The voice of the process, as defined by the natural process limits, and the voice of the customer, as defined by the specification limits are the two immovable objects of process control. The capability of a process is a measure of how well the one matches up to the other.

At the simplest level, capability can be thought of in terms of how much 'elbow room' a process has. We can find this out by converting the specified tolerance (the distance between the upper and lower specification limits) into sigma units, using the formula:

To take an example, imagine a metal plating process, where the thickness of the plate is specified to be 1mm ±0.03mm. The process is in control, and from 25 samples of 4 items, the mean range has been calculated to be 0.01. By using the formula we can calculate the value of sigma(X) to be 0.005. (You can find the appropriate value for d₂ by clicking on the link in the toolbar.)

The total specified tolerance is 1.03 - 0.97, which equals 0.06. If we divide this by sigma(X) we find that the elbow room for the process is 12 sigma units. Since we can reasonably predict that more than 99% of the output of the process will fall within the range 3 sigma units above and below the process average, we can see that this process has twice the elbow room that it actually needs.