The Psychology of Quality and More

Control Chart: Practical variations

The Quality Toolbook > Control Chart > Practical variations

Practical variations

• Another significant set of points that can be identified on a Control Chart is a bias, where more points that might be expected are on one side of the center line. They need not be sequential, as in a shift. Significant sets are:
•

• Ten out of eleven consecutive points on one side of the center line.
• Twelve out of fourteen consecutive points on one side of the center line.
• Fourteen out of seventeen consecutive points on one side of the center line.
• Sixteen out of twenty consecutive points on one side of the center line.

• Draw one additional horizontal line two standard deviations away from either side of the central line (these occur at two-thirds of the way towards the control limits for most Control Charts - this excludes range charts, which do not have a symmetrical distribution). These lines are called the Upper Warning Limit (UWL) and the Lower Warning Limit (LWL), and catch additional sequences that may indicate out-of-control situations. Warning limits are illustrated below in Fig. 1.
• Additional sequences (to those in Table ) that may now indicate out-of-control situations include:
• Two out of three consecutive points are between a warning limit and the corresponding control limit.
• Three out of seven consecutive points are between a warning limit and the corresponding control limit.
• Five or more points which are all increasing or decreasing (a trend) and which cross a warning limit.
• Fig. 1. Additional limit lines

• Draw a third and fourth line in addition to the warning limits, at one standard deviation either side of the central average line. Additional sequences to check for now include:
• Fifteen consecutive points which lie entirely between these two lines.
• Four or more consecutive points beyond one of these lines.
•

• If the cost of looking for problems in the process is high and the consequence of problems is not serious, then wider control limits may be used, for example at four standard deviations from the central average line. Conversely, control limits may be tightened, for example to two standard deviations, if the cost of looking for problems is low and the consequence of problems is serious.
• A Multi-Vari Chart (Fig. 2) is a simple way of showing the ranges of each of a set of samples, where the range is shown by a vertical line, as illustrated. Each line typically represents between 3 and 5 measurements. Specification limits are used instead of control limits, so it can be seen whether any items are getting near or exceeding these constraints. Fig. 2. Multi-Vari Chart

• A variation on the Multi-Vari Chart is the Box Plot (Fig. 3), where the simple line is enhanced with a box to show the center 50% of measurements, with a line to show the center measurement (the median). Each sample is thus visually divided into four quartiles. This requires a number of measurements per sample (typically at least 25).

A variation on this is to change the box width in order to show any change in sample size. Fig. 3. Box Plot

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