 Levinson Productivity
Systems, P.C.William A. Levinson, P.E. Principal 570-824-1986  |
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Effect of subgrouping
Shift in the process mean
Increase in process variation
Six Sigma process capability
Ordering information
This interactive training program is designed to teach production workers how to read and interpret statistical process control (SPC) charts in an hour or even less. It also facilitates very rapid training in the concepts of variation and accuracy. It achieves this through animated figures that relate something familiar (like a target) to the control charts. It also incorporates an animated histogram (like the popular quincunx classroom tool) that shows the distribution as it is being simulated. Download the instruction file (Word .doc file, 1 Mb) for free.
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."
- 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).
- 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.
- 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.
Figure 2 shows the effect of subgrouping. Note how the control limits for the x-bar chart are tighter (100 +/- 3*sigma/SQRT(n)) and it is possible to have a range chart.
Figure 2. Simulation for mean = 100, sigma = 1, and sample size = 4
Figure 3 shows the effect of a shift in the mean. The target shows how the shots are, on average, now hitting above the bullseye (nominal). If the audience is familiar with how one sights in a firearm, corrective action would consist of lowering the back sight to bring the shots' center of gravity back onto the bullseye. The histogram also has been shifted to the right.
A very key point to make is that, although no measurements have yet gone out of specification, the out-of-control 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 animation teaches why production personnel must react to the first out-of-control point even though all the parts are in specification.
Figure 3. Simulation for mean = 100.5, sigma = 1, and sample size = 4
Figure 4, "Ye Musket," shows the effect of an increase in the process variation. Key lessons of this animation are as follows:
- 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.
- 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).
- 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 bullseye.
- 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.
- The histogram also shows how the increase in variation is causing many units to be out of specification (shown in red).
- 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 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 4 was "Ye Musket," Figure 5 is an Olympic match rifle. There will be two defects per billion opportunities, i.e. 2 ppb 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 5. Olympic Match Rifle. mean = 100, sigma = 2/3, and sample size = 4. Process capability index Cp = 2
Ordering Information: Price = $50.00 including shipping within the U.S.
- Download the instruction file (link corrected 04/21/05. Word .doc file, 1 Mb) for free. (It will be included with the installation CD.)
- Ordering: (1) Make a check for $50.00 payable to Levinson Productivity Systems, P.C. Mail to 6 Lexington Court, Wilkes-Barre PA 18702. Inquiries, TheBoss "at" ct-yankee.com or 570-824-1986 (2) Order via PayPal E-commerce using the button AND E-mail me (TheBoss "at" ct-yankee.com) to let me know you have placed an order. Be sure to include your shipping address! When ordering, please indicate if you need an older version of PowerPoint, and also if the item is to be shipped to a Pennsylvania address. (We absorb sales tax on items sold in PA.)
- If, for example, you want to install the program on six computers so six students can use it simultaneously, you must buy six licenses. If, however, you want to install it on one computer that is equipped with a projector, you need purchase only one license.
- 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. It must be installed in the same directory as the executable file!)