Also called: statistical process control Variations:
variables charts:–
X and R chart (also called averages and range chart), –
X and s chart, chart of individuals (also called X chart, X-R chart, IX-MR chart, XmR chart, moving range chart), moving average–moving range chart (also called MA–MR chart), target charts (also called difference charts, deviation charts, and nominal charts), CUSUM (also called cumulative sum chart), EWMA (also called exponentially weighted mov-ing average chart), multivariate chart (also called Hotellmov-ing T2)
attributes charts: p chart (also called proportion chart), np chart, c chart (also called count chart), u chart.
charts for either kind of data: short run charts (also called stabilized charts or Z charts), group charts (also called multiple characteristic charts)
Description
The control chart is a graph used to study how a process changes over time. Data are plotted in time order. A control chart always has a central line for the average, an upper line for the upper control limit, and a lower line for the lower control limit. These lines are determined from historical data. By comparing current data to these lines, one can make conclusions about whether the process variation is consistent (in control) or is unpredictable (out of control, affected by special causes of variation).
There are many types of control charts. Each is designed for a specific kind of process or data. Control charts for variable data are used in pairs. The top chart moni-tors the average, or the centering of the distribution of data from the process. The bottom chart monitors the range, or the width of the distribution. If your data were shots in tar-get practice, the average is where the shots are clustering, and the range is how tightly they are clustered. Control charts for attribute data are used singly.
When to Use
• When controlling ongoing processes by finding and correcting problems as they occur, or . . .
• When predicting the expected range of outcomes from a process, or . . .
3 9
4 8
5 7
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• When determining whether or not a process is stable (in statistical control), or . . .
• When analyzing patterns of process variation from special causes (nonroutine events) or common causes (built into the process), or . . .
• When determining whether your quality improvement project should aim to prevent specific problems or to make fundamental changes to the process Control Chart Decision Tree
Figure 5.20 is a decision tree for deciding which control chart should be used, depending on the type of data. The two broadest groupings are for variable data and attribute data.
Variable data are measured on a continuous scale. For example, time, weight, dis-tance, or temperature can be measured in fractions or decimals. The only limit to the precision of the measurement is the measuring device. If you are using a measuring device that can only give you whole numbers, such as 78 degrees, or if you only need the precision of the nearest whole number, such as five days, you are still using variable data. The possibility of measuring to greater precision defines variable data.
Attribute data are counted and cannot have fractions or decimals. Attribute data arise when you are determining only the presence or absence of something: success or failure, accept or reject, correct or not correct. For example, a report can have four
Are the data
Figure 5.20 When to use the basic control charts.
errors or five errors, but it cannot have 41⁄2errors. A longer discussion of attribute data can be found on page 177.
Basic Procedure
1. Choose the appropriate control chart for your data.
2. Determine the appropriate time period for collecting and plotting data.
3. Follow the procedure for that control chart on the following pages to collect data, construct your chart, and analyze the data.
4. Look for out-of-control signals on the control chart. When one is identified, mark it on the chart and investigate the cause. Document how you investigated, what you learned, the cause, and how it was corrected.
• A single point outside the control limits. In Figure 5.21, point sixteen is above the UCL.
• Two out of three successive points are on the same side of the centerline and farther than 2s from it. In Figure 5.21, point four sends that signal.
• Four out of five successive points are on the same side of the centerline and farther than 1s from it. In Figure 5.21, point eleven sends that signal.
• A run of eight in a row are on the same side of the centerline. Or ten out of eleven, twelve out of fourteen, or sixteen out of twenty. In Figure 5.21, point twenty-one is eighth in a row above the centerline.
• Obvious consistent or persistent patterns that suggest something unusual about your data and your process.
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
UCL = 3σ
LCL = 3σ 2σ 1σ Average 1σ 2σ
Time X
X
X
X
Figure 5.21 Out-of-control signals.
5. Continue to plot data as they are generated. As each new data point is plotted, check for new out-of-control signals.
6. When you start a new control chart, the process may be out of control. If so, the control limits calculated from the first 20 points are conditional limits. When you have at least 20 sequential points from a period when the process is operating in control, recalculate control limits.
Considerations
Out-of-Control Signals
• Some control charts have special requirements for their out-of-control signals.
Check the analysis section of the particular control chart.
• The distribution of ranges is not symmetrical but skewed right. Therefore, one would expect more points below –
R than above it. To allow for this, the fourth out-of-control signal is often modified for range charts to require a run of 12 points in a row below –
R.
