Process capability (Cpk)
Capability compares what the process actually does with what the customer needs. Cpk puts that comparison into one number.
About 5 minutes to read.
Key idea
Two voices meet in a capability study. The customer’s voice sets the limits: a bottle must hold between 495 and 505 millilitres, an invoice must be paid within 30 days. The process has its own voice: how much it naturally varies, and where it is centred.
Cp compares the width the customer allows with the natural spread of the process, ignoring where the process is centred. Cpk adds the centring: it measures the distance from the average to the nearer limit, in units of three standard deviations. A Cpk of 1 means the nearer limit sits exactly three standard deviations away, so a small share of results already falls outside. Many organisations ask for at least 1.33.
Capability only means something for a stable process. If the control chart shows special causes, fix those first. A capability figure for an unstable process describes a moment, not the process.
Example: filling bottles
Centred, then drifting
A juice line fills bottles with an average of 500 ml and a standard deviation of 1.2 ml. The limits are 495 and 505, so the nearer limit is 5 ml away, a little over four standard deviations, and Cpk is about 1.39.
After a nozzle wears, the average creeps to 502 ml while the spread stays the same. The upper limit is now only 3 ml away, and Cpk falls to about 0.83. The spread did not change at all. Only the centring did, which is exactly what Cpk is built to catch.