Question

What is a control chart? What are its main features and how is it used?

I included the definition of a control chart so there isn't any confusion. Please include an explantion in your own words.

Control Chart

Assuming production engineers have gotten everything to work such that the process conforms to specifications (the average of the process is close to the target value and the variability [standard deviation] is very small), after that they have to ensure that the process doesn’t change. If, say, the current manufacturing process meets requirements 99.99% of the time, and managers consider that good enough, then some way is needed to monitor and control the process to make sure it stays that way. The assumption here is that as long as the process does not change, it is OK; if, however, the process changes, it might not be OK and something will have to be done to get the process back to where it was. The problem is every process eventually changes. The producer needs to know exactly when a change has occurred or is about to occur so the cause can be found and necessary corrections made to get the process back to the desired state.

The tool used to monitor a process for potential change is the control chart. The significant features of the control chart, shown in Figure 4.4, are a center line and upper and lower control limits, all of which are computed from sample data and statistical formulae. Once the values for these lines are set, the control chart is used to monitor the process by taking periodic samples of the process output and plotting the results on the chart.

For example, an assembly worker (Figure 4.5) performs tests every hour on a sample of five units of process output. The results of the tests are averaged and plotted on a control chart like Figure 4.4. The test results will vary slightly from sample to sample due to random variation in the process, but as long as they remain within the control limits and exhibit random variation (not too many points in succession trending upward or downward, nor too many lying above or below the center line), the process is considered in control, which means the variation from sample to sample is random and the process has not changed. If otherwise—points lie outside the control limits or in succession exhibit nonrandom behavior—the process will be suspected of having changed. In that case the worker will stop the process to investigate what might have happened.

There are no guarantees. Although the variation might in fact be entirely random, sometimes points fall outside the control limits or appear nonrandom, leading the worker to mistakenly conclude that the process has changed, even though it hasn’t.

A “good” process is one where both the mean and the variability of the process in combination result in a very high percentage of process output meeting product or process requirements.

Thus, two kinds of control charts are used together: one to track the process mean and the other to track the process range or standard deviation (two ways to measure variability). If either chart indicates a potential change in the process, the process is stopped and investigated for the cause.

UCL = 0.0245 CL 0.0235 LCL = 0.0135 1 2 3 4 5 6 7 8 9 10 Sample Number Figure 4.4 Example control chart.

Answer 1

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, you can draw conclusions about whether the process variation is consistent (in control) or is unpredictable (out of control, affected by special causes of variation).

Control charts for variable data are used in pairs. The top chart monitors 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 target 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 a Control Chart

• When controlling ongoing processes by finding and correcting problems as they occur.
• When predicting the expected range of outcomes from a process.
• When determining whether a process is stable (in statistical control).
• When analyzing patterns of process variation from special causes (non-routine events) or common causes (built into the process).
• When determining whether your quality improvement project should aim to prevent specific problems or to make fundamental changes to the process.

Control Chart Basic Procedure

0 1 2 3 4 5 67 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Time

Figure 1 Control Chart: Out-of-Control Signals

1. Choose the appropriate control chart for your data.
2. Determine the appropriate time period for collecting and plotting data.
3. 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.

   Out-of-control signals

   • A single point outside the control limits. In Figure 1, point sixteen is above the UCL (upper control limit).
   • Two out of three successive points are on the same side of the centerline and farther than 2 σ from it. In Figure 1, point 4 sends that signal.
   • Four out of five successive points are on the same side of the centerline and farther than 1 σ from it. In Figure 1, point 11 sends that signal.
   • A run of eight in a row are on the same side of the centerline. Or 10 out of 11, 12 out of 14 or 16 out of 20. In Figure 1, point 21 is eighth in a row above the centerline.
   • Obvious consistent or persistent patterns that suggest something unusual about your data and your process.
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.

Statistical tool used in quality control to (1) analyze and understand process variables, (2) determine process capabilities, and to (3) monitor effects of the variables on the difference between target and actual performance. Control charts indicate upper and lower control limits, and often include a central (average) line, to help detect trend of plotted values. If all data points are within the control limits, variations in the values may be due to a common cause and process is said to be 'in control'. If data points fall outside the control limits, variations may be due to a special causeand the process is said to be out of control.