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Variability of Chemical Analysis of Reinforcing Bar Produced in Saudi Arabia
A. Salman1, F. Djavanroodi2
1Department of Civil Engineering, Prince Mohammad Bin Fahd University, Al Khobar, KSA 2Department of Mechanical Engineering, Prince Mohammad Bin Fahd University, Al Khobar, KSA
Abstract: In view of the importance and demanding roles of steel rebar’s in the reinforced concrete
structures, accurate information on the properties of the steels is important at the design stage. In the
steelmaking process, production variations in chemical composition are unavoidable. Included in this
variation is the residual element content of steels produced from scrap. The application of statistics by
engineers dates back a long while in solving industrial, management, and research problems. The aim of
this work is to study the variability of the chemical composition of reinforcing steel produced throughout
the Saudi Arabia by experimentation and asses the quality of steel rebar’s which satisfy the minimum
requirements established by ASTM International A615. The variability of the chemical composition of steel
reinforcing bars is evaluated and expressions are developed to represent the probability distribution
functions for different chemical. 68 samples of ASTM A615 Grade 60 from different manufacturers were
collected and tested using the Spectrometer test to obtain Chemical Compositions. A statistical analysis of
bar Chemical Composition is conducted.
EasyFit (5.6) software is utilized to determine the distribution type and to perform the statistical analysis.
The analysis showed that chemical compositions follow different types of continuous distributions. Finally,
control charts are generated for these compositions in order to identify values above or below the 3 sigma.
Results showed that some compositions are above the upper line of the control chart (UCL).
Finally, the analyses show that less than 3% of the steel failed to meet minimum ASTM standards for
chemical composition.
Keywords: reinforcement, chemical composition, statistics, Carbon, Phosphor.
1. Introduction Conventional reinforced concrete is a composite material of reinforcing steel bars embedded in a
hardened concrete matrix. The accurate information on the properties of the reinforcing steels as a
construction material is important at the design or construction stage. There are many codes which specify
the limits on the properties and testing procedures of the steel rebar. These are ASTM A615, BS4449, ISO
6935-2 etc. Saudi Arabia have adopted ASTM A615 standard [1] for the steel rebar testing. Reinforcing
bars tests in most construction sites have been restricted to tensile and bend tests with little or no information
about chemical composition as they relate to the structural performances of the bars.
Chemical composition variations in producing reinforcing steel bars are unavoidable. Table 1 gives the
list of chemical ingredients that influences the property of steel rebar’s [2]. Carbon is the main strengthening
element that participates in two strengthening mechanisms, solid solution and second phase formation
(cementite). Although carbon increasing the strength (mainly the tensile TS), but on the other hand decrease
the ductility and Hardness, in addition to affecting the weldability [3]. The carbon equivalent represents the
contribution of carbon and other elements to the formation of structures susceptible of hydrogen
embrittlment during welding. In the carbon equivalent diagram (Figure 1) the transformation is
schematically represented. The rebar steels moved from a region of optimum-medium weldability to region
of high risk weldability. The ASTM A615 reflects this problem and explicitly excludes the weldbality.
Other properties of the rebar are compromised when the carbon steel with medium carb on content is used
for fabricating rebar. Among these is the elastic - plastic behavior. Most theories of concrete reinforced
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structure design considers that the steel in the structure deforms elastically and then it will yield plastically
at constant stress. The elastic –perfectly plastic behavior of the steel is assumed by most of the model or
code for earthquake resistance construction. Metallurgically, hot rolled plain low carbon steel (carbon
content less than 0.3 wt. %) produces steel with near elastic-perfectly plastic behavior (i.e. stress – strain
curve with wide Luders deformation after yielding). One method to fabricate steel rebar with high strength
combined with high ductility, weldability and toughness is Tempcore process. In this method hot rolled
deformed bars are quenched at the end of rolling mill by applying high pressure jets of cold water on the
red hot steel surface. This process hardens a crust near the steel surface while the bar core remains with
high ductility. This procedure produces steel with low carbon, high strength, high ductility, good weldable
property and tough material [4].
