How to use the Cp and Cpk process capability calculator
Capability indices compare the width of your specification to the spread of the process. Cp = (USL โ LSL) รท 6ฯ looks at spread alone, while Cpu = (USL โ mean) รท 3ฯ and Cpl = (mean โ LSL) รท 3ฯ give Cpk as the smaller of the two, so Cpk also penalizes a process that has drifted off center. With a one-sided specification Cp is not defined and Cpk is simply the index on the side that exists.
Worked check: limits of 9.5 and 10.5 with a mean of 10.1 and a standard deviation of 0.1 return Cp 1.667, Cpu 1.333, Cpl 2.000 and Cpk 1.333. The expected defective rate under a normal distribution comes out near 32 ppm, matching the textbook pairing of Cpk 1.33 with roughly 32 ppm beyond one limit.
The verdict shown here treats 1.33 as good and 1.67 as excellent, with anything below 1.00 flagged as not capable. Those thresholds are customer and internal requirements, not a legal standard, so confirm the target in your control plan. The ppm figure also assumes a stable normal distribution: skewed, bimodal or drifting data will not match it. Finally, remember the naming convention that short-term within-subgroup sigma gives Cp and Cpk, while long-term overall sigma gives Pp and Ppk.
Frequently asked questions
Cp looks only at spread, while Cpk looks at spread and centering together. If the spread is tight but the process mean has drifted toward one limit, Cp stays the same and only Cpk drops. The fix is to recenter the process before trying to reduce variation.
Most production agreements ask for Cpk of at least 1.33, and 1.67 or higher for new processes and critical characteristics. These are customer and internal requirements rather than any legal limit, so check the control plan or quality agreement that applies to your part.