Process Capability Analysis (Cp, Cpk)
Also known as: Process Capability Indices, Capability Study, Süreç Yeterlilik Analizi, Process Performance Analysis
Process Capability Analysis quantifies how well a manufacturing or business process produces output within specified tolerance limits. Introduced formally by Victor Kane in 1986, it summarises process spread and centering into dimensionless indices — most notably Cp and Cpk — allowing engineers and quality managers to judge whether a stable process is inherently capable of meeting customer or design specifications consistently.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
+11 more
When to use it
Use Process Capability Analysis when a manufacturing or transactional process is in statistical control and outputs can be measured on a continuous scale against defined specification limits. It is appropriate for quality audits, supplier qualification, and Six Sigma projects. Key assumptions are normality of the output distribution and process stability. It should not be applied to unstable processes, attribute (pass/fail) data without adaptation, or when specification limits are absent. For non-normal data, consider Pearson or Johnson transformation methods or non-parametric capability indices.
Strengths & limitations
- Condenses complex process performance data into a single, easily communicated ratio.
- Directly links process variation to customer or engineering specification limits.
- Widely accepted in automotive (AIAG), aerospace, and manufacturing standards (e.g., IATF 16949).
- Facilitates objective comparison of multiple processes or suppliers on a common scale.
- Assumes the process output follows a normal distribution; violations inflate or deflate index values.
- Requires the process to be in statistical control before capability can be meaningfully assessed.
- Does not capture dynamic shifts over time; a snapshot index may miss long-term drift.
- Specification limits must be predefined and meaningful; arbitrary or overly tight limits distort conclusions.
Frequently asked
What is the difference between Cp and Cpk?
Cp measures potential capability — how wide the specification range is relative to the process spread — without regard to where the mean is located. Cpk incorporates centering by measuring the distance from the process mean to the nearest specification limit. A process can have a high Cp but a low Cpk if it is precise but off-center, making Cpk the more actionable index in practice.
How many data points are needed for a reliable capability study?
A commonly cited minimum is 30 observations collected in a manner that represents typical process variation. However, some standards (e.g., AIAG MSA) recommend 100 or more subgroups for stable estimates. With fewer points, wide confidence intervals around Cp and Cpk make it risky to draw firm conclusions, and bootstrapped or Bayesian confidence intervals are advisable.
What should I do if my process output is not normally distributed?
When the normality assumption fails — confirmed via a Shapiro-Wilk or Anderson-Darling test — options include transforming the data (Box-Cox, Johnson transformation), fitting an alternative distribution and computing percentile-based capability indices, or using non-parametric methods. Applying standard Cp and Cpk formulas to markedly non-normal data can severely misestimate the true defect rate.
Sources
- Kane, V. E. (1986). Process capability indices. Journal of Quality Technology, 18(1), 41–52. DOI: 10.1080/00224065.1986.11978984 ↗
How to cite this page
ScholarGate. (2026, June 2). Process Capability Analysis (Cp, Cpk). ScholarGate. https://scholargate.app/en/statistics/process-capability-analysis
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Shewhart Control ChartStatistics↔ compare
- Six Sigma DMAICQuality Management↔ compare