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Process capability

Calculate Cp/Cpk and Pp/Ppk to summarize process capability against specification limits.

Summary

This calculator uses ISO 22514-1 definitions for Cp/Cpk and Pp/Ppk, aligned with expectations from FDA Process Validation (2011) and ICH Q8/Q9/Q10 for statistical process monitoring.

Process capability indices quantify how well a stable process fits within specification limits. Cp and Cpk summarize short-term capability using within-process variation, while Pp and Ppk use overall variation to describe long-term performance.

A higher Cp or Cpk indicates a process that is both precise and well-centered. When only one specification limit applies, the single-sided capability (Cpu or Cpl) is reported.

Capability analysis should be performed on representative data from a stable process. Use consistent units for limits, mean, and standard deviations.

Step-by-step: Assess process capability

  1. Define the critical quality attribute and limits

    Document the lower and/or upper specification limits (LSL/USL) and ensure all measurements share the same unit.

  2. Collect representative data

    Use stable, in-control data to estimate the mean and both the within-process and overall standard deviations.

  3. Calculate capability and performance indices

    Cp/Cpk use within-process variation. Pp/Ppk use overall variation for long-term performance.

  4. Interpret results in context

    Compare results to your internal acceptance criteria and the criticality of the attribute.

Process capability inputs

Use consistent units for LSL, USL, and mean. Sigma inputs represent standard deviation.

How to estimate sigma

Use subgrouped data (recommended) or individual measurements to estimate within and overall standard deviation.

  • Within sigma (short-term): use rational subgroups and estimate from within-subgroup variation, e.g. sigma within = Rbar / d2 or pooled subgroup standard deviation.
    sigma within =Rbard2

    Rbar is the average of subgroup ranges (max - min) across all subgroups.

    d2 is a control chart constant based on subgroup size (n) (e.g., n=5 -> d2=2.326; n=4 -> 2.059; n=3 -> 1.693; n=2 -> 1.128).

    or

    sigma within =√(sum((n_i - 1) * s_i^2)sum(n_i - 1))

    n_i is the sample size of subgroup i.
    s_i is the standard deviation of subgroup i.

  • Overall sigma (long-term): standard deviation of all data points combined, including shifts or drift.

Short-term capability (Cp/Cpk)

Cp =USL - LSL6 * sigma within
Cpk =min(USL - mean, mean - LSL)3 * sigma within

Provide limits and within sigma to calculate Cp/Cpk.

Long-term performance (Pp/Ppk)

Pp =USL - LSL6 * sigma overall
Ppk =min(USL - mean, mean - LSL)3 * sigma overall

Provide limits and overall sigma to calculate Pp/Ppk.

Regulatory references

Read-only guidance aligned with major regulatory bodies.

FDAEMAICHUSPISPEPDA