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Note: Use this test for control sparingly. There is a tendency to overcontrol the system when using this test. Use it only when there is some doubt about the system’s stability.
When four out of five consecutive points lie beyond the 1-sigma limit on one side of the average, the system is declared unstable.
See also: >> Any nonrandom pattern >> Too close to the average >> Too far from the average >> Cycles >> Trends >> Sawtooth >> Clusters >> 2 of 3 points beyond 2 sigma
The control limits drawn on control charts are located three standard deviations away from the average (or center line) of the chart. These are called “3-sigma” control limits. Sigma is the name of the symbol for standard deviation. The distance from the center line to the control limits can be divided into three equal parts, one sigma each, as shown below. If two out of three consecutive points on the same side of the average lie beyond the 2-sigma limits, the system is said to be unstable. The chart below demonstrates this rule.
See also: >> Any nonrandom pattern >> Too close to the average >> Too far from the average >> Cycles >> Trends >> Sawtooth >> Clusters >> 4 of 5 points beyond 1 sigma
The chart below shows a typical sawtooth pattern. Observe how the data points alternate above and below the center line. For some reason, alternate subgroups have greater and smaller averages. Stratifying or splitting the data by key variables may assist in analyzing this problem. This may occur if you alternate samples from two machines or production lines.
See also: >> Any nonrandom pattern >> Too close to the average >> Too far from the average >> Cycles >> Trends >> Clusters >> 2 of 3 points beyond 2 sigma >> 4 of 5 points beyond 1 sigma
When clustering is occurring, data appears in groups, even though there is no group of seven points in a row above or below the average. This pattern suggests that the system is “jumping” from one setting to another.
When trying to improve this process, questions should be asked about the transition periods between the clusters. What is causing the system to “jump”?
See also: >> Any nonrandom pattern >> Too close to the average >> Too far from the average >> Cycles >> Trends >> Sawtooth >> 2 of 3 points beyond 2 sigma >> 4 of 5 points beyond 1 sigma
Notice that the plot of averages drifts upward on this example, even though there is no group of seven points in a row going up. This pattern indicates a gradual change over time in the characteristic being measured.
See also: >> Any nonrandom pattern >> Too close to the average >> Too far from the average >> Cycles >> Clusters >> Sawtooth >> 2 of 3 points beyond 2 sigma >> 4 of 5 points beyond 1 sigma
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