Identification and Determination of the Desired QET in Main Processes
These processes divided into relevant subprocesses based on the suggested QET are exhibited in Figure 3.2.
A Numerical Application of QET in the Determined Scope for Main Processes
• Product design (Quality Function Deployment + Value Engineering)
Bullethead drills with 27.8inch HSD, powerful explosive devices in which immediate and concentrated release of energy are stored can penetrate oil and natural gas. Intense pressure from the explosion creates holes in the wall of the well from which oil and gas flow out. These types of bullets contain no caps and are fired by authorized participants. The main specifications that meet customers’ requirements are presented in Table 3.1 (Karimi Gavareshki et al., 2017).
In this section, the proposed model for a bullethead drill of 27.8inch HSD is determined in triple matrices of quality function deployment (QFD).
FIGURE 3.2 Desired QET in main processes.
In the product design matrix (QFD matrix 1), the output is to select the product quantitative specifications:
Priority 1: Minimum diameter of arrival and departure
Priority 2: Minimum pressure
Priority 3: Maximum safe stretch
Priority 4: Gun degree
Priority 5: Gun diameter
TABLE 3.1
Specifications of Technical Product
N 
Description 
Specification 
1 
Gun thickness 
73 mm 
2 
Gun degree 
60 
3 
Bullet numbers per unit 
6spf 
4 
Bullet distances from one another 
50.8mm 
5 
Gun length 
1.5m6.3m 
6 
Permissible gun weight 
100kg. 50kg. 25kg 
7 
Maximum pressure 
25kpsi 
8 
Maximum safe stretch 
190klb 
9 
Minimum pressure 
Obars 
10 
Minimum diameter of arrival and departure 
86mm 
In the process design matrix (QFD matrix 2), the output is to select the manufacturing process requirements:
Priority 1: Permissible limit for the gun diameter Priority 2: Permissible limit for degree Priority 3: Permissible limit for the gun length
In the process control matrix (QFD matrix 3), the output is to select the process control requirements:
Priority 1: Performance on proposed steel Priority 2: Performance on proposed concrete Priority 3: Performance at a temperature of 190 °C
Finally, the proposed model in the Value Engineering (VE) matrix is determined together with prioritizing the product control tests:
Priority 1: Performance test at a temperature of 190 °C Priority 2: Performance test on proposed steel Priority 3: Performance test on proposed concrete
It should be noted that in the proposed model, we have used three matrices with four possible matrices in QFD.
Also, our focus is on the row requirements over the column requirements at each matrix in QFD. This means that the points in column (E) in each matrix are multiplied by the points in the same column. In fact, the reason why these points in the same column are selected is that the column requirements are satisfied such that the numbers between 1, 3, and 9 are chosen. The results of the proposed model can be
QFD Matrix 1 
Product’s quantitative specifications 
QFD parameters 

Bullethead drill. 27.8inch HSD 
Gun diameter7 3mm 
Gun degree=60 
Bullet numbers perunit6spf 
Bullet distances from one anotlier=50.8mm 
Gun length=l. 5m6.3m 
Permissible gun weight100kg50kg25kg 
Maximum pressure=25kpsi 
Maximum safe stretch 190klb 
Minimum pressureObar 
Minimum diameter of amval and departure86mm 
A (Importance degree) 
N (Organization assessment) 
P (Organization plan) 
В (Improving ratio) 
C (Correction factor) 
D (Absolute weight) 
E (Relative weight) 

Customer qualitative requirements 
Suitable performance of product 
9 
9 
9 
3 
3 
1 
1 
3 
3 
9 
5 
5 
5 
1 
1.5 
7.5 
24 
Good appearance of product 
1 
1 
1 
9 
9 
9 
9 
1 
1 
1 
3 
2 
4 
2 
1.2 
7.2 
23 

