What Is Cp and Cpk?
Also known as: process capability index, Cpk
Definition
Cp and Cpk are process capability indices. Cp compares the specification width to the process spread, assuming perfect centering, while Cpk also accounts for how far the process mean has drifted from the center of the tolerance.
Cp and Cpk Explained
Cp equals the total tolerance width divided by six standard deviations of the process, so a Cp of 1.0 means the natural process spread exactly fills the tolerance. Cpk is the minimum of two one-sided ratios: the distance from the mean to the upper specification limit divided by three standard deviations, and the distance from the mean to the lower limit divided by three standard deviations. Because Cpk takes the worse side, Cpk can never exceed Cp, and the gap between them is a direct measure of off-centering.
Common thresholds are 1.33 as a minimum for a capable process, corresponding to a four sigma distance to the nearest limit, and 1.67 for critical or safety-related characteristics. Automotive PPAP submissions commonly require Ppk of 1.67 on significant characteristics for initial approval, with ongoing Cpk of at least 1.33. Aerospace and defense programs frequently apply similar or tighter expectations to key characteristics flagged on the drawing.
Cp and Cpk are only valid when the process is stable and reasonably normal. Calculating capability on an out-of-control process produces a number with no predictive value, because the underlying distribution is not one distribution but several. This is why the correct sequence is always control chart first, confirm stability, then compute capability. Software that computes Cpk from any dataset makes it easy to skip this step and report a confidently wrong figure.
Cpk uses within-subgroup, short-term variation, while Pp and Ppk use the total observed standard deviation over the full data set and therefore reflect long-term performance. A large gap between Cpk and Ppk indicates significant between-subgroup drift, typically from tool wear, lot changes, or shift-to-shift differences. Reporting Cpk when a customer asked for Ppk, or comparing one supplier's Cpk to another's Ppk, is a routine source of disagreement in supplier quality reviews.
Why It Matters
- Translates process variation into a single number customers, quality engineers, and auditors interpret the same way.
- The gap between Cp and Cpk isolates whether the fix is reducing spread or simply recentering the process, which are very different projects.
- Capability thresholds are contractual in automotive PPAP and increasingly expected on key characteristics in aerospace and defense.
- Capability data drives inspection strategy, since demonstrably capable characteristics justify reduced sampling and lower cost of quality.
In Practice
A bore has a specification of 25.00 plus or minus 0.05 mm, so tolerance width is 0.10 mm. Measured standard deviation is 0.012 mm and the mean sits at 25.022 mm. Cp = 0.10 / (6 x 0.012) = 1.39, which looks capable. Cpk takes the tight side: (25.05 - 25.022) / (3 x 0.012) = 0.78. The spread is fine and the centering is not. The correct action is a tool offset of about 0.022 mm, after which Cpk approaches Cp, rather than a process capability project or a machine purchase.
Frequently Asked Questions
What is the difference between Cpk and Ppk?
Cpk uses within-subgroup standard deviation and estimates short-term capability, essentially what the process could do if it stayed stable. Ppk uses the overall standard deviation of all data and reflects actual long-term performance including drift between subgroups. Ppk is usually lower. A wide gap indicates instability from tool wear, material lots, or shift differences.
Why is a Cpk of 1.33 the usual minimum?
A Cpk of 1.33 places four standard deviations between the process mean and the nearest specification limit, implying roughly 63 defects per million on that side under normality. It gives enough margin that ordinary process drift does not immediately produce nonconforming parts. Critical characteristics typically require 1.67, or five sigma of margin, for the same reason.
Related Terms
SPC (Statistical Process Control)
SPC (Statistical Process Control) is the use of control charts and statistical rules to monitor a process in real time, distinguishing normal common-cause variation from special-cause variation that signals a genuine change requiring action.
Six Sigma
Six Sigma is a data-driven improvement methodology that reduces process variation and defects using statistical analysis, targeting a capability level of 3.4 defects per million opportunities, typically executed through the five-phase DMAIC cycle.
PPAP (Production Part Approval Process)
PPAP (Production Part Approval Process) is a standardized supplier approval package, originating in the automotive industry, that demonstrates a supplier's production process can consistently produce conforming parts at the quoted rate before shipments are authorized.
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