Outputs from a controlled process will exhibit variability due to a constant set of common causes over time. Those variabilities can be described by statistical measures such as the mean and standard deviation, as well as being approximated by a normal distribution.

To build statistical models to represent product/process characteristics of interest we must make sure that the data collected indicate consistency over time, i.e. the data have to be plotted as they evolve over the time of production. This way we can analyze whether there are any special causes that could drive the process out of control.

Figure 1 Process behavior over time

Figure 1 Process distribution over time (y-axis is statistical variation in output)

On the figure above, we have four process plotted over time. In fig. 1(a), the process is under statistical control driven solely by common causes of variation, however in fig. 1(b), the process mean begins to shift at 10 A.M and come back to normal at 13 P.M. This instability (out of control behavior) is driven by any special cause of variation that was probably fixed at 13 P.M. In fig. 1(c), the process variation level has changed over time, which is also a presence of special cause condition. Finally, in fig. 1(d) we have the worst of all cases, i.e. the process is unstable in terms of mean and level of variation.