Inherent variability

When a production process is monitored, there is usually variability in the output. A certain level of variability is unavoidable, at least without substantial changes to the process. In the terminology of quality control, we say that this 'acceptable' level of variability is a result of common causes (or random causes). If this is the only source of variability, the process is said to be in control.

Systematic changes

Our aim is to detect changes to the output that are not the result of common causes. Such systematic changes are said to be the result of special causes (or assignable causes) and could result in...

Systematic changes usually indicate problems with the quality of the output.

Run chart

Successive measurements are recorded at regular intervals as part of the process monitoring. These values are used to detect special causes so that the process can be quickly adjusted to maintain quality.

The aim is to detect problems as soon as possible.

In a control chart, values are plotted in time order, giving a type of time-series plot. As each value is plotted, it is compared to earlier points and, depending on the value, it may be taken as a warning that the process is out of control.

The simplest kind of control chart occurs when an individual measurement is made from the process at regular intervals. The plot of these measurements against time is called a run chart. The challenge is to detect systematic changes in the run chart (due to special causes) over the background level of variability (due to common causes).

Milk carton filling

A milk bottling factory fills plastic cartons with a nominal 2 litres of milk. Randomness in the filling process means that the actual volume varies from carton to carton. The manager has determined that it is possible to achieve a mean volume of 2040 ml with almost all cartons holding between 2000 and 2080 ml; variability within this range is considered to be due to common causes.

The diagram above shows the successive milk volumes in cartons that were sampled from the process output during one shift. Drag the slider to display the values in the order that they were recorded. Click on individual crosses to see the milk volume (g) in the individual sampled cartons.

Lines have been drawn on the plot at 2000 and 2080 ml. Values outside these limits are displayed in red — they might be taken to indicate special causes.

The process starts 'in control' with variation that seems to conform to common causes. However between observations 30 and 70 there seems to be an increasing trend in the process. At observation 70, the operators checked the filling machine and found a loose valve which was tightened. The final observations again seem to conform to common causes with the possible exception of observation 76 which was unusually low though no special cause could be found for this outlier.

Use the scroll bar to again look at the observations in the order they arise. How soon would you detect the increasing trend?