Process Capability Analysis (Cp, Cpk, Pp, Ppk)
Measure how well a process meets its specification limits. Compute Cp, Cpk, Pp and Ppk, check the normality assumption, and translate capability into a sigma level and expected defect rate.
Run Capability Analysis →What is Process Capability Analysis?
Process capability analysis compares the natural spread of a process to the width of its specification limits. It answers a direct question: given how much the process varies, can it reliably produce output within the customer's tolerance?
The potential capability index Cp compares the specification width to six standard deviations of process variation, but it ignores centering. Cpk corrects this by measuring the distance from the process mean to the nearer specification limit, so it captures both spread and location. A process can have a good Cp yet a poor Cpk if it is off-center.
Cp and Cpk use the within-subgroup (short-term) standard deviation and describe potential capability when the process is stable. Pp and Ppk use the overall (long-term) standard deviation and describe actual performance including drift between subgroups. Capability analysis is only valid once the process is in statistical control.
In plain terms: You have a target window (the spec) and a process that wobbles. Capability tells you whether the wobble fits inside the window with room to spare. Cp asks 'is the wobble narrow enough?'; Cpk also asks 'is it aimed at the middle?'. A high Cp but low Cpk means the process is precise but off-target.
The Four Indices
Cp (Potential)
Spec width divided by six short-term standard deviations. Measures whether the spread could fit the tolerance, ignoring centering.
Cpk (Actual, Short-term)
The smaller of the distances from the mean to each spec limit, over three sigma. Accounts for both spread and centering.
Pp & Ppk (Performance)
The same calculations using the long-term standard deviation, capturing real-world variation including shifts and drift between subgroups.
Key Formulas
Interpreting the Indices
A Cpk of 1.00 means the nearer spec limit sits three standard deviations from the mean, corresponding to roughly 0.27 percent defects for a centered process. A Cpk of 1.33 is a common minimum target and 1.67 or above is often required for critical characteristics.
Compare Cp with Cpk to diagnose the problem. If Cp is good but Cpk is much smaller, the process is capable but off-center, so recentering the mean will fix it. If Cp itself is low, the process is too variable and centering alone will not help; you must reduce variation.
Assumptions & Validation
Statistical Control
The process must be stable, shown by control charts, before capability is meaningful.
If violated: Bring the process into control first; capability of an unstable process is not predictive.
Normality
Standard indices assume an approximately normal distribution; check with a histogram or normality test.
If violated: Use a data transformation or non-normal capability methods (for example Weibull-based indices).
Adequate Sample
Enough data across enough subgroups to estimate variation reliably.
If violated: Collect more subgroups spanning normal operating conditions.
Valid Measurement System
Measurement error must be small relative to process variation.
If violated: Run a Gage R&R study before trusting capability numbers.
⚠️ Check assumptions first
Capability indices are meaningless for an out-of-control process, because an unstable process has no single predictable spread to compare against the specification. Always confirm statistical control with a control chart and validate the measurement system with a Gage R&R study first. Reporting Cpk for an unstable or poorly measured process gives false confidence.
When NOT to Use Process Capability Analysis
Unstable Process
If control charts show special-cause variation, capability cannot be projected. Achieve control before computing indices.
Strongly Non-normal Data
For skewed or bounded data, normal-based Cpk misstates the defect rate. Use a transformation or non-normal capability method.
No Specification Limits
Capability requires customer specification limits. Without them, use control charts to study variation instead.
Industry Applications
Manufacturing Quality
Demonstrate that a machined dimension or fill weight reliably meets tolerance before full production.
Supplier Qualification
Require a minimum Cpk (often 1.33 or 1.67) as evidence a supplier's process can meet specifications.
Process Improvement
Track Cpk before and after an improvement to quantify the reduction in variation or shift in centering.
Design Verification
Confirm a new process is capable of meeting engineering tolerances during validation.
Frequently Asked Questions
What is the difference between Cp and Cpk?
Cp compares the specification width to six standard deviations of process variation but ignores where the process is centered. Cpk measures the distance from the process mean to the nearer specification limit, so it captures both variation and centering. A process can have a high Cp yet a low Cpk if it is running off-center; comparing the two reveals whether the issue is spread or location.
What is the difference between Cpk and Ppk?
Cpk uses the within-subgroup, short-term standard deviation and describes the potential capability of a stable process. Ppk uses the overall, long-term standard deviation and describes actual performance including shifts and drift between subgroups. Cpk tends to be more optimistic; a large gap between Cpk and Ppk signals instability or between-subgroup variation.
What is a good Cpk value?
A Cpk of 1.33 is a widely used minimum for many processes, corresponding to about four standard deviations between the mean and the nearer spec limit. Critical characteristics often require 1.67 or higher. A Cpk of 1.00 means the nearer limit is only three standard deviations away, which typically allows too many defects for demanding applications.
Why must the process be in control before measuring capability?
Capability projects the future defect rate from the current spread. If the process is out of statistical control, its spread and mean are not stable, so any projection is unreliable. Control charts must show only common-cause variation before capability indices carry meaning; otherwise Cpk describes a snapshot that will not hold.
What if my data is not normally distributed?
Standard capability indices assume approximate normality to translate the indices into defect rates. For skewed or bounded data, this translation is wrong. Options include transforming the data, for example with a Box-Cox transformation, or using non-normal capability methods that fit an appropriate distribution such as Weibull before computing the indices.
How does capability relate to sigma level?
For a centered process, the short-term sigma level is approximately three times Cpk on the nearer side. A Cpk of 1.33 corresponds to roughly a four-sigma process on that side. Many organizations also apply the conventional 1.5-sigma long-term shift when converting capability to the familiar sigma-level and DPMO figures used for benchmarking.
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