What is a good Cpk value?

A Cpk of 1.33 is the figure most customer scorecards ask for on an established process, and 1.67 is common for new processes and safety characteristics. Below 1.00 the specification is narrower than the process spread, so out-of-tolerance parts are expected.

What is the difference between Cp and Cpk?

Cp measures whether the process spread would fit inside the specification if it were perfectly centred. Cpk measures how close the actual mean is to the nearer limit. Cpk is always less than or equal to Cp, and equal only when the process is centred.

Can I calculate Cpk with only one specification limit?

Yes. Leave the other limit blank. Cpk is then Cpu or Cpl, whichever exists, and Cp is not defined because there is no specification width.

How do I convert Cpk to PPM or to a sigma level?

PPM beyond one limit is Φ(−3·Cpk) × 1,000,000. The calculator does both tails and also prints Z.bench, the single z-value that would give the same total PPM; adding the conventional 1.5 shift to Z.bench gives the sigma level quoted in Six Sigma tables.

Should I use Cpk or Ppk?

Use the one your customer asks for, and say which you reported. Cpk uses a within-subgroup standard deviation and describes what the process could do; Ppk uses the overall standard deviation and describes what it did. PPAP submissions commonly ask for Ppk on the initial study.

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Cpk Calculator — Cp, Cpk, Pp and Ppk from Mean and Standard Deviation

Enter a mean, a standard deviation and your specification limits to get Cp, Cpk, Cpl, Cpu and Cpm, the expected PPM out of specification, the yield, Z.bench, and a confidence interval for Cpk. Free, in your browser.

The standard deviation is

Mean (x̄)

Std. deviation (σ)

LSL

USL

Target (optional)

Sample size n

Loaded with the NIST/SEMATECH worked example (§6.1.6): USL 20, LSL 8, x̄ 16, s 2. Leave a limit blank for a one-sided specification.

Cpk

0.667

1.000

Cpl

1.333

Cpu

0.667

Expected PPM

22,782

outside spec, normal model

Yield

97.7218 %

Z.bench

2.00

sigma level 3.50 with 1.5 shift

Cpm

—

needs a target and both limits

PPM below LSL: 31.67
PPM above USL: 22,750
95 % CI for Cpk: 0.506 … 0.828
95 % CI for Cp: 0.802 … 1.197
k (off-centre fraction): 0.3333

Cpk 0.67: below 1.00 — the specification is narrower than the process spread, so nonconforming product is expected as a matter of arithmetic rather than bad luck. Intervals use NIST’s normal approximation for Cpk and the chi-square interval on n − 1 degrees of freedom for Cp.

NIST: the interval approximation needs n ≥ 25, and n ≥ 100 is better.

Have the raw measurements instead?

The process capability tool estimates the within and overall sigma from your subgrouped data itself, prints Cpk and Ppk side by side with a histogram and the normal fit, and names the estimator on the figure. Check the shape first with the free histogram and normality test.

Cpk to PPM table

Expected parts per million under the normal model
Cpk / Cp	PPM, one limit	PPM, centred, both limits	Yield (centred)
0.50	66,807	133,614	86.63856 %
0.67	22,216	44,431	95.55688 %
0.75	12,224	24,449	97.55511 %
0.83	6,387.2	12,774	98.72257 %
1.00	1,349.9	2,699.8	99.73002 %
1.10	483.4	966.8	99.90332 %
1.20	159.1	318.2	99.96818 %
1.33	33.04	66.07	99.99339 %
1.50	3.40	6.80	99.99932 %
1.67	0.272	0.544	99.99995 %
1.83	0.020	0.040	100.00000 %
2.00	9.87e−4	1.97e−3	100.00000 %

Cpk you need to measure, by sample size

Smallest observed Cpk whose lower 95 % confidence bound reaches the target
Parts measured	To show 1.00	To show 1.33	To show 1.67
25	1.34	1.76	2.20
30	1.30	1.71	2.14
50	1.22	1.61	2.01
75	1.17	1.55	1.94
100	1.14	1.52	1.90
125	1.13	1.49	1.87
200	1.10	1.46	1.83

One-sided lower bound, Ĉpk − 1.645·√(1/(9n) + Ĉpk²/(2(n − 1))), from the NIST normal approximation. A guide to planning, not a substitute for the interval on your own data.

