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Control charts (part 1: interpreting them)
Understanding variation is at the heart of much quality work. If you can control variation then you can deliver consistent products and services. If you can reduce variation, then you can deliver higher quality and hence sell more, at higher prices.
Drawing out the Histogram
The Histogram is a common tool used for showing the distribution of a set of measures and often appears in a bell-shaped ‘Normal’ or ‘Gaussian’ graph, where the majority of measures are clustered around the centre. What the Histogram does not show, however, is the way in which those measurements changed over time. If you turned a Histogram on its side, and ‘pulled out’ the measures as they appeared over time, they might appear as in Fig. 1.
Fig. 1. Histogram and measures over time
What may be found here is that something interesting is going on. After some early fairly random variation, the measures go up and them go down in a nice straight line. The question here is ‘Is this significant?’ Is what looks like something important actually worth going to investigate? Can we safely ignore it or should we do something? Indeed should we ignore it, such that tampering with the process might just make things worse?
This is the purpose of Control Charts: to understand variation over time and decide whether investigation or action is appropriate or not.
Adding control limits
The Control Chart’s first trick is to add horizontal lines, called ‘Control Limits’. To show the centre of the distribution, an average (or ‘mean’) line is also added, as in Fig. 2. An important point here is that Control Limits are calculated. They are not ‘action limits’ that somebody estimates. They are used to show statistical significance and hence require the use of a simple, statistically-derived formula (this calculation will be discussed in a later article).
Fig. 2. Adding Control Limits
The control limits are known as the Upper Control Limit (UCL) and Lower Control Limit (LCL).
If a point falls outside these limits, it indicates a statistically significant event (or ‘special cause of variation’) which should be investigated. This does not happen in Fig. 2.
Shifts, Trends and Cycles
As well as being used to identify special causes of variation, the Control Chart also can be used to identify patterns within the sequence of measurements.
Shifts occur where the mean of a sequential set of measures has shifted from the overall mean of the whole set of measures. This is detected when seven or more sequentiall points appear, one after the other, on one side of the central average line.
Trends happen where a set of sequential measures keeps increasing or decreasing. Again, the magic number for statistical significance is seven.
Finally, Cycles occur where a repeating up-and-down pattern can be seen in the Control Chart. Seven cycles again is the number that indicates something significant is going on.
To summarise, the four ways of identifying statistical significance are shown in the table below.
This article first appeared in Quality World, the journal of the Chartered Quality Institute
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