• These signals are based on statistics. The points plotted from an in-control process are random but, taken together, match a predictable distribution, such as a normal curve. The out-of-control signals highlight patterns that are statistically unlikely to be random outputs of that distribution, such as too many points far from the centerline. In Figure 5.21, the last three out-of-control signals show more output above and far from the average than one would expect from a random process, an indication that the process average has shifted up.
• The signals do not indicate whether patterns are desirable or undesirable.
A change in the process may be toward better performance or toward worse performance. It is just as important to do something to understand and maintain good performance as it is to eliminate bad performance.
• Additional out-of-control signals are often used. For example:
– Fifteen points in a row within 1s of the centerline – Six points in a row steadily increasing or decreasing – Fourteen points in a row alternating up and down
– Eight points in a row all farther than 1s from the centerline, on either side – A jump of 4s
– Additional rules for runs and trends
• However, using too many out-of-control signals can cause a false positive—a problem signaled when one doesn’t really exist. (This is called a type I error. See hypothesis testing for more information.) Every out-of-control signal has a small probability of occurring from random chance. For example, an in-control process will generate a point outside the control limits 0.27 percent of the time. When many signals are used simultaneously, those small chances multiply. Using just four signals—single point out, two-out-of-three, four-out-of five, and eight-in-a-row—
the chance of a false positive is one in twelve. Use no more than four or five signals, or you will be looking frequently for problems that don’t exist. For most processes, just a few signals, plus thinking carefully about what the charts might be revealing about your process, will reveal many improvement opportunities.
• The out-of-control signals listed on the previous page and in the procedure are not in order of probability but rather in an order that aids remembering. For example, four out of five points on one side of the centerline is less probable than a single point outside the control limits. Thus, four out of five is a more sensitive signal than the single point outside. See Hoyer and Ellis in the Resources for a discussion of the probabilities and sensitivities of different signals.
• There is also such a thing as a type II error: an out-of-control process that does not show any of the out-of-control signals. For example, if the process average shifts slightly, the standard out-of-control signals will be slow to identify the change.
• Out-of-control signals should be marked on the chart. Put an X beside the point that completes the pattern, or circle the set of points that form the signal.
Autocorrelation
• The time period chosen for collecting and plotting data should be based on how fast variation occurs in the process. The process should have time to change between samples. If not, the data will be autocorrelated.
• For example, suppose liquid is continually flowing both into and out of a tank so that the contents are completely replaced every three hours. If you are monitoring concentration, you should not plot it more often than every three hours. Data taken more frequently will be autocorrelated. Temperature is a variable that is often autocorrelated because it usually does not change rapidly.
• A good test for autocorrelation is to use correlation analysis or a scatter diagram to graph the measurement taken at one time against the measurement taken at the previous time. If samples are being taken too frequently, the scatter diagram will show correlation. See scatter diagram or correlation analysis for more information.
Control Limits
• Control limits are not specification limits. In fact, specification limits should never be placed on a control chart. Specifications reflect customer requirements, whereas control limits reflect the historical performance of the process.
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• Control limits should be recalculated only when the process has experienced a permanent change from a known cause and at least 20 plot points have been generated by the changed process. You should not recalculate limits after each 20 points or subgroups or after each page of the chart.
• Choose numerical scales that include the values for the control limits plus a little extra.
Other Considerations
• For controlling an ongoing process, control charts are most useful when plotted as soon as the data is generated and analyzed by the people who are working with the process. Collecting lots of data on a check sheet and plotting them by computer later will create charts that are prettier but of limited use.
• Computer software is available for generating control charts. Sometimes computerized control systems in manufacturing automatically generate control charts. These are useful to remove the labor required and to ensure that calcu-lations are accurate. However, computers should never substitute for the most important aspect of control charting: people who understand the purpose and meaning of the charts and who watch them closely, using them as a tool to monitor and improve their processes.
• Blank control chart forms and worksheets are provided for each type of chart.
Permission is granted to copy these charts for individual use.
• Control charts are easy and powerful to use, but they are often applied incorrectly.
The more knowledgeably they are used, the more they can improve your pro-cesses. This summary contains only the basics of control charts, intended as a reference. The theory behind them and fine points about their use are beyond the scope of this book. Take a class, study some books, or obtain expert help to get the most value out of control charts in your processes.