KEVOS® MAKEOS · Quality
Process Capability Check (σ from R̄, Cp, Cpk, Rejects, Limits)
From my control chart averages, how capable is this process against the tolerance, what share will fall out of tolerance, and what are the control limits?
Capability check of a stable process from an X̄–R control chart: process standard deviation from the average range and the d₂ constant, X̄ and R control limits (as the X-bar R limits tool), capability indices Cp and Cpk against the specification limits, the predicted parts per million outside each limit from the normal distribution (as the normal out-of-spec tool), and the check against your least Cpk.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Grand average X̄ | Average of the subgroup averages from the chart. | |
| Average range R̄ | Average of the subgroup ranges. | |
| Subgroup size | choice | Number of parts in each subgroup. |
| Lower specification limit | Lower tolerance limit. | |
| Upper specification limit | Upper tolerance limit. | |
| Least Cpk accepted | Least Cpk the customer or your plan requires (often 1.33 or 1.67). |
Method and formulas
- σ = R̄ ÷ d₂; X̄ limits = X̄ ± A₂ R̄; R limits D₃ R̄ and D₄ R̄ (as the X-bar R limits tool, standard Shewhart constants).
- Cp = (USL − LSL) ÷ 6σ; Cpk = min(USL − X̄, X̄ − LSL) ÷ 3σ.
- Rejects from the normal distribution below LSL and above USL (as the normal out-of-spec tool).
- Example: σ = 0.012898, Cp 1.5507, Cpk 1.5507, about 3.2873 ppm out of tolerance.
Limitations
- Valid only for a stable (in-control), roughly normal process.
- Short-term σ from ranges; long-term performance (Ppk) is usually lower.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a process before a production approval
- Turn chart data into a reject rate
- Decide whether to centre the process or reduce spread
Who it is for
- Quality engineers
- Process engineers
- Production supervisors
What you get
- Process σ and control limits
- Cp and Cpk
- Predicted rejects
Interpreting the result
- If Cp is high but Cpk is low, centring the process fixes it; if both are low, the spread must come down.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 128–133. Topic reference; no source tables or recommended settings are reproduced.
- ISO 7870-2 Control charts — Shewhart control charts
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Process Capability Check (σ from R̄, Cp, Cpk, Rejects, Limits) calculator
