When modern companies use Statistical Process Control, rules are applied to the charts to indicate that something has changed. The rules used are usually a sub-set of eight rules that are known as the Western Electric Rules.
Statistical Process Control: Background
A more detailed explanation is available of the background at this link to Statistical Process Control. To summarize briefly, an SPC Chart has limits that are calculated based on how much variation a process has. They are not related to customer specifications, and the points plotted on the chart should be random. The chart should not show any patterns or trends.
One more key point is that the points should be distributed "Normally", and should fit the Gaussian "Bell" Curve. This means that around 68% of the points lie within one standard deviation of the mean, 95% of the points should lie within two standard deviations of the mean, and 99.7% of the points should lie within three standard deviations of the mean.
Western Electric Rules: Point Outside Upper or Lower Control Limits
The Upper and Lower Control Limits are set at three standard deviations from the mean. If a point lies outside either of these limits, there is only a 0.3% chance that this was caused by the normal process.
Western Electric Rules: Eight Points on the Same Side of the Mean
There is an equal chance that any given point will fall above or below the mean. The chances that a point falls on the same side of the mean as the one before it is one in two. The odds that the next point will also fall on the same side of the mean is one in four. The probability of getting eight points on the same side of the mean is only around 1%.
Western Electric Rules: Eight Points Increasing or Decreasing
The same logic is used here as for "Eight Points on the Same Side of the Mean". Sometimes this rule is changed to seven points rising or falling.
Western Electric Rules: Two of Three Points Outside Warning Limits
The Warning Limits are usually set at two standard deviations (i.e. two sigma) from the mean. The probability that any point will fall outside the warning limit is only 5%. The chances that two out of three points in a row fall outside the warning limit is only about 1%.
Western Electric Rules: Four of Five Points Falling Outside One Sigma
In normal processing, 68% of points fall within one sigma of the mean, and 32% fall outside it. The probability that 4 of 5 points fall outside of one sigma is only about 3%.
Western Electric Rules: Fourteen Points Alternating Direction
This rule treats each pair of adjacent points as one unit. The chances that the second point is always higher than (or always lower than) the preceding point, for all seven pairs is only about 1%.
Western Electric Rules: Fifteen Points in a Row Within One Sigma
In normal operation, 68% of points will fall within one sigma of the mean. The probability that 15 points in a row will do so, is less than 1%.
Western Electric Rules: Eight Points in a Row Outside One Sigma
Since 68% of points lie within one sigma of the mean, the probability that eight points in a row fall outside of the one-sigma line is less than 1%.
Western Electric Rules: Summary
The Western Electric Rules are a set of rules that exist to highlight when something improbable happens in a process. The rationale is that if something happens that is improbable due to normal causes, it has happened due to abnormal causes. The abnormal cause is usually a change, and since change to the product is undesirable, action needs to be taken.
The rules, or a sub-set of them, are almost universally used by companies today in their SPC Charts, and a definition of standard deviation can be found here.
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