Table 1. Influence of different chemical ingredients in steel on properties of rebars [2]
Chemicals Property Effects on the Rebar’s
Carbon (C)
Hardness,
strength,
weldability and
brittleness
Higher carbon contributes to the tensile strength of steel, that is,
higher load bearing capacity and vice versa. Lower carbon
content less than 0.1 percent will reduce the strength. Higher
carbon content of 0.3 percent and above makes the steel bar
unweldable and brittle.
Manganese
(Mn)
Strength and
yield strength
Higher manganese content in steel increases the tensile strength
and also the carbon equivalent property.
Sulphue (S)
It is impurity in
steel which
increases its
brittleness.
Presence of sulphur should be limited. Presence of higher
sulphur makes the bar brittle during twisting, as higher sulphur
content brings the hot shot problem during rolling
Phosphorus (P)
It is an impurity
which increases
strength brittleness
Higher phosphorus content contributes to the increase in
strength and corrosion resistance properties but brings
brittleness due to the formation of low euctoid phosphicles in the
grain boundary. Also lowers the impact and value at subzero
temperature level (transition temperature).
Copper (Cu)
Strength and
corrosion
resistance
Being a pearlite stabiliser, it increases the strength and resistance
corrosion property
Chromium (Cr)
Weldability
and corrosion
resistance
Present as an impurity from the scrap and influences carbon
equivalent; weldability and increases corrosion resistance
property.
Carbon
Equivalent
(CE or Ceq)
Hardness,
tensile strength
and weldability
This property is required to set the cooling parameters in TMT
(Thermo mechanically treated) process and a slight variation in
carbon equivalent may alter the physical properties. In case of
CTD (Cold twisted deformed) bars, carbon equivalent has a
maximum limit of 0.42 percent but there is no lower limit
prescribed. As such, as long as the chemical composition and
physical properties of raw materials are within specified limits,
the variation in carbon equivalent as in the case of TMT bars.
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Figure 1. Carbon – carbon equivalent diagram indicating the area of optimum weldability, regular and
high risk of cold crack formation [4].
There has been number of statistical studies dealing specifically with the variability of the mechanical
properties of reinforcing steel [5-17]. In these studies, variations in yield and tensile strengths were
examined. These variations were believed to be caused by variation in the rolling practices and quality
control measures used by different manufacturers, as well as possible variations in cross-sectional area,
steel strength, and rate of loading. On the other hand there has been very few studies on variability of
chemical composition reinforcing steel [18, 19]. Jibrin and Ejeh [19] studied the Chemical composition of
reinforcing steel in the Nigerian Construction Industry. A total of 14 companies supplied nineteen samples
were tests. Most of the bars showed absence of some element such as Molybdenum, Vanadium, etc which
is a strength and coefficient of weldability determinants BS4449. Also, it is shown that the high percentage
of elements such as Silicon and Phosphorus impacted negatively on the strength and deformation
characteristics of the bars.
Saudi Arabia’s steel demand has made the country one of the largest consumer in the GCC region. The
country also accounts for significant number of construction activities in the Middle-East region. Over the
past decade, steel consumption in the Kingdom has increased considerably buoyed by construction boom,
growing investment in the real estate sector and rapid infrastructure developments. In addition, the steel
industry has witnessed tremendous growth in terms of production, as various players are expanding their
production capacities to meet the soaring steel demand [20].
