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Is my process actually capable of meeting the specification?

Get Cp, Cpk, Pp and Ppk from your raw measurements — and find out first whether the process is stable and normal enough for those numbers to mean anything.

Process Capability (Cp, Cpk, Pp, Ppk) · measure · Yellow Belt · free, no account needed

Use this when

  • A customer or auditor has asked for a Cpk
  • You want to know whether the specification is achievable before promising it
  • Somebody has quoted a Cpk and you want to know whether it is warranted

Process Capability· fill volume

sandbox

The conditions for a capability index are met.

Stable
yes
Normal
yes
n ≥ 30
yes(n = 30)

Cp · within

1.293

Cpk · within

1.227

Pp · overall

1.245

Ppk · overall

1.181

n
30
Mean
9.9847
σ within
0.0773
σ overall
0.0803

Cp/Cpk use within-subgroup sigma (within:mrbar-over-d2); Pp/Ppk use overall sigma (overall:sample-sd-n-minus-1).

The two sigma estimates are close, so short-term and long-term variation are much the same here. The process is behaving consistently between the moments you sampled it.

Anderson–Darling A² = 0.367, p = 0.432. Consistent with a normal distribution, which is what the expected-PPM figures assume.

Expected parts per million of fill volume outside the specification under a normal model, split by which limit is breached, for the within-subgroup and the overall sigma estimate.
Expected ppm out of specBelow LSLAbove USLTotal
Within (short-term)the sigma behind Cp and Cpk116.322.8139.1
Overall (long-term)the sigma behind Pp and Ppk197.443.3240.7

These are MODEL outputs for fill volume, not counts of what happened: they are the normal distribution’s tails beyond each limit, so they are only as good as the normality check above. The within row is what the process could deliver if it held still; the overall row is what the customer received. Which tail is larger says which way the mean has to move, and the total says nothing about that.

One per line. Order matters — stability is checked from it.

How this is calculated
  • Within-subgroup sigma = mean moving range ÷ d₂ (d₂ = 1.128 for n = 2), the short-term variation. Feeds Cp and Cpk.
  • Overall sigma = the sample standard deviation, dividing by n − 1. Feeds Pp and Ppk. Dividing by n understates the spread and inflates every index — it is the most common defect in hand-built capability spreadsheets.
  • Cp = (USL − LSL) / 6σ; Cpk = min[(USL − μ), (μ − LSL)] / 3σ.
  • Stability is measured from an individuals-and-moving-range chart on the same data, not asserted. Normality by Anderson–Darling at α = 0.05.

Source: Montgomery, D.C., Introduction to Statistical Quality Control 7e, Ch. 8 (process capability) and §6.4 (individuals charts); AIAG, Statistical Process Control 2nd ed., for the within/overall distinction.

How this is calculated

Within-subgroup sigma = mean moving range / d2, feeding Cp and Cpk. Overall sigma = the sample standard deviation dividing by n-1, feeding Pp and Ppk; there is no code path from a long-term sigma to a Cp. Cp = (USL - LSL) / 6 sigma; Cpk = min[(USL - mean), (mean - LSL)] / 3 sigma. Stability is measured from an individuals-and-moving-range chart on the same data rather than assumed, normality by Anderson-Darling at alpha 0.05, and the sample size is checked against a floor of 30.

Source: Montgomery, D.C., Introduction to Statistical Quality Control 7e, Ch. 8 (process capability) and Sec. 6.4 (individuals charts); AIAG, Statistical Process Control 2nd ed., for the within/overall distinction.

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