ISE 408/508: Quality Assurance
Mini Project 4: Process Control and Capability
Electromagnet Bearing Transfer
4/25/2016
Submitted to
Dr. Harrison Kelly
Submitted By:
Group 10
Leonard Arambam (50054165)
Brian Chen (50049012)
Su Ryun Jeong (50091818)
DongYouel Eddie Lee (36941307)
Alison Park (50031522)
Jianheng Tan (50040201)
Table of Contents
Introduction
2
Methodologies
3
Analysis
4
Results
11
Conclusions
12
1
Introduction
A company is asking an industrial engineer to see if the electromagnet process of picking up
ball bearings and transferring them from one container to another. This process has been
optimized previously; now it will be seen if the process is controlled. In Mini Project 3, the
optimal set-up is determined for picking up the maximum amount of ball bearings via an
electromagnet. In this project, we will determine whether or not the process is stable, if the
process is in a state of control, and the process can meet the requirements. This is done by
analyzing Xbar and R charts, analyzing Normal Probability plots, and Process capability reports.
To increase of the results generated, the team will collect 25 average sample data of size 5 and
analyze the data to see if the process is in control, if the process is not in control then we will
collect 10 more sample points and calculate a control limit to meet the specifications of the
customer.
2
Methodology
Using the same materials as Mini Project 3, the electromagnet is assembled in the
optimal set-up as to pick up as many ball bearings as possible. The optimal set-up is a thin core,
long wire, 3 batteries, two passes, six seconds, and corner. Two shot containers were set up so
that ball bearings could be transferred from one to another. Then, five subgroups of data were
taken, with five trials in each subgroup. This results in 25 total data points. Five minutes passes
before starting the experiment again, and another five subgroups of five trials were created. This
is repeated until there are a total of 25 subgroups.
From mini project 3, DOE offers an optimized design and statistical evidence for the
process in order to know whether or not the process is in-control by the means of statistical
process control. The purpose of a SPC is monitoring, controlling, and improving a process over
a period of time. For this project, the statistical process control is used to monitor the process of
retrieving ball bearings and to determine whether or not new trial control limits need to be
established. The eventual goal of SPC is reduction or elimination of variability in the process by
identification of assignable causes. SPC is approximately equivalent to repeated hypothesis
tests comparing the short-term variability to long term variability.
Then, the data is analyzed via Minitab. The trial control limits are determined and
interpreted then additional control limits are chosen for usage on the next set of trials. Then, 10
more subgroups of five trials each are taken and analyzed. The process capability will be
determined, and then the process performance will be estimated. The purpose of the process
capability report is to show whether or not the data collected meets the requirements. It also is
to compare the process specification to the process output and determine statistically if the
process can meet specifications. The less variation present in the process, the more capability
the data will be to meet specifications. The report also represents the overall and potential
capability of the data.
3
Analysis
The initial 25 subgroups with 125 data points (Trial1) has an Xbar-R chart shown below:
Figure 1. Xbar- R Chart of Trial 1
As shown in Figure 1. the R-bar chart, all points are randomly distributed around the
central line and within the control limit. Therefore, process variation for this data set is in control.
Also, from X-bar chart, all points are randomly distributed around the central line and within the
control limit. This indicates that the electromagnet is stable and under control for the whole
experiment.
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Figure 2. Probability Plot of Trial 1
As shown in Figure 2. probability plot, the average for trial 1 is 10.25 and the standard
deviation is 3.573. Data points follow the straight line with P-value greater than 0.05. Therefore,
the normal distribution is a good fit for sample set.
Figure 3. Process Capability Report for Trial 1
As shown Figure 3. Lower Specific Control Limit set to 5 and Trial 1 process was not
within the specification limits. Cpk is 0.49 which is less than 1, therefore; some of the data
points did not meet specification. Therefore, this process is incapable of producing output that
meets LSL of 5 requirements even if it’s in statistical control.
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Figure 4. Process Capability Sixpack Report for Trial 1
From Figure 4, we can see that The Xbar Chart and R chart have no out of control points
for each subgroup, and therefore do not need any tweaking in the process. The Last 25
subgroups is also displayed, which show the total 125 points displayed among the 25
subgroups. The Capability Histogram shows the data set, as well as the LSL, which is 5. This
indicates that the Process is incapable of satisfying the LSL, because there are data points
below the LSL. The Normal Probability Plot is also shown, which has a P-value of .067, which is
greater than .05, which indicates that the data fits a normal distribution.