The purpose of this study is to assess the quality of rebar’s manufactured in KSA. The tasks to deliver
these objectives will cover mechanical and the chemical composition testing of the rebars produced from
all the steel manufacturing plants in the KSA and to derive and investigate the relevant parameters related
to the quality of reinforcing bars. This paper reports on the variability of the chemical composition of
reinforcing steel produced throughout the Saudi Arabia by experimentation and asses the quality of steel
rebar’s which satisfy the minimum requirements established by ASTM International A615. The variability
of the chemical composition of steel reinforcing bars is evaluated and expressions are developed to
represent the probability distribution functions for different chemical. 68 samples ASTM A615 Grade 60
from different manufacturers were collected and tested using the Spectrometer test to obtain Chemical
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Compositions. A statistical analysis of bar Chemical Composition is conducted. Trends in the data are
evaluated based on production mill. Normal Q-Q plots and histogram are developed to represent the
probability distribution functions for different chemical elements in all the bars.
2. Experimental method
Samples of steel bars ASTM A615 Grade 60 were collected and labeled from eight local steel
manufacturing companies in Saudi Arabia as shown in Table 2. Seventy one specimens were randomly
selected from the manufactures stockpiled. All the samples were prepared and tested for the chemical
properties of the steel using a Spectrolab Foundry Master X-lin analytical instrument. These tests were
performed at three different laboratories namely Saudi Arabia standard organization, SABIC and Imperial
College London.
Table 2: List of steel rebars manufactures
Usaimi SABIC Al Rajhi Al Ittefaq Jazira Watania Taybah Al Yamamah
US HA RA IT JA WA TA YA
3. Results and Discusion
The chemical analysis of the tests carried on the steel samples shows that the steel bars from these
manufacturers possessed percentage average Carbon, Phosphors, Sulphuer, Copper, Chromium,
Manganese and Carbon Equivalent contents of 0.26, 0.02, 0.013, 0.079, 0.061, 0.852 and 0.402,
respectively. The results of the chemical tests are presented in Table 3.
EasyFit 5.6 is utilized to obtain necessary statistical results. Table 4 includes a summury of statistical
analysis of chemical compositions. Table 5 shows full statisctal results of the ten chemical compositions.
These compositions follow different types of continuous distributions as depicted in Figure 2. Mean,
standard deviation, and other statistical functions are determined according to distribution type. Carbon (C)
Copper (Cu), and Manganese (Mn) follow Generalized Extreme Value distribution; Phosphorus (P) follows
Log-Logistic distribution; Sulphur (S) follows Log-Pearson distribution; Chrome (Cr) follows Weibull
distribution, Molybdenum (Mo) follows Generalized Pareto distribution; Nickel (Ni) follows Fatique Life
distribution; Vanadium (V) follows Johnson SB distribution; Silicon (Si) follows Gamma distribution; and
Carbon Equivalent (C.E.) follows Dagum. Carbon (C) is the only composition that has left skewed, the
other compositions have right sekewed. Phosphorus (P) has highet value of coefficient of variation (CV),
which is a function of mean and standard deviation. While, Carbon (C) has the lowest value of CV.
Furthermore, control charts are generated for each chemical composition to verify samples that are
below 3 sigma or more than 3 sigma, as shown in Figure 3. Carbon (C), Sulphur (S), Molybdenum (Mo),
Vanadium (V), and Manganese (Mn) , and Carbon Equivalent (C.E.) are 100% validation. All values
between the upper control line (UCL) and the lower control line (LCL). One sample has Copper (Cu)
upper the control line, the validation of Phosphorus (P) is 98%. Finally, two samples have Phosphorus
(P), Chrome (Cr), Nickel (Ni), and Silicon (Si) more than the upper control line, the validation of the
previous four chemical compositions are 97%. These results are considered acceptable according to
ASTM standards.
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Table 3. Chemical composition A 615 Grade 60 Reinforcement steel rebar’s
No Sample Identification Sample Diameter (mm) C% P% S% Cu% Cr% Mo% Ni% V% Si% Mn% C.E.
