Capability indices also give an indication of the level of safety margin that a process has.
If the natural spread of a process is exactly the same as the specified tolerance then, in order for the process' outputs to remain in spec., the process must be exactly centred on the nominal value, and there must never be any assignable causes.
In practice, this is unlikely to be the case, so it is desirable for the natural process spread to be less than the specified tolerance. The benefits of this safety margin should be clear. If an assignable cause should occur, causing either a change in the process aim, or a widening of the proccess spread, then there is still a reasonable chance that the process' outputs will remain in spec., while the assignable cause is identified and dealt with.
The higher the capability index, the greater the degree of safety.
The two most commonly used indices are Cp and Cpk, and customers will often require minimum values of 1.33 or higher for Cp and Cpk.