Statistical Process Control Chart Simulator
© 2005 by Levinson Productivity Systems P.C.
www.ct-yankee.com
TheBoss@ct-yankee.com 570-824-1986
Statistical Process Control Chart Simulator
License and Conditions of Use
Installation
Instructions
Using the Program to Teach SPC
Effect of subgrouping
Shift in the process mean
Increase in process variation
Six Sigma process capability
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Statistical Process Control Chart Simulator
License and Conditions of Use
You may have the program in use (executing) on one computer at a time for every
copy you purchase. As an example, you may install the program on your office computer
and laptop but only one copy may be in operation at any given time. If you sell your
copy, the license transfers to the purchaser and you must dispose of all backups and
uninstall the program from all your computers.
Disk guarantee: Files are burned onto a CD using Roxio software. Experience is that
these disks work in most computers. If it does not work in yours, your money will be
refunded if a workable copy cannot be provided. (If necessary, the installation files can
be provided by E-mail or direct download from www.ct-yankee.com.)
Installation
The following files are required for installation and operation of the program:
(1)
(2)
(3)
(4)
setup.exe
ChartSim.CAB (Cabinet file)
ChartSim.LST (List file)
factors.txt (control chart factors for the range chart; read by the program on
startup)
Copy the files to the desired directory and run setup.exe. It is a standard installation
program.
Instructions
The program simulates a process with a specification range of [96,104], a nominal or
target of 100, and a standard deviation of 1. The process capability index is therefore
USL  LSL 8 4
Cp 
  , which is the minimum standard for a process to be considered
6
6 3
capable. Figure 1 shows the control interface.
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Figure 1. Program Controls



Buttons
o Start: starts the simulation.
o Stop: stops the program.
o Nominal: restores the initial settings for speed = 1 second, process mean
= 100, process standard deviation = 1, and sample size = 1.
Check Box
o Six Sigma sets the standard deviation to 2/3, thus changing the process
USL  LSL
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
 2 . This option's purpose
capability as follows: Cp 
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6
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is to show the resulting level of quality on the target and histogram. Note
that the control chart limits do not readjust; the user or instructor should
note how the points on the X/x-bar chart cluster with unusual tightness
around the center line while those on the R chart tend to run below the
center line. In actual practice, the control limits must be recalculated once
a process improvement (such as reducing the process variation) is
verified.
Sliders
o Speed: seconds per sample. Settings of 0.1 to 20 seconds are possible.
Use slow settings to allow an instructor to discuss what is happening in
detail. Use fast settings to "grow" a histogram as rapidly as possible.
(Note, however, that the histogram and target will clear themselves once a
histogram bar reaches the top, which is about 280 measurements in the
cell.)
o Process mean: ranges from 98 to 102, with 100 being nominal. Use this
slider to simulate a shift in the process mean. This will cause the shot
pattern on the target display to be off center, and the histogram also will
be off center. The results will be observable on the X/x-bar chart.
o Process variation: ranges from 0.3 to 2.0, with 1.0 being nominal. Use
this slider to simulate a change in process variation. An increase will
cause a wider dispersion of the shots on the target display, and a wider
histogram. The results will be observable on both the X/x-bar chart and
the R chart. It is important for the instructor to explain that the change in
process variation invalidates the control limits for the X/x-bar chart, and
that the R chart should be interpreted first.
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o Sample Size: ranges from 1 to 25. A sample of at least 2 is required for a
range chart to appear. Larger sample sizes will result in quicker detection
of out-of-control conditions.
Using the Program to Teach SPC
This section shows how to use the program to teach statistical process control. For
classroom purposes, it can be run from a computer with a projector attachment.
Figure 1 shows a good way for the instructor to introduce the concepts of variation
and accuracy. The program simulates a process with a nominal mean of 100, a nominal
standard deviation of 1, and specification limits of [96,104]. The process capability is
therefore 1.33, the standard minimum for a process to be considered "capable."
Figure 1. Simulation for mean = 100, sigma = 1, and sample size = 1

The target is a circle whose radius is 4. It is easy to understand that a shot inside
the target ring is good (in specification) and one outside the target ring is bad (out
of specification). The distribution of the shots shows both the dispersion
(variation) and accuracy (whether the center of the shot distribution is centered on
the bullseye).
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
The target's radius is the same as the specification width and the process
mean determines the aiming point. The simulation (in terms of shots inside
and outside the target) is truly accurate only when the aiming point is the
bull's-eye or nominal but it is more important for the audience to relate
what they see on the target to the neighboring histogram and the two
control charts.
The histogram is a standard histogram of the individual measurements, with the
specification limits shown in red. The histogram will automatically refresh (start a
new histogram) when any bar reaches the top, at about 280 counts in the cell. Its
behavior is similar to the familiar quincunx demonstration tool.
The X chart shows that, when the process is in control, the points will mostly be
within the control limits. (2.7 out of 1000, the standard false alarm risk for a
Shewhart control chart, can be expected to be out.) They will also scatter
randomly around the center line.
Effect of subgrouping
Figure 3 shows the effect of subgrouping. The instructor should point out that:
(1)
The control limits for the x-bar chart are now tighter. If the audience has a
basic mathematical background, it can be pointed out that the control limits
are   3

