Case 3 Alejandro Alcoser
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Industrial Engineering
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Jan 9, 2024
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IE 431
Design for Six Sigma
Prof. Harrison Kim
Case Study 3
Alejandro Alcoser
664687230
11/15/2023
DEFINE
“LiquiRubber.com” is a manufacturer of liquid rubber used in molding. They reported having
encountered customer dissatisfaction due to the necessity for frequent temperature adjustments in
the molding process for each new batch of liquid rubber received. These continual modifications that their customers are forced to perform result in an average loss of thirty minutes per day, which affects production efficiency. To address this issue, the management at LiquiRubber.com decided to assemble a team comprising Process Engineers, Chemists, Operators, and Supervisors, in order to conduct a Six Sigma evaluation on the situation. Following the collection
of a variety of data, the team is now in charge of identifying and implementing a solution to streamline the temperature adjustment process, aiming to improve customer satisfaction and reduce the financial impact of lost production hours. In order to understand which failures are the most representative, a Pareto Chart was created using the data collected. It can be seen that the majority of failures arise due to the parts not curing properly, making this a factor the team should focus on. Other factors such as the scorch, underfilling of parts, mold flash and flowlines seem to have a lesser impact on the problem. Figure 1. Pareto chart of possible failures
MEASURE
The team identified the outputs measured for each sample with their respective specification limits to be met before being considered as defective, shown in the following table.
Table 1. Outputs and spec. limits
Following the data, a capability analysis for each output is going to be performed in order to measure their respective defect level. For this, it’s necessary to perform a distribution analysis as well. The data shown in Table 2 corresponds to a summary of the distribution type and overall DPM for each of these outputs. The actual graphs can be seen in the “Annexes” section of the report.
Table 2. Distributions and DPM
Based on the results, it can be evidenced that CIR (Cure Initiation Temperature) is the most common cause of defects, with a DPM of 105918.56, for which it can be considered the dominant output. Other outputs, such as Type B tear strength and VMAX, also seem to have high
DPM values.
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In order to visualize the brainstormed causes for rubber failure, a cause-effect diagram was made, which can be seen on Figure 2.
Figure 2 Rubber failure fishbone diagram.
ANALYZE
With the purpose of examining the effects of the mentioned incomes on the dominant output (CIR), a correlation matrix was created, showing the correlation coefficient and interaction between the CIR and each of the inputs. Its important to note that the variable “Supplier” was replaced into a binary indicator variable, so that the analysis could be performed. Figure 3. Correlation matrix CIR vs inputs
Figure 4. Values corerlation
It can be observed that the inputs with the highest correlation with our dominant output are Catalyst Weight, Catalyst Dispenser and Supplier, meaning that they have the highest effect on the Cure Initiation Temperature (CIR), and can be considered as dominant inputs.
Having established our main inputs, individual regression charts were created in order to visualize the linear relation between the output and dominant inputs.
It can be evidenced that the CIR and Catalyst Weight have the highest value of R
2
(84.5%), meaning that 84.5% of the variance in the Cure Initiation Temperature can be explained
by the Catalyst Weight.
In order to confirm the inputs that should be considered as dominant, a stepwise regression was performed. The model generated followed the form of:
The results of the regression were:
Figure 6. Stepwise Regression
Figure 5. Regression charts for inputs
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It can be seen that the model has an R
2
of 87.33%, which can be considered as a high value and indicates that 87.33% of the variance in CIR can be explained by the input variables of
Supplier and Catalyst Weight. Additionally, it is observed that the variable of “catalyst dispensed” is no longer shown in the final model. This indicates that it doesn’t contribute to a better linear model, which can be due to a possible multicollinearity with another input variable. Finally, it is shown that the dominant input is clearly the catalyst weight, having the highest correlation coefficient.
It is now important to analyze the effect of the supplier in the model since it is seen to also be
involved in it. A boxplot evaluating the effect of each supplier in the CIR is shown below.
Figure 7. Suppliers Boxplot
It can be observed that supplier B’s material has a greater variation in their CIR than supplier A, as well as a higher average temperature, being above 140 degrees.
As it was previously defined, the supplier is now represented as a binary variable (0 for supplier A and 1 for supplier B). For the purpose of analyzing its effect in combination with the dominant input (catalyst weight), a new variable is going to be created, being mainly the multiplication of both terms. Using multiple regression, the model is presented as follows:
Figure 8. Regression of new model
It is observed that now the value of R
2
went up to 89% for the new model. This can also be expressed as two models, one for each supplier, as shown below:
Where x
cw
represents catalyst weight, and x
s
represents the suppliers.
By replacing the ideal CIR in both equations (140 C), it results in a catalyst weight value of 0.2137 for Supplier A and 0.2112 for Supplier B, which is similar to the stated target of 0.21 for the catalyst dispenser, and means the suppliers create a lower amount of variation in the model. On the other hand, the slope in Supplier B’s equation is significantly greater than the one of Supplier A. This means that the CIR when using Supplier B’s material changes more than using Supplier A’s based on the catalyst weight.
IMPROVE AND CONTROL
Knowing that CIR is the dominant output in the model, it is essential to bring it to control in order to reduce the number of defects. In the first place, by setting a target value of
21
±
0.01%
to the catalyst weight, the company would be able to reduce their defects in a significant way. To perform this, the values of CIR that have their respective catalyst weight between 0.20 and 0.22 are selected and used to perform the new capability analysis, shown below.
Figure 9. Capability Analysis post-improvement
It is observed that now the DPM value dropped to 2838.53, which is more than 100000 units from the initial value. This shows that changing the catalyst weight’s target is a good strategy for reducing the number of defects in CIR.
The company could also benefit from reducing the number of inputs and outputs involved in the process. Most of the inputs have very low correlation with the analyzed outputs so they could
be monitored less strictly, such as inhibitor, cross-linker, and mix time. In the same way, T10 time and elongation percentage are outputs with a low number of defects, so the company could focus on reducing the defects of the other outputs instead. However, it is recommended that they do this with caution since some factors could be more significant to the performance efficiency than others.
Finally, to keep the production in control, it is recommended to perform a constant monitoring of the process in order to assure there are no significant changes happening due to
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certain inputs or outputs being removed, as well as to assure CIR stays within the spec limits, since this output was shown to be the most significant and the most likely to cause defects. Additionally, the company should try to stop working with Supplier B or find another supplier to replace them, due to the fact that they are causing CIR to be outside of the limits established. The
company could also benefit from implementing training sessions to their workers since some of their problems identified in the Fishbone diagram were caused by poor performance of operators.
ANNEXES
Output’s Distribution Analysis
Output’s Capability Analysis
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