Product reliability 
3 
3 
3 
1 
1 
1 
1 
9 
9 
9 
4 
3 
5 
1.7 
1.5 
10.2 
33 

After sale services 
3 
3 
1 
1 
1 
1 
1 
1 
1 
1 
4 
3 
4 
1.3 
1.2 
6.2 
20 

Absolute weight 
398 
398 
358 
332 
332 
284 
284 
^{412} 
^{412} 
556 
3766 
Total 
31.1 
100 

Relativeveight 
l ^{1065} 
l ^{1064} 
1 ^{95} 
1 ^{88} 
1 ^{88} 
1 ^{15} 
1 ^{15} 
 10.9^{s} 
 10.9^{2} 
 14. S^{1} 
100 
FIGURE 3.3 Product design matrix.
seen in Figures 3.3 to 3.6 (Karimi Gavareshki et al., 2017). The relevant formulas are as follows (3.1):
В: Improving ratio P: Organization plan N: Organization assessment
QFD Matrix 2 
Manufacturing process requirements 
QFD parameters 

Bullethead drill. 27.8inch HSD 
Permissible limit for gun diameter =±0.5mm 
Permissible limit for degree ±0.5 
Permissible limit for bullet distances =±0.5mm 
Permissible limit for gun length ±0.1m 
Permissible limit for gun weights =±0.5kg 
Permissible limit for Pressure ±0.5kpsi 
A (Importance degree) 
К (Organization assessment) 
P (Organization plan) 
В (ImproMng ratio) 
C (Correction factor) 
D (Absolute weight) 
E (Relative weight) 

Product' s quantitative specifications 
Minimum diameter of arrival and departure = 86mm 
1 
1 
1 
1 
1 
1 
5 
5 
5 
1 
1.5 
7.5 
20 
Minimum pressure = Obar 
1 
1 
1 
1 
1 
1 
3 
2 
4 
2 
1.2 
7.2 
19 

Maximum safe stretch = 190klb 
1 
1 
1 
3 
1 
1 
4 
3 
4 
1.3 
1.5 
7.8 
21 

Gun degree = 60 
3 
9 
1 
3 
3 
1 
5 
5 
5 
1 
1.5 
7.5 
20 

Gun diameter = 73mm 
9 
3 
1 
3 
3 
1 
5 
5 
5 
1 
1.5 
7.5 
20 

Absolute weight 
300 
300 
100 
222 
180 
100 
1202 
Total 
37.5 
100 

Relative weight 
25^{1} 
2S^{2} 
8.3 
18.S^{3} 
15 
8.3 
100 
FIGURE 3.4 Process design matrix.
D: Absolute weight A: Importance degree В: Improving ratio C: Correction factor
E: Relative weight D: Absolute weight
QFD Matrix 3 
Process control requirements 
QFD parameters 

Bullethead drill, 27.8mch HSD 
Bullet inflicting no damage, no injury, no scratch 
Meetmg packaging requirements 
Performance on object steel according to instructions No 1 
Performance on object concrete according to instructions No.2 
Performance at a temperature of 190 °C according to instructions No.3 
A (Importance degree) 
N (Organization assessment) 
P (Organization plan) 
В (Improving ratio) 
C (Correction factor) 
D (Absolute weight) 
E (Relative weight) 

Manufacturing process requirements 
Permissible limit for gun diameter = ±0.5mm 
1 
1 
9 
9 
3 
5 
5 
5 
1 
1.5 
7.5 
35 
Permissible limit for degree = ±0.5 
1 
1 
9 
9 
3 
5 
5 
5 
1 
1.5 
7.5 
35 

Permissible limit for gun length = ±0.1 m 
1 
1 
9 
9 
9 
4 
3 
4 
1.3 
1.2 
6.2 
30 

Absolute weight 
100 
100 
900 
900 
4S0 
2480 
Total 
21.2 
100 

Relative weight 
4 
4 
36.3^{1} 
36.3^{2} 
19.3^{5} 
100 
FIGURE 3.5 Process control matrix.
• Suppliers Selection and Assessment (Time Series Analysis)
In a selected industry affiliated with DIO, a supplier assessment was carried out by a supervisor on site using a checklist prepared and arranged on a scale of 1000 points for a period of 9 years. The results are shown in Tables 3.2 to 3.4.
Value engineering in product control tests based on standard EN12973:2000 