1 US-06-1 6 0.189 0.018 0.012 0.08 0.06 0.0012 0.03 0 0.21 1.03 0.370143
2 US-08-2 8 0.0982 0.031 0.021 0.01 0.39 0.001 0.14 0.0069 0.2 0.43 0.215407
3 US-08-1 8 0.114 0.025 0.017 0.01 0.37 0 0.01 0.0084 0.186 0.372 0.21291
4 US-12-2 12 0.322 0.016 0.008 0.1 0.11 0.019 0.06 0.011 0.266 1.08 0.51702
5 US-12-3 12 0.318 0.017 0.008 0.09 0.11 0.019 0.06 0.011 0.262 1.09 0.514437
6 US-14-1 14 0.228 0.011 0.005 0.07 0.09 0 0.05 0.0039 0.276 0.24086
7 US-14-2 14 0.313 0.018 0.024 0.3 0.08 0.03 0.09 0.0046 0.236 1.36 0.558607
8 US-14-3 14 0.319 0.009 0.016 0.25 0.08 0.03 0.09 0.001 0.226 1.32 0.55705
9 US-16-1 16 0.338 0.024 0.018 0.11 0.14 0.02 0.05 0.0083 0.322 1.31 0.574353
10 US-16-2 16 0.32 0.019 0.015 0.1 0.15 0.021 0.05 0.004 0.29 1.31 0.557513
11 HA-12-1 12 0.19 0.015 0.007 0.02 0.01 0.01 0.02 0.001 0.22 0.88 0.338867
12 HA-12-3 12 0.19 0.009 0.006 0.05 0.03 0.01 0.03 0.002 0.22 0.83 0.333683
13 HA-12-2 12 0.19 0.01 0.005 0.03 0.01 0.01 0.02 0 0.22 0.89 0.340883
14 HA-14-1 14 0.32 0.011 0.015 0.05 0.01 0 0.02 0.003 0.22 0.67 0.434617
15 HA-14-2 14 0.3 0.007 0.013 0.06 0.01 0 0.02 0.003 0.22 0.72 0.4232
16 HA-14-3 14 0.31 0.007 0.011 0.05 0.01 0 0.02 0.003 0.22 0.7 0.429617
17 HA-14-4 14 0.306 0.097 0.012 0.12 0.02 0.0026 0.04 0.0047 0.281 0.726 0.433478
18 HA-16-1 16 0.3 0.008 0.017 0.03 0.02 0 0.02 0.005 0.23 0.61 0.404917
19 HA-16-2 16 0.3 0.007 0.014 0.02 0.01 0 0.02 0.003 0.22 0.69 0.4172
20 HA-16-3 16 0.3 0.008 0.017 0.02 0.02 0 0.02 0.003 0.2 0.67 0.414867
21 HA-16-4 16 0.279 0.014 0.007 0.03 0.02 0.001 0.03 0.0068 0.265 0.709 0.400717
22 HA-18-1 18 0.288 0.015 0.007 0.03 0.02 0.001 0.02 0.0049 0.25 0.764 0.418573
23 HA-20-1 20 0.29 0.009 0.004 0.02 0.01 0.01 0.02 0.001 0.33 0.86 0.435533
24 HA-20-2 20 0.29 0.011 0.004 0.01 0 0.01 0.01 0.001 0.34 0.86 0.433783
25 HA-20-3 20 0.28 0.009 0.005 0.03 0.01 0.01 0.02 0.001 0.33 0.84 0.42245
26 HA-20-4 20 0.293 0.017 0.011 0.04 0.02 0.001 0.03 0.0049 0.361 0.867 0.44149
27 HA-20-5 20 0.293 0.013 0.006 0.03 0.02 0.001 0.21 0.0045 0.344 0.878 0.452113
28 HA-25-1 25 0.28 0.007 0.005 0.02 0.01 0.01 0.02 0.001 0.41 0.96 0.4422
29 HA-25-2 25 0.28 0.01 0.004 0.04 0.01 0.01 0.03 0.002 0.43 1 0.449767
30 HA-25-3 25 0.3 0.011 0.005 0.03 0.01 0.01 0.02 0.001 0.41 1.01 0.470783
31 HA-25-4 25 0.28 0.015 0.011 0.05 0.02 0.001 0.27 0.0054 0.501 1.01 0.464523
32 HA-32-2 32 0.297 0.014 0.01 0.05 0.02 0.001 0.03 0.0047 0.487 0.951 0.45976
33 RA-12-1 12 0.34 0.011 0.009 0 0.02 0.011 0.01 0.002 0.264 1.41 0.57708
34 RA-12-2 12 0.339 0.009 0.008 0 0.01 0.011 0.01 0.001 0.266 1.41 0.57518
35 RA-12-3 12 0.338 0.01 0.009 0 0.02 0.011 0.01 0.002 0.27 1.42 0.576747
36 RA-16-3 16 0.212 0.008 0.023 0.24 0.05 0.012 0.08 0.0031 0.232 0.713 0.345283
37 RA-16-1 16 0.215 0.004 0.022 0.23 0.05 0.013 0.07 0 0.204 0.716 0.348323
