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Histogram and Cpk

Process capability against spec limits.

When to use it

Use it to check whether a process can hold its tolerance. Paste measurements and the specification limits, and it draws the histogram and works out Cp, Cpk and the share out of spec.

What you enter

  • Lower spec limit (LSL)
  • Upper spec limit (USL)
  • One measurement per line

Leave one blank if the spec is one-sided.

Paste a single column from Excel. Use at least 30 points for a reliable capability figure.

What you get

  • Capability
  • Histogram
  • Reading the result

How it works

Cpk = the smaller of (USL − mean) and (mean − LSL), divided by 3 × sample standard deviation. Cpk of 1.33 or more is a common minimum for a capable process. It assumes the data are roughly normal and the process is stable, so check a control chart first. This tool uses the overall sample standard deviation, so the figure is closer to Ppk than a within-subgroup Cpk.

How to use the Histogram and Cpk

Process capability compares the spread of your process with the tolerance the customer allows.

Cp = (USL − LSL) ÷ 6σ and Cpk = min(USL − mean, mean − LSL) ÷ 3σ.

  1. Paste measurements from a stable process (check the control chart first).
  2. Enter the upper and lower specification limits.
  3. Read the histogram, Cp and Cpk. A Cpk of 1.33 or more is a common minimum target.

Worked example

A shaft diameter has limits of 20.00 ± 0.05 mm. Data show a mean of 20.02 mm and σ of 0.01 mm. Cp = 0.10 ÷ 0.06 = 1.67, but Cpk = (20.05 − 20.02) ÷ 0.03 = 1.00. The spread is fine; the process is off-centre and needs adjusting.

Common mistakes to avoid

Frequently asked questions

What is a good Cpk value?

1.33 is a common minimum. Safety-critical or automotive characteristics often require 1.67 or more.

What is the difference between Cp and Cpk?

Cp measures spread only. Cpk also accounts for how well the process is centred between the limits.

How many samples do I need?

At least 30, preferably 50 to 100, taken from a process that is in statistical control.

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