6
The new 50 data points and 10 new subgroups of size 5 (Trial2) has an Xbar-R chart shown
below:
Figure 5. Xbar-R Chart of Trial 2
As shown in Figure 5. the R-bar chart, all points are randomly distributed within the
control limit. Therefore, process variation for this data set is in control. Also, from X-bar chart, all
points are randomly distributed around the central line and within the control limit. This indicates
that the electromagnet is stable and under control for the whole experiment.
7
Figure 6. Probability Plot of Trial 2
In Figure 6, the P-value for the probability plot of Trial 2 is less than 0.05, which indicates
that the data does not fit to a normal distribution. For this, a Box-Cox transformation is
necessary.
Figure 7. Box-Cox Plot of Trial 2
In Figure 7, the Box-Cox Plot of Trial 2 is displayed. This shows the normalization of our
data set. From Box-Cox plot, Lambda is determined as 0.50 and this Lambda will be used to
transform the data in process capability.
8
Figure 8. Process Capability Report for Trial 2
Figure 8 shows transformed data with Lambda 0.5 and it indicates that the process is
incapable of meeting the requirements which LSL of 5. The Cpk Value of 0.48 is below 1, and
therefore some of the requirements will not be met.
9
Figure 9. Process Capability Sixpack Report for Trial 2
Figure 9 first has the Xbar Chart as well as the R chart, both which indicate that there
are no out of control points of subgroups, as well as show the entire 125 data points within the
25 subgroups. The Capability histogram indicates that there are points below the LSL, and
therefore the process is incapable of meeting the requirements. The Normal Probability plot ha
a P-value of 0.01, which is below 0.05, and therefore the data set does not fit the normal
distribution.
10
Results
In Figure 1, the Xbar-R chart of trial 1 shows that there are no out of control points for
the average of subgroups, which indicates that no trial control limits need to be introduced to the
process. In Figure 2 the Probability Plot of Trial 1 has a P-value of .067, which is above .05.
This indicates that the data is a good fit to the normal distribution. The Cpk for Trial 1 is .49,
which is below 1. This indicates that some output of the process will not meet requirements. The
Process Capability Sixpack report for trial 1 also shows the .067 P-value for the normal
probability plot.
According to this data, there were no out of control data points of the average of
subgroups, and is within the normal probability plot, and therefore there was no need to change
the process control limits from trial 1 to trial 2.
In Figure 5, the Xbar-R chart of trial 2 shows that there are no out of control points for the
average of subgroups, which indicates that there is no change needed in the process. In Figure
6, the P-value is <.005, which indicates that the data does not fit the normal distribution. In
figure 8, the Box-Cox chart is used to normalize the data set with a lambda value of .5. In figure
7, the Cpk for Trial 2 is .48, which also indicates that some of the output processes will not meet
requirements. In figure 9, Trial 2 has a P-value of .01 for the Normal Probability Plot, and
therefore it is not above .05, and does not represent a normal distribution.This is most likely due
to the battery losing power as the experiment went on, giving inconsistent and biased data.
11
Conclusion
Based on our data, the consistently low Cpk values indicate that the process is
incapable of meeting the requirements set which posed as a problem during the experiment. A
method to control Cpk values is to increase the sample size of data collected, and therefore
increasing the Cpk. The process is also incapable of meeting the requirements set based on
the histogram of capability, in which there are data points below the LSL. The data does not
have any points on the Xbar and R charts that are out of control, so therefore the process trial
control limits do not need to be altered. The Normality probability chart of Trial 1 indicates that it
fits a normal distribution, but the normality probability chart of trial 2 indicates that the second
data set does not fit a normal distribution, therefore highlighting possible inconsistencies in the
data. This could be due to the fact that the batteries have been not used for over a month, and
could have different voltages, resulting in inconsistent.
Therefore, the Process is Stable and in a state of control, but is not capable of meeting
the process requirements. This is shown in the Xbar and R charts, the Normal probability plot,
and the Process capability reports.
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