38 RA-16-2 16 0.212 0.005 0.028 0.23 0.05 0.012 0.07 0 0.193 0.707 0.343843
39 RA-16-3 16 0.214 0.005 0.027 0.23 0.05 0.01 0.07 0 0.2 0.745 0.352217
40 RA-20-2 20 0.351 0.011 0.016 0.13 0.05 0.0012 0.05 0.0047 0.251 1.45 0.602923
41 IT-12-1 12 0.21 0.01 0.006 0.05 0.02 0.009 0.02 0 0.236 0.926 0.368403
42 IT-14-1 14 0.268 0.011 0.011 0.06 0.03 0.0014 0.02 0.0046 0.217 0.645 0.380512
43 IT-16-1 16 0.201 0.018 0.013 0.09 0.06 0.0036 0.03 0.0053 0.247 1.04 0.383481
44 IT-20-4 20 0.269 0.007 0.009 0.1 0.02 0.01 0.04 0 0.179 0.687 0.3898
45 IT-25-3 25 0.287 0.009 0.011 0.07 0.04 0.011 0.03 0.0043 0.253 0.711 0.4121
46 IT-25-1 25 0.24 0.006 0.008 0.06 0.04 0.011 0.02 0 0.187 0.715 0.365447
47 JA-14-1 14 0.248 0.195 0.0195 0.13 0.11 0.018 0.08 0.0114 0.24 0.743 0.388583
48 JA-14-3 14 0.24 0.019 0.013 0.01 0.12 0.02 0.07 0.005 0.182 0.739 0.378017
49 JA-14-2 14 0.229 0.013 0.009 0.09 0.12 0.02 0.07 0.009 0.205 0.779 0.375283
50 JA-16-2 16 0.269 0.022 0.012 0.09 0.08 0.015 0.05 0.0095 0.285 0.753 0.406
51 JA-16-1 16 0.264 0.016 0.009 0.07 0.08 0.015 0.04 0.005 0.231 0.761 0.401783
52 JA-16-3 16 0.26 0.019 0.011 0.08 0.08 0.02 0.04 0.004 0.218 0.755 0.397033
53 JA-20-2 20 0.239 0.021 0.021 0.13 0.08 0.0092 0.06 0.008 0.269 0.734 0.374599
54 JA-20-1 20 0.24 0.02 0.015 0.11 0.09 0.0166 0.05 0.003 0.22 0.733 0.375785
55 JA-25-3 25 0.259 0.02 0.016 0.06 0.07 0.0071 0.05 0.0074 0.257 0.763 0.396285
56 JA-25-1 25 0.245 0.017 0.013 0.06 0.07 0.015 0.04 0 0.203 0.756 0.3812
57 JA-25-2 25 0.26 0.017 0.012 0.06 0.07 0.014 0.04 0.002 0.2 0.753 0.39552
58 JA-32-1 32 0.239 0.019 0.031 0.11 0.07 0.0087 0.05 0.0088 0.269 0.931 0.405363
59 JA-32-2 32 0.232 0.016 0.034 0.1 0.07 0.018 0.04 0.003 0.209 0.903 0.39334
60 WA-14-1 14 0.254 0.211 0.032 0.13 0.08 0.0038 0.04 0.0053 0.295 0.718 0.386311
61 WA-16-1 16 0.237 0.017 0.017 0.12 0.08 0.0067 0.05 0.0068 0.188 0.531 0.338186
62 WA-18-1 18 0.304 0.018 0.027 0.13 0.08 0.0028 0.05 0.006 0.39 0.703 0.434261
63 TA-14-1 14 0.312 0.021 0.018 0.1 0.11 0.001 0.04 0.0123 0.328 0.646 0.433917
64 TA-16-1 16 0.296 0.024 0.023 0.1 0.18 0.0011 0.04 0.0065 0.378 0.561 0.411328
65 YA-16-2 16 0.243 0.011 0.007 0.05 0.06 0 0.04 0.0061 0.29 0.855 0.39414
66 YA-18-1 18 0.231 0.008 0.004 0.06 0.06 0.0025 0.04 0.0046 0.269 0.872 0.385323
67 YA-20-1 20 0.208 0.009 0.008 0.06 0.07 0.0025 0.04 0.0048 0.273 0.878 0.364303
68 YA-25-1 25 0.22 0.008 0.006 0.06 0.05 0.0013 0.05 0.0044 0.259 0.831 0.367034
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The result of Spectormeter tests on steel rebar chemical composition are shown in Table 3. The
ASTM A615 does not specify any restriction on Carbon content; the only restriction is on the