Mam specifications m product control tests 
Total columns need 
Importance of testmg (I=N*A) 
Test cost per unit (Rials of IRI) 
Test cost C (normalized) 
Test Value (Yalue=I/C) 

Bullethead drill. 27.8mch HSD 
Ease of training and testmg 
Impact of testmg on mam function of product 
Correlation with other control tests 
Safety testing for person and environment 
Minimum environmental considerations 

Need 
0.15 
0.50 
0.20 
0.10 
0.05 
1 

product control tests headings 
Performance test on object steel 
4 
5 
5 
3 
2 
4.5 
750000 
0.42 
10.71^{2} 

Performance test on object concrete 
4 
4 
4 
3 
1 
3.75 
650000 
0.36 
10.42^{J} 

Performance test at temperature of 190 ^{n}C 
4 
3 
3 
4 
4 
3.3 
400000 
0.22 
15^{1} 

Total 
1S00000 
1 
36.13 
FIGURE 3.6 Value engineering matrix.
In this formula, b is the angle coefficient of the line equation. So, we have:
In this formula, (a) is the distance from (0, 0) on the Yaxis and («) is the number of data or samples. Therefore, we have:
TABLE 3.2
Supplier Data of Organization
N 
X based on year 
Y based on score (out of 1000) 
1 
2007 
650 
2 
2008 
700 
3 
2009 
720 
4 
2010 
750 
5 
2011 
730 
6 
2012 
710 
7 
2013 
800 
8 
2014 
820 
9 
2015 
780 
TABLE 3.3
Calculated Supplier Data (Three Years Moving Average)
N 
X based on year 
Y based on score (out of 1000) 
Sum of 3 years 
Average of 3 years 
1 
2007 
650 