n
where n is the sample size. In this case, the limits are
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 [98.5,101.5] .
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The range (R) is the difference between the largest and smallest
measurements in the subgroup. This difference will be, on average, larger
when the process variation is higher. For sample sizes of five or less, there is
no lower control limit.
100  3
(2)
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Figure 3. Simulation for mean = 100, sigma = 1, and sample size = 4
Shift in the process mean
Figure 4 shows the effect of a shift in the mean. The target shows how the shots are,
on average, now hitting above the bull's-eye (nominal). If the audience is familiar with
how a hunter or target shooter sights in a firearm, corrective action would consist of
lowering the back sight to bring the shots' center of gravity back onto the bull's-eye. The
histogram also has been shifted to the right. The instructor should highlight the following
concepts:
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(1)
(2)
Although no measurements have yet gone out of specification, the out-ofcontrol points (highlighted with red circles) are a clear warning that one is
likely to do so if the process is allowed to keep operating without correction.
This is why production personnel must react to the first out-of-control point
even though all the parts are in specification.
It is a common misconception that, if a point is outside the control limits, it
is acceptable to "wait and see if the next point comes back into control."
o As shown by more than a dozen points at the beginning of the chart,
points inside the control limit never prove that the process is in control.
Furthermore, the points go back inside the control limits after the second
out-of-control signal even though the process mean is still running high!
o It is in fact never possible to prove that the process is in control. The
process is only assumed to be in control until there is evidence— namely
a point outside the control limit— that it is not.
Figure 4. Simulation for mean = 100.5, sigma = 1, and sample size = 4
Increase in process variation
Figure 5, "Ye Musket," shows the effect of an increase in the process variation. The
instructor should highlight the following key concepts:
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(1) An out-of-control point on the range chart indicates that the process variation has
increased. If the process was represented by a rifle, the rifle has been replaced by
a smoothbore musket.
(2) The target figure shows that, even though the musket is aimed at the bullseye
(nominal), the spread or variation in the shots is causing many of them to miss the
target (be out of specification).
o The histogram also shows how the increase in variation is causing many units
to be out of specification (shown in red).
o Putting Daniel Boone or Annie Oakley behind this "process" will not achieve
better results so don't blame the operator. The instructor can in fact use the
analogy of putting the musket in a bench rest and using a laser sight to aim it
at the bull's-eye.
o The tool is simply not capable of achieving better results. These animations
can, in fact, be used to teach the concept of a non-capable process.
(3) The x-bar chart has out-of-control points at both the upper and lower control
limits. The instructor should point out that, when the range (or sample standard
deviation) chart shows an out-of-control condition, it is not possible to interpet
the x-bar chart. This is because the assumptions under which this chart was set up
are no longer valid. In this case, the x-bar chart relies on the assumption sigma=1,
and this is no longer true.
Figure 5. "Ye Musket." mean = 100, sigma = 2, and sample size = 4.
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USL  LSL
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
 , which is not considered
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capable. Remember that the generally-accepted standard is 1.33.
The process capability is now Cp 
Six Sigma process capability
Figure 6 shows a process with Six Sigma process capability (Cp=2). The key items
are the target and the histogram, which show the very tight distribution of the
measurements. If Figure 5 was "Ye Musket," Figure 6 is an Olympic match rifle. There
will be two defects per billion opportunities, i.e. 2 parts per billion, under these
conditions.
Less attention should be paid to the x-bar and R chart, noting that both still assume
that sigma=1. The instructor should point out, however, that a verified improvement in
process capability (reduction in variation) requires re-calculation and tightening of the
control limits for both charts.
Figure 6. Olympic Match Rifle. mean = 100, sigma = 2/3, and sample size = 4.
The process capability is now Cp 
USL  LSL
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
 2.
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Figure 7 shows the rationale behind the "3.4 ppm" (or "3.4 defects per million
opportunities") that is associated with Six Sigma process capability. This model assumes
a process shift of 1.5 sigma. In this case =0.667, 1.5 is 1.0, and the process shift can be
simulated by setting the process mean to either 99 or 101.
The sample size is not really relevant, nor are the control charts. The instructor
should emphasize the target and histogram, and indicate that the 3.4 defects per million
opportunities will be found almost exclusively in the upper tail of the distribution.
Figure 7. Olympic Match Rifle. mean = 101, sigma = 2/3, and sample size = 16.
Figure 8 shows, however, just how quickly any decent control chart will catch a
1.5-sigma process shift. When the sample size is 4, in fact, the average run length (ARL)
is 2.0. This is because the process is actually running at a control limit, which means
there is a 50:50 chance of it going outside for any sample.
Figure 8. Process with 1.5-sigma shift. mean = 101.5, sigma = 1, and sample size = 4.
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