phosphorus content with a maximum of 0.06 %.and 0.075% from the heat of steel and the product,
respectively. The analyses shows that out of the 68 test performed only two samples did not meet the
standard i.e. less than 3% of the steel failed to meet minimum ASTM standards for chemical
composition.
The statistical analysis including the values of maximum, minimum, average, median and standard
deviation for each element is calculated and shown in Table 4. The carbon equivalan was calculated
using the following equation [21].
Moreover, it shows that chemical compositions among samples is not normally distributed which
indicates variability among manufacturers row material used for producing rebar’s. It is evident that,
for most bars sizes of A 615 Grades 60, the mean for the chemical composition is not situated at the
midpoint of the data range, indicating non-normal distributions.
5. Conclusion, Recommendations and Benefits
Chemical composition tests conducted on 68 samples of locally manufactured steel reinforcing rebar’s in
Saudi Arabia. The results of the tests have shown that less than 3% of the steel failed to meet minimum
ASTM standards for chemical composition. It is evident that, for most bars sizes of A 615 Grades 60, the
mean for the chemical composition is not situated at the midpoint of the data range, indicating non-normal
distributions, therefore, the characteristic chemical composition of locally produced steel bars is not
consistent. The following recommendation and benefits can be deduced from this study.
1. The results are very important for the long term financial stability and mechanical viability and structural
safety for this sector in KSA
2. Reinforcing bars tests in most construction sites have been restricted to tensile and bend tests with little
or no information about chemical composition as they relate to the structural performances of the bars.
Saudi Arabia Standard organization should make study on chemical composition of the rebar at least every
5 years to collect a large set of data from the manufacturers as to observe the consistency in the production
process.
3. Saudi Arabia Standard organization board should make sure, the standard given by them is strictly
observed by all the local producers.
4. The expected immediate and long term benefits from this study include:
Assessment of current production of rebar’s in Kingdom;
Identification of potential improvements to existing standard, for reduced risks of accepting
lower quality materials;
Using variability analysis procedures for assessing product variability based on production data
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Acknowledgment:
This research was supported by Prince Mohammad Bin Fahad University. The support is greatly
acknowledged.