2 
2008 
700 
2070 
690 
3 
2009 
720 
2170 
723 
4 
2010 
750 
2200 
733 
5 
2011 
730 
2190 
730 
6 
2012 
710 
2240 
747 
7 
2013 
800 
2330 
777 
8 
2014 
820 
2400 
800 
9 
2015 
780 
TABLE 3.4
Calculated Supplier data of Organization (Squares Minimum Method)
N 
X based on year 
Y based on score (out of 1000) 
Xj 
Xi^{2} 
Xi Yj 
1 
2007 
650 
4 
16 
2600 
2 
2008 
700 
3 
9 
2100 
3 
2009 
720 
2 
4 
1440 
4 
2010 
750 
1 
1 
750 
5 
2011 
730 
0 
0 
0 
6 
2012 
710 
1 
1 
710 
7 
2013 
800 
2 
4 
1600 
8 
2014 
820 
3 
9 
2460 
9 
2015 
780 
4 
16 
3120 
S 
6660 
0 
0 
1000 
As a result, we can write the equation related to the above line as follows:
To show the general equation related to the suppliers, we give for the variable X, two values such as ± 2
X= ± 2 and with calculating the corresponding values for Y:
To predict the supplier's score in the year 2016, in exchange for variable X, we place 5. So, we have:
Figure 3.7 shows the supplier’s score chart obtained by the squares minimum method.
• Production Control (Process Capability Analysis)
Appropriate specifications for a piece are set at 2.05 ± 0.02. If the size of the piece is less than the bottom limit of the specification, it is rejected; and if it exceeds the upper limit of the specification, it is corrected. Process Capability Analysis has been
FIGURE 3.7 Supplier's score chart by squares minimum method.
used to control the production of this piece. Assuming that the distribution of the production process is normal and under statistical control, the following results are obtained:
In this equation statement, the mean X, is in a subgroup, R, is the subgroup range, к is the number of subgroups, and n is the number of subgroup members.
1. Determine the process standard deviation.
So, we have: R = 0.016 Moreover, we have:
<7: Estimated standard deviation
d_{2}: Fixed coefficient related to the number of subgroup members In this example, for the four members in the subgroup, we will have:
2. Determine the process capability index (potential) CP and the process capability index (actual) CPK.
So, we have:
Moreover, we have:
USL is the upper limit and LSL is the lower limit of the piece tolerance. Therefore, we have:
Moreover, we have:
So, we have:
3. Calculate the standard deviation from the manufacturing process.
USL is the upper limit and LSL is the lower limit of the piece tolerance. Thus, we have:
Also, with the formula in the form of the same result is obtained.
4. What percentage of these pieces is rejected and what percentage needs correction?
• Production Control (Statistical Process Control for variable data)
Data on the internal diameter measurements of a sample series related to special project pieces are given in Table 3.5 (nominal diameter of the piece is 1.51 ± 0.33).
 1. What method of process analysis do you use?
 2. Define the control limits. (The upper and lower limits).
 3. Is the manufacturing process under control?
 1. Y&R
 2.1. The following formulas are used to determine the control limits of the mean value chart:
TABLE 3.5
Internal Diameter Data of a Piece under Four Groups
1 
1.50 
1.51 
1.50 
1.51 
1.505 
0.01 
2 
1.51 
1.52 
1.50 
1.51 
1.510 
0.02 
3 
1.50 
1.51 
1.51 
1.51 
1.507 
0.01 
4 
1.51 
1.51 
1.50 
1.51 
1.507 
0.01 
5 
1.50 
1.50 
1.51 
1.51 
1.505 
0.01 
6 
1.49 
1.50 
1.50 
1.50 
1.497 
0.01 
7 
1.50 
1.50 
1.51 
1.50 
1.502 
0.01 
8 
1.49 
1.51 
1.50 
1.50 
1.500 
0.02 
9 
1.50 
1.50 
1.50 
1.49 
1.497 
0.01 
10 
1.50 
1.49 
1.50 
1.51 
1.500 
0.02 
11 
1.50 
1.50 
1.50 
1.51 
1.502 
0.01 
12 
1.50 
1.49 
1.49 
1.50 
1.495 
0.01 
13 
1.50 
1.49 
1.49 
1.49 
1.492 
0.01 
14 
1.50 
1.48 
1.49 
1.49 
1.490 
0.02 
15 
1.49 
1.49 
1.50 
1.49 
1.492 
0.01 
16 
1.50 
1.49 
1.49 
1.49 
1.492 
0.01 
17 
1.49 
1.48 
1.49 
1.49 
1.487 
0.01 
18 
1.48 
1.49 
1.48 
1.49 
1.485 
0.01 
19 
1.48 
1.49 
1.49 
1.49 
1.487 
0.01 
20 
1.49 
1.50 
1.49 
1.49 
1.492 
0.01 
21 
1.49 
1.49 
1.48 
1.49 
1.487 
0.01 
22 
1.48 
1.47 
1.48 
1.49 
1.480 
0.02 
23 
1.47 
1.48 
1.49 
1.48 
1.480 
0.02 
24 
1.47 
1.48 
1.50 
1.49 
1.485 
0.03 
35.876 
0.32 
In this formula, X is the total mean value in all subgroups and к is the number of subgroups. So, we have:
In this formula, UCL^is the upper limit of the mean value control chart and A_{2} is the fixed coefficient and R is the mean value of ranges. So, we have:
In this formula, LCL^is the lower limit of the mean value control chart and A, is the fixed coefficient and R is the mean value of ranges. So, we have:
The value for A_{2} can be obtained from the table of coefficients and the value of R from the table given in the next section.
2.2. The following formulas are used to determine the control limits related to the range chart:
In this formula, R is the average of ranges in all subgroups and к is the number of subgroups. So, we have:
In this formula, UCL^ is the upper limit of the range control chart and D_{4 }is the fixed coefficient and R is the average of ranges. So, we have:
In this formula, LCL^ is the lower limit of the range control chart and D_{} }is the fixed coefficient and R is the average of ranges. So, we have:
Therefore:
The control limits of the mean value control chart are calculated as:
The control limits of the range control chart are calculated as:
 3. Analysis
 • Considering the data in Table 3.5, and comparing the data in columns of X, to X_{4} with those of the control limits of the mean value control chart, note that our data is not under control. (As there are some points that are outside of these control limits.).
 • Considering the data in Table 3.5, and comparing the data in column of R, with those of the control limits of the range control chart, note that our data is under control. (As there are no points that are outside of these control limits.)
