For a process to be in control, the statistical distribution of the measurements being used to monitor the process shoulod be the same whenever the process is observed - the measurement distribution should be 'repeatable and predictable'. Provided the distribution is constant, it doesn't matter what form the distribution takes.
Some measurements are inherently non-normal in their distribution.
The distribution of such times is therefore skewed, and so disticntly non-normal. As a further illustration, consider the distribution of times, in days, taken to repair breakdowns. The histogram of 4688 of these times, recorded during August 1993, is shown as Figure 1. Clearly the distribution is not normal. We can use this data to set control limits for future observations on the process.