Identification and Determination of the Desired QET in Main Processes
These processes divided into relevant sub-processes 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)
Bullet-head drills with 27.8-inch 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 bullet-head drill of 27.8-inch 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
Specifications of Technical Product
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
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
FIGURE 3.4 Process design matrix.
D: Absolute weight A: Importance degree В: Improving ratio C: Correction factor
E: Relative weight D: Absolute weight
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.
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 Y-axis and («) is the number of data or samples. Therefore, we have:
Supplier Data of Organization
Calculated Supplier Data (Three Years Moving Average)
Calculated Supplier data of Organization (Squares Minimum Method)
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
d2: 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).
Internal Diameter Data of a Piece under Four Groups
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 A2 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 A2 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 D4 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:
The control limits of the mean value control chart are calculated as:
The control limits of the range control chart are calculated as:
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 out-of-control 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.
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 Non-conformity of four defects.
In this formula, Cis the total average of non-conforming cases, and n is the total number of pieces. So, we have:
In this formula, UCLc is the upper limit of C chart, and Cis the total average of non-conforming cases. So, we have:
Number of the Non-Conformities in Project Pieces
In this formula, LCLc is the lower limit of C chart, and Cis the total
average of non-conforming cases. So, we have:
The control limits of C chart are calculated as:
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 non-conformities, 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 non-conforming cases in project pieces.
Registered Non-Conformities in the Project Pieces
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
Causes of Customer Dissatisfaction
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.
• After-Sales 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 after-sales 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
Score Model for Customer Satisfaction
Customer Satisfaction Data (after-sales services)
Where a and b are fixed coefficients of the line equation.
So, we have: a = Y -bX —> a = (34 14)- 0.49 x (61-H4) = 0.293 As a result, the line equation is as follows:
FIGURE 3.13 Dispersion chart of customer satisfaction (after-sales 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_92j0
The overall result of this calculation indicates that roughly 92% of the share related to customer satisfaction is derived from the index of after-sales 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.