So, in general, the manufacturing process related to these pieces is not under control.
The control charts on the mean value and range of the latter variable data are given in Figure 3.8.
As is shown, in the range chart, the data are under control, however, the mean value chart indicates that there are at least two types of outofcontrol patterns.
• Production Control (Statistical Process Control for descriptive data +
Descriptive Statistics—Pareto Chart)
Samples of four defects are detected in the inspection processes: Inhomogeneity, fragmentation, friction, and cracks. These defects are presented in Figure 3.9.
The data related to these four defects are provided in Table 3.6.
 • What process analysis method do you use?
 • Define control limits.
 • Is the manufacturing process under control?
 • Is the process capability index (actual) or C_{PK} calculable?
 • Can you prioritize the corrective actions with Pareto’s analysis?
 1. C technique
2. The following formulas are used to determine the control limits of the C technique:
FIGURE 3.8 Control charts for mean value and range of variable data.
FIGURE 3.9 Nonconformity of four defects.
In this formula, Cis the total average of nonconforming cases, and n is the total number of pieces. So, we have:
In this formula, UCL_{c} is the upper limit of C chart, and Cis the total average of nonconforming cases. So, we have:
TABLE 3.6
Number of the NonConformities in Project Pieces
N 
Inhomogeneity 
Fragmentation 
Friction 
Crack 
C, 
1 
0 
1 
0 
1 
2 
2 
0 
1 
2 
0 
3 
3 
0 
2 
0 
0 
2 
4 
0 
1 
0 
0 
1 
5 
0 
1 
0 
1 
2 
6 
1 
2 
0 
0 
3 
7 
1 
2 
0 
0 
3 
8 
0 
1 
1 
1 
3 
9 
0 
1 
2 
0 
3 
10 
1 
2 
0 
0 
3 
II 
0 
1 
1 
0 
3 
12 
1 
0 
1 
0 
2 
13 
0 
1 
2 
0 
3 
14 
1 
1 
1 
0 
3 
15 
1 
2 
1 
0 
4 
16 
1 
1 
0 
1 
3 
17 
1 
2 
1 
0 
4 
18 
1 
2 
1 
0 
4 
19 
0 
1 
1 
0 
2 
20 
0 
2 
0 
0 
2 
21 
1 
0 
1 
0 
2 
22 
0 
2 
0 
1 
3 
23 
0 
1 
2 
0 
3 
24 
0 
0 
1 
1 
2 
S 
10 
30 
18 
6 
64 
In this formula, LCL_{c} is the lower limit of C chart, and Cis the total
average of nonconforming cases. So, we have:
Therefore:
The control limits of C chart are calculated as:
3. Analysis
Considering the data in Table 3.6 and comparing the data in the column of Q with those of the control limits of the C chart, note that our data is under control (As there are no points that are outside of these control limits). The C chart is visible in Figure 3.10. As can be seen, the relevant chart shows the data that are under control.
4. The process being under control, we will have:
5. Considering the four types of nonconformities, we have listed them in Table 3.7.
Figure 3.11 shows the Pareto chart of prioritizing corrective actions. • Customer Satisfaction (Descriptive Statistics—Pareto Chart)
FIGURE 3.10 C control chart of nonconforming cases in project pieces.
TABLE 3.7
Registered NonConformities in the Project Pieces
N 
NonConformity (defects) 
Frequency 
1 
Inhomogeneity 
10 
2 
Fragmentation 
30 
3 
Friction 
18 
4 
Crack 
6 
S 
64 
FIGURE 3.11 Pareto chart of prioritizing corrective actions.
In order to analyze and examine the causes of customer complaints in the selected scope in one industry in DIO during the one year, the information relevant to these complaints are extracted and presented in Table 3.8.
The Pareto chart in Figure 3.12 demonstrates the information relevant to Table 3.8 complete with the cumulative line on the chart.
The Pareto chart serves as a useful tool for prioritizing corrective actions to address customer dissatisfaction. Even so, it should be noted that in some cases the cause(s) of a problem in the organization might be interrelated and that it is not always easy to relegate a problem to a specific unit or department. Another point to remember is that, if Pareto charts are used to indicate the arrangement of the data ^{* 1 2 3 4 5 6}
TABLE 3.8
Causes of Customer Dissatisfaction
N 
Causes of dissatisfaction 
Frequency 
1 
Dissatisfaction with product quality 
5 
2 
Dissatisfaction with delivery time 
12 
3 
Dissatisfaction with product quality (packaging) 
18 
4 
Dissatisfaction with aftersales services 
10 
5 
Dissatisfaction with price set for product 
8 
6 
Dissatisfaction with employees’ performance in organization 
2 
Total 
55 
FIGURE 3.12 Pareto chart of customer dissatisfaction.
from the highest frequency to the lowest one for the determination of the causes related to the costs, most certainly this chart satisfies our needs to determine the highest cost items. However, there is a possibility that the second chart does not conform to the first one. For the causes related to the highest dissatisfactions do not always match causes related to the highest costs. The cumulative line shows the process slope related to causes.
• AfterSales Services and Customer Satisfaction (Descriptive Statistics— Dispersion Chart)
In the selected and determined scope in one industry in DIO, data on the relationship between the duration of aftersales services related to different key products and customer satisfaction (14 customers) are extracted and presented in Table 3.9.
The relevant data is presented in Table 3.10.
In this formula, b is the line angle coefficient and n is the number of data
„ . , (14xl90)(6lx34) . ,_{Q}
So, we have: b =,— = 0.49
14x351(61)^{2}
TABLE 3.9
Score Model for Customer Satisfaction
Duration of aftersales services (in terms of years) 
Satisfaction level (quantitative) 
Satisfaction level (qualitative) 
1 
1 
Low 
3 
2 
Moderate 
5 
3 
Good 
7 
4 
Very good 
9 
5 
Excellent 
TABLE 3.10
Customer Satisfaction Data (aftersales services)
N 
Duration of aftersales services (X in term of year) 
Satisfaction level (quantitative) (V in term of 1 to 5) 

