Control Charts

Whilst the other six tools have only a passing involvement with what we think of as statistics, we’re getting to it more with Control Charts.  These are sometimes attributed to Deming, who certainly encouraged their use.  There are several types of Control Chart available to us, split into variable and attribute types.  These come with their own formulae for use but I want to start with the basic idea.

Let’s consider a production line which produces 10 widgets a minute.  For this exercise, it doesn’t matter what a widget is, nor what parameter we’re going to measure – but we will have one that will give us a series of values.  From those values we can calculate the arithmetic mean and the standard deviation.  We will also assume the reading follow a normal distribution and that our production line is operating normally.  The mean will tell us the average value of our reading and the standard deviation a idea of the variation – we’ll do some rounding and should be confident that at least 95% of our readings fall within two standard deviations of the mean.  The variation will be a result of a range of factors over which we have no real control and is called the ‘natural variation’; it’s a feature of the process and is as good as it gets.  Conversely, when something extra happens to throw our measurements out, we term that ‘special variation’; that extra might be a machine fault, shift change, material change, a change in the weather – almost anything.  The purpose of a Control Chart is to let us identify a ‘special cause’ variation as soon as possible.  So we start with our stable process and take a series of sequential measurements (typically about 30) and calculate mean and standard deviation.  We then set up a graph where we mark the mean plus UCL (Upper Control Limit) and LCL (Lower Control Limit); for this exercise UCL and LCL will be plus and minus two standard deviations from the mean, respectively.  We then plot subsequent readings on this chart:

This shows a process under control; the variation may look extreme but it’s within limits and ‘natural’ – there’s probably little we can do to improve on it.  One reading is below the LCL – but that isn’t unexpected.  However, more readings there (or above the UCL should prompt investigation (at least, if we start to get several in sequence or more than one or two in any 20 readings).  We also want to look out for trends where there is a series of sequential readings (four or five) on an upward or downward slope, or above or below the mean.

If Control Charts look useful, this one tool where you definitely need further research and reading.