Cp vs Cpk: spread and centring
Check whether the variation of a stable process fits within the required limits.
What to prepare
Numeric measurements, unit, chronological order, LSL and USL limits, and the sampling method. Limits come from requirements, not from the minimum and maximum of the data.
Method and steps
Cp = (USL − LSL) / (6σ within). Cpk = min((USL − μ)/(3σ within), (μ − LSL)/(3σ within)). Pp and Ppk use overall dispersion. The sigma estimator must be stated; the results are not interchangeable.
- Define the decision and the criterion you are tracking.
- Check the data and the method assumptions.
- Calculate and review the chart together with its context.
- Document the limitation of the result and the next action.
Practical example
With LSL 90, USL 110, μ 102 and σ within 2, Cp is 1.67 and Cpk is 1.33. The difference shows the mean shifted towards the upper limit. This is a hypothetical example, not a result from 15 data points.
Mistakes to avoid
Do not interpret Cpk as proof of stability. First check the control chart, measurement system and distribution. The acceptance threshold is the one agreed for the process; a generic value does not replace the customer requirement.
Applying it in QAPP
Start from the existing form and define how the data is validated. Link the result to the person responsible for checking it. During the pilot, compare data quality and reporting time with the initial situation; do not assume automation validates the analysis by itself.