BIZOMAT 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.
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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). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Grand average X̄
- What it is
- The average of all subgroup averages from your control chart data, in the same unit as the specification limits.
- Units and format
- Enter a plain number with no unit. The form accepts -1000000 to 1000000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25.01 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from a period when the chart was in control.
What this means: Average range R̄
- What it is
- The average of the subgroup ranges (largest minus smallest reading in each subgroup), used to estimate the process standard deviation.
- Units and format
- Enter a plain number with no unit. The form accepts 1e-9 to 1000000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.03 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- σ is R̄ ÷ d₂, so Cp and Cpk fall in inverse proportion as R̄ grows.
What this means: Subgroup size
- What it is
- The number of parts measured in each subgroup, which selects the d₂ and A₂ control chart constants.
- Units and format
- Choose one of 9 options from the list: 2; 3; 4; 5; 6; 7; 8; 9; 10.
- Example
- The form opens with “5” selected as a worked example. Choose the option that matches your case.
- Get it right
- Must match the subgroup size used to calculate R̄.
What this means: Lower specification limit
- What it is
- The lowest acceptable value of the characteristic, from the drawing or specification.
- Units and format
- Enter a plain number with no unit. The form accepts -1000000 to 1000000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 24.95 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Upper specification limit
- What it is
- The highest acceptable value of the characteristic, from the drawing or specification.
- Units and format
- Enter a plain number with no unit. The form accepts -1000000 to 1000000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25.07 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Least Cpk accepted
- What it is
- The lowest Cpk your customer or quality plan accepts for this characteristic.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 3. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.33 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
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
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Explains the concept · BIZOMAT original book
Capability and control of a leak test
In Production Leak Testing by the Numbers
What it covers: Why leak data are log-normal and mixed, why a Cpk misleads, p-charts of reject rates, charting the reference leak, what a customer audit can show, and a capability claim corrected.
Method explained here · BIZOMAT original book
Capability from a stable process
In Control Charts by the Numbers
What it covers: Cp, Cpk and predicted rejects from a stable process, capability against performance, the confidence bound on a capability index and how many parts a capability claim needs.
Method explained here · BIZOMAT original book
Electrostatic powder coating
In Electrostatics in the Factory by the Numbers
What it covers: How a corona gun charges powder, why charged powder wraps round an earthed part, what causes back-ionisation and thin inside corners, and how transfer efficiency drives powder cost.
Method explained here · BIZOMAT original book
Coating thickness, uniformity and measurement
In Plasma Surface Engineering by the Numbers
What it covers: Why PVD coating thickness varies with line of sight, rotation, distance and loading, how to measure it with the ball crater test, and how to judge a coating process's capability from witness coupons.
Method explained here · Library collection
Proving a process is ready for production: measurement, stability, capability and PPAP-style evidence
In Product Development and Launch
What it covers: Why good samples do not prove a process is ready to scale, and how measurement checks, control charts, capability indices and a traceable evidence chain show it can repeat.
Useful alongside · Library collection
Statistical process control on the shop floor: control charts, real signals and when to leave a process alone
What it covers: Control charts separate the normal noise of a process from real change. How to choose a chart, set limits, read the signals and stop well-meant adjustments that make variation worse.
BIZOMAT 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