Establishing Control

There are two types of error possible when attempting to determine whether a process is in a state of control. These are referred to as errors of the first and second kind.

1. We may react to a false alarm. In this case, we interpret the data to indicate the presence of an assignable cause, when in fact there is none.
   
   
2. We may fail to react to a signal of loss of control. In this case, we interpret the data as indicative of only chance cause variation, when in fact it stems from an assignable cause.

It is a reasonably simple matter to avoid committing one of these errors. For example, we can treat everything as a signal of an assignable cause, in which case we're not likely to miss the real signals, but we will waste most of our time chasing false alarms. Alternatively, we could go the other way and treat everything as random noise, in which case we wouldn't react to any false alarms, but we would also miss any genuine signals.

The hard part is finding a reliable way to ensure that we strike the balance between these two errors. Fortunately, the hard part has already been done for us by Walter Shewhart when he first devised the charts.

The calculation for control limits was devised in such a way as to minimise the possibility of committing either type of error. This means that it is still possible that a control chart will give a false alarm, or will fail to indicate an assignable cause, but either possibility has been reduced to an economic minimum. In practice, when the charts are set up and used correctly, they are very sensitive to changes in the process, and give very few false alarms.

Control charts use 3 sigma limits to establish the upper and lower bounds for a given statistic. A sigma unit is a standardised measure of dispersion for use with control charts. The upper control limit for the statistic being charted is placed at 3 sigma units above the centre line, and the lower control limit at 3 sigma units below the centre line. The centre line is placed at the average for the particular statistic being charted. Shewhart stated that the choice of sigma as a measure of the expected dispersion of a stable process was based on statistical theory. The decision to place the action limits on the control chart at 3 sigma units above and below the central line was based on empirical evidence.¹