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The formulas

Cp = (USL − LSL) / 6σ compares the width of the specification with the width of the process. It ignores where the process is centred, so a process can have a Cp of 2 and still make every part out of tolerance.

Cpk = min(Cpu, Cpl), where Cpu = (USL − μ) / 3σ and Cpl = (μ − LSL) / 3σ. It is the distance from the mean to the nearer limit, in units of three sigma. With only one limit, Cpk is simply the index on that side and Cp does not exist.

Cpm = (USL − LSL) / 6√(σ² + (μ − T)²) is the Taguchi index. It penalises distance from a target T rather than from the limits, so it needs a target, and this calculator does not assume one.

Cp and Cpk, or Pp and Ppk?

The arithmetic is identical; what differs is which standard deviation goes in. A within-subgroup sigma — R̄/d₂ from an X̄-R chart, or MR̄/d₂ from an I-MR chart — measures short-term variation and gives Cp and Cpk. The overall sample standard deviation of every reading gives Pp and Ppk, which include the drift between subgroups as well.

A summary calculator cannot tell which sigma it has been handed, so it asks. If Ppk is much lower than Cpk, the process is moving between subgroups, and that movement is what a control chart is for.

From Cpk to PPM, and what the numbers assume

The expected PPM is the area of the fitted normal curve beyond each limit: Φ(−3·Cpl) + Φ(−3·Cpu), times a million. A Cpk of 1.00 puts about 1,350 parts per million beyond the nearer limit; 1.33 puts about 33; 1.67 about 0.3.

Those numbers are only as good as the normal model behind them. A skewed process — flatness, runout, concentricity, anything bounded at zero — can have a respectable Cpk and a reject rate many times what the table says. Check the shape with the histogram and Anderson-Darling test before quoting a PPM to a customer.

How many parts does a capability study need?

A Cpk computed from 30 parts is an estimate with a wide error bar. With the sample size filled in, the calculator prints the NIST normal-approximation interval for Cpk and the chi-square interval for Cp. NIST notes the approximation needs at least 25 observations, and 100 is better.

The table under the calculator turns that around: it shows how high the Cpk you measure has to be before the lower 95 % confidence bound reaches the Cpk you are asked to demonstrate. On 30 parts, demonstrating 1.33 takes an observed Cpk of about 1.71.

Common questions

What is a good Cpk value?: A Cpk of 1.33 is the figure most customer scorecards ask for on an established process, and 1.67 is common for new processes and safety characteristics. Below 1.00 the specification is narrower than the process spread, so out-of-tolerance parts are expected.
What is the difference between Cp and Cpk?: Cp measures whether the process spread would fit inside the specification if it were perfectly centred. Cpk measures how close the actual mean is to the nearer limit. Cpk is always less than or equal to Cp, and equal only when the process is centred.
Can I calculate Cpk with only one specification limit?: Yes. Leave the other limit blank. Cpk is then Cpu or Cpl, whichever exists, and Cp is not defined because there is no specification width.
How do I convert Cpk to PPM or to a sigma level?: PPM beyond one limit is Φ(−3·Cpk) × 1,000,000. The calculator does both tails and also prints Z.bench, the single z-value that would give the same total PPM; adding the conventional 1.5 shift to Z.bench gives the sigma level quoted in Six Sigma tables.
Should I use Cpk or Ppk?: Use the one your customer asks for, and say which you reported. Cpk uses a within-subgroup standard deviation and describes what the process could do; Ppk uses the overall standard deviation and describes what it did. PPAP submissions commonly ask for Ppk on the initial study.