We are also thankful to Dr. M. M. Al Motari at Saudi Arabia Standard Organization (SASO) for providing
their laboratories and assistance for the project. The support is greatly acknowledged.
We would like to show our gratitude to Dr K. F. Al-Hajeri, Mr M. Yaghoub at SABIC, Saudi Basic
Industries Corporation who provided experimental assistance for the project. The support is greatly
acknowledged.
We would like to show our gratitude to Mr. H. M. Dowla at Al Ittifaq steel that provided experimental
assistance for the project. The support is greatly acknowledged.
Finally, we thank I. Babbili1; I. Ansari1; R. Al-Roqaiti1; O. Qassar2; N. Qahtani1; S. Aladhyani1; A.
Alunaiz1; M. Almatrook1; M. Najar3, A. Asiz1 for their valuable input and assistance.
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Table 4. Statistical analysis of Chemical Composition of A 615 Grade 60 steel rebar’s
Elements C% P% S% Cu% Cr% Mo% Ni% V% Si% Mn% C.E.
Distribution
Type
Generalized
Extreme
Value
Log-
Logistic
Log-
Pearson
Generalized
Extreme
Value
Weibull Generalized
Pareto
Fatique
Life
Johnson
SB Gamma
Generalized
Extreme
Value
Dagum
Parameters k, σ, μ α, β, γ α, β, γ k, σ, μ α, β, γ k, σ, μ α, β, γ γ, δ, λ
ξ α, β, γ k, σ, μ
k,α, β, γ
Maximum 0.35 0.211 0.03 0.3 0.39 0.03 0.27 0.012 0.50 1.45 0.60
Minimum 0.098 0.004 0.004 0 0 0 0.01 0 0.17 0.37 0.21
Mean 0.2 0.02 0.01 0.07 0.06 0.008 0.04 0.004 0.26 0.85 0.41
Standard
deviation 0.05 0.03 0.007 0.06 0.06 0.007 0.04 0.003 0.07 0.23 0.07
Coefficient of
Variation (CV) 19% 168% 56% 82% 109% 89% 89% 75% 27% 28%
19%
Skewness Left Right Right Right Right Right Right Right Right Right Right
Validation of
Control Chart
(± 3 σ ) 100 % 97 % 100 % 98% 97% 100% 97% 100% 97% 100% 100%
9
(a) Carbon (C) (b) Phosphorus (P) (c) Sulphur (S)
(d) Copper (Cu) (e) Chrome (Cr) (f) Molybdenum (Mo)
(g) Nickel (Ni) (h) Vanadium (V) (i) Silicon (Si)
(i) Manganese (Mn) (j) Carbon Equivalent (C.E.)
Table 5. Statistical analysis of chemical compositions
10
(a) Carbon (C): (b) Phosphorus (P) (c) Sulphur (S)
Generalized Extreme Value Log-Logistic Log-Pearson
(d) Copper (Cu) (e) Chrome (Cr) (f) Molybdenum (Mo) Generalized Extreme Value Weibull Generalized Pareto
(g) Nickel (Ni) (h) Vanadium (V) (i) Silicon (Si) Fatique Life Johnson SB Gamma
(i) Manganese (Mn) (j) Carbon Equivalent (C.E.)
Generalized Extreme Value Dagum
Figure 2. Statistical analysis of chemical compositions
11
(a) Carbon (C): (b) Phosphorus (P) (c) Sulphur (S)
100% 97% 100%
(d) Copper (Cu) (e) Chrome (Cr) (f) Molybdenum (Mo) 98% 97% 100%
(g) Nickel (Ni) (h) Vanadium (V) (i) Silicon (Si) 97% 100% 97%
(i) Manganese (Mn) (j) Carbon Equivalent (C.E.)
100% (one point is missing) 100%
Figure 3. Control charts of chemical compositions