1

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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[20] http://www.metalsteelsaudi.com/?page_id=17

[21] ASTM A706/A706M - 2014, Standard Specification for Deformed and Plain Low-Alloy Steel Bars

for Concrete Reinforcement. ASTM standards, Philadelphia: American Society for Testing and Materials.

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