1 
1 
1 
1 
1 
1 
2 
2 
1 
4 
1 
2 
3 
3 
2 
9 
4 
6 
4 
4 
2 
16 
4 
8 
5 
7 
4 
49 
16 
28 
6 
5 
3 
25 
9 
15 
7 
6 
3 
36 
9 
18 
8 
2 
1 
4 
1 
2 
9 
3 
2 
9 
4 
6 
10 
8 
4 
64 
16 
32 
11 
9 
5 
81 
25 
45 
12 
4 
2 
16 
4 
8 
13 
1 
1 
1 
1 
1 
14 
6 
3 
36 
9 
19 
S 
61 
34 
351 
104 
190 
I
Where a and b are fixed coefficients of the line equation.
So, we have: a = Y bX —> a = (34 14) 0.49 x (61H4) = 0.293 As a result, the line equation is as follows:
FIGURE 3.13 Dispersion chart of customer satisfaction (aftersales services).
Moreover, we have:
In this formula, r is the correlation coefficient and n is the number of data So, we have: r = (14x !90)(6l x 34) _{R}, _{= 0}__{92}j_{0}
^[(14x35 1(61)^{2})(14x104(34)^{2})]
The overall result of this calculation indicates that roughly 92% of the share related to customer satisfaction is derived from the index of aftersales services time. This shows the importance of the latter index in obtaining customer satisfaction. The dispersion diagram of the information given above, along witli the line calculated is displayed in Figure 3.13.
The dispersion diagram in this numerical application has a linear and positive correlation pattern.