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When cycles are occurring, the data rises and falls in a rhythmic pattern. The pattern is definitely not random. This could be caused by some regular, periodic change in the system.
A positive aspect of cycles is that they tend to indicate that there is one major cause of variation, which will typically be changing in a similar cyclic fashion. If the cause of the cycle can be established and reduced, this should result in a major improvement to the process.
See also: >> Any nonrandom pattern >> Too close to the average >> Too far from the average >> Trends >> Clusters >> Sawtooth >> 2 of 3 points beyond 2 sigma >> 4 of 5 points beyond 1 sigma
Notice how most of the points in the chart shown below are close to one control limit or the other. This pattern may indicate that subgroups have been drawn from two sources and the data has been mixed—for example, from two machines, two processes, or from two shifts. If this is the case, stratify (separate) the data and re-plot on two charts, or resolve the differences. If the data is not from two sources, the chart may indicate that overcontrolling or tampering is occurring. That is, the process or system is being constantly changed, causing the process to have increased variation.
See also: >> Any nonrandom pattern >> Too close to the average >> Cycles >> Trends >> Clusters >> Sawtooth >> 2 of 3 points beyond 2 sigma >> 4 of 5 points beyond 1 sigma
Notice that nearly all the points lie close to the average. This pattern could be caused by a number of circumstances, including:
When this pattern occurs, try to establish why. Is this apparent improvement genuine? Can the improvement be maintained? If the improvement can be maintained, then the control limits need to be recalculated. Although the data looks more stable than normal, this condition is referred to statistically as “unstable”.
See also: >> Any nonrandom pattern >> Too far from the average >> Cycles >> Trends >> Clusters >> Sawtooth >> 2 of 3 points beyond 2 sigma >> 4 of 5 points beyond 1 sigma
This is the most complex test for stability. If the system is in control, one could imagine tilting the chart on one end and letting all the points slip down to form a normal curve. Roughly half the points would fall above and half below the centerline. Dividing the distance between the centerline and the control limits into three equal divisions up and three down, one could expect to find about two thirds of the total points in the middle two regions, and no repeatable patterns in the data.
Patterns in data are not random, and are, therefore, cause for investigation. To apply these tests, look for patterns in the plot. The following are examples of typical patterns:
>> Too close to the average >> Too far from the average >> Cycles >> Trends >> Clusters >> Sawtooth >> 2 of 3 points beyond 2 sigma >> 4 of 5 points beyond 1 sigma
For this test, look for groups of points moving up or down in succession. Count consecutive points, including horizontal runs within the run. This pattern is probably the result of a trend in one of the system resources. The chart below shows a group of seven points moving downward.
See also: >> Analyze for special causes of variation >> Any point lying outside the control limits >> 7 or more points in a row above or below the centerline >> Any nonrandom pattern
To apply this test, look for groups of points above or below the average or centerline. Count consecutive points. Are there groups of seven or more? This is probably the result of a shift in one of the system resources (materials, people, methods, environment, information aids, equipment, and measurement). The following chart, which can be created using SQCpack, shows two groups, one with eight above the centerline and one with seven below.
See also: >> Analyze for special causes of variation >> Any point lying outside the control limits >> 7 or more points in one direction >> Any nonrandom pattern
This is the quickest and easiest test for system stability. Look above the upper control limit and below the lower control limit to see whether any points fall in those regions of the chart. If you are looking at a chart pair (X-bar and R, X-bar and s, or X and MR), look at both charts.
Points falling outside the control limits may be the result of a special cause that was corrected quickly, either intentionally or unintentionally. It may also point to an intermittent problem. The chart below shows two points outside the control limits.
See also: >> Analyze for special causes of variation >> Any point lying outside the control limits >> 7 or more points in a row above or below the center line >> 7 or more points in one direction >> Any nonrandom pattern
The key to chart interpretation is to initially ascertain the type of variation in the system—that is, whether the variation is coming from special or common causes. When the system has only common causes of variation, it is referred to as stable or in control. If, however, the system has special causes of variation, it is referred to as unstable, or out of control.
Look any of the conditions listed below, which indicate that the process is statistically unstable:
When you have determined whether or not there is special cause variation, declare the system stable or unstable.