7.7 7.56 7.55 7.5 7.63 7.7 7.56 7.57 7.45 7.66
5 7.56 7.34 7.56 7.57 7.67 7.5 7.55 7.75 7.55 7.44 7.56 7.45 7.56 7.56 7.5 7.4 7.5 7.67 7.36 7.58 7.61 7.57 7.56 7.55
6 7.17 7.27 7.55 7.67 7.47 7.55 7.75 7.54 7.56 7.45 7.5 7.47 7.61 7.55 7.56 7.5 7.4 7.55 7.54 7.58 7.54 7.5 7.55 7.6
7 7.76 7.67 7.46 7.57 7.78 7.61 7.3 7.44 7.5 7.56 7.55 7.55 7.6 7.45 7.46 7.55 7.56 7.63 7.45 7.45 7.45 7.55 7.55 7.6
8 7.55 7.56 7.62 7.66 7.57 7.45 7.66 7.5 7.6 7.45 7.56 7.4 7.54 7.65 7.45 7.65 7.56 7.66 7.47 7.42 7.6 7.6 7.56 7.45
9 7.67 7.5 7.55 7.5 7.45 7.6 7.45 7.5 7.5 7.5 7.57 7.63 7.6 7.54 7.36 7.5 7.55 7.58 7.57 7.63 7.45 7.68 7.5 7.55
10 7.47 7.57 7.56 7.6 7.6 7.65 7.44 7.56 7.56 7.45 7.56 7.45 7.5 7.45 7.56 7.65 7.5 7.64 7.61 7.44 7.57 7.65 7.6 7.7
11 7.68 7.5 7.56 7.65 7.5 7.65 7.45 7.56 7.6 7.5 7.4 7.57 7.54 7.6 7.4 7.56 7.45 7.57 7.41 7.46 7.55 7.56 7.56 7.5
12 7.6 7.6 7.56 7.43 7.58 7.53 7.42 7.46 7.54 7.62 7.65 7.7 7.44 7.46 7.46 7.42 7.55 7.65 7.55 7.53 7.45 7.55 7.6 7.47
13 7.56 7.5 7.75 7.57 7.65 7.58 7.7 7.56 7.56 7.62 7.45 7.67 7.5 7.45 7.63 7.6 7.56 7.55 7.65 7.53 7.56 7.4 7.5 7.6
2418 19 20 21 22 2312 13 14 15 16 176 7 8 9 10 11unit no
batch no
1 2 3 4 5
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Table 4: The mean and the standard deviation for each dimension
St andard
deviat ion
mean
St andard
deviat ion
mean
St andard
deviat ion
mean
0.0610 7.5642 0.1463 11.5004 24.0129 0.2573
0.0926 7.5579 0.1793 11.4483 24.0088 0.2803
0.0827 7.5504 0.1521 11.5246 24.0792 0.2416
0.0671 7.5863 0.1605 11.4679 24.0942 0.1597
0.0941 7.5383 0.1522 11.3975 23.9538 0.1589
0.1166 7.5179 0.1607 11.4775 23.9888 0.1201
0.1062 7.5438 0.1370 11.5292 24.0259 0.1992
0.0829 7.5496 0.1690 11.4233 23.9921 0.1411
0.0756 7.5388 0.1429 11.3967 23.8613 0.1942
0.0774 7.5558 0.1522 11.3471 24.0050 0.1850
0.0776 7.5325 0.1285 11.4167 24.0450 0.1322
0.0812 7.5342 0.1718 11.4054 24.0113 0.1606
0.0821 7.5708 0.1702 11.3525 24.0142 0.1615
Average
=0.084396
Average
=7.549263
Average
=0.155592
Average
=11.43747
Average
=24.00709
Average
=0.183968
T hickness widt h lengt h
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172
a: the mean chart
b: the standard deviation chart
Figure (1): Control chart for the brick length a: the mean chart b: the standard deviation chart
23.8
23.85
23.9
23.95
24
24.05
24.1
24.15
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
T
h
e
m
e
a
n
Patch number
L.C.L = 23.8907
U.C.L = 24.1232
̿= 24.007
0
0.05
0.1
0.15
0.2
0.25
0.3
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
T
h
e
s
ta
n
d
a
rd
d
e
v
a
ti
o
n
Patch number
L.C.L =0.10210
U.C.L = 0.26583
σ̅=0.183968
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173
a: the mean chart
b: the standard deviation chart
Figure (2): Control chart for the brick width a: the mean chart b: the standard deviation chart
11.3
11.35
11.4
11.45
11.5
11.55
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
T
h
e
m
e
a
n
Patch number
L.C.L = 11.3391
U.C.L = 11.5358
̿= 11.43747
0
0.05
0.1
0.15
0.2
0.25
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
T
h
e
s
ta
n
d
a
rd
d
e
v
ia
ti
o
n
Patch number
L.C.L =0.086496
U.C.L = 0.22483
σ̅=0.155592
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174
a: the mean chart
b: the standard deviation chart
Figure (3): Control chart for the brick thickness a: the mean chart b: the standard deviation chart
7.48
7.5
7.52
7.54
7.56
7.58
7.6
7.62
7.64
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
T
h
e
m
e
a
n
Patch number
L.C.L = 7.4957
U.C.L = 7.6022
̿= 7.495
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
T
h
e
s
ta
n
d
a
rd
d
e
v
ia
ti
o
n
Patch number
L.C.L =0.04678
U.C.L = 0.12181
σ̅=0.0853
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a- method of width test
b- method of thickness test
Figure (4): method of tests a- method of width test b- method of thickness test