# Pp and Ppk Calculator

> Source: https://netray.co/tools/pp-ppk-performance-index-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Compute Pp and Ppk from overall standard deviation, compare them with Cp and Cpk from within-subgroup sigma, and estimate parts per million out of spec.

## Category

quality

## Industry

Manufacturing

## Audience

- Quality engineer
- Supplier quality
- Process engineer

## Tool

**Kind:** calculator

**Inputs:**

#### Upper spec limit (USL)

**Key:** usl

**Type:** number

**Default:** 25.05

**Step:** 0.001

**Help:** Same units as the measurement.

#### Lower spec limit (LSL)

**Key:** lsl

**Type:** number

**Default:** 24.95

**Step:** 0.001

#### Process mean

**Key:** mean

**Type:** number

**Default:** 25.004

**Step:** 0.001

#### Overall standard deviation

**Key:** sd_overall

**Type:** number

**Default:** 0.0165

**Min:** 0

**Step:** 0.0001

**Help:** Sample standard deviation of all readings (n-1).

#### Within-subgroup sigma (R-bar / d2)

**Key:** sd_within

**Type:** number

**Default:** 0.0122

**Min:** 0

**Step:** 0.0001

**Help:** Short-term sigma from a control chart. Used for Cp and Cpk.

**Outputs:**

#### Pp

**Key:** pp

**Expr:** (usl - lsl) / (6 * sd_overall)

**Format:** decimal

#### Ppu

**Key:** ppu

**Expr:** (usl - mean) / (3 * sd_overall)

**Format:** decimal

#### Ppl

**Key:** ppl

**Expr:** (mean - lsl) / (3 * sd_overall)

**Format:** decimal

#### Ppk

**Key:** ppk

**Expr:** min(ppu, ppl)

**Format:** decimal

**Primary:** true

**Description:** Long-term performance including drift between subgroups.

#### Cp (within sigma)

**Key:** cp

**Expr:** (usl - lsl) / (6 * sd_within)

**Format:** decimal

#### Cpk (within sigma)

**Key:** cpk

**Expr:** min((usl - mean) / (3 * sd_within), (mean - lsl) / (3 * sd_within))

**Format:** decimal

**Primary:** true

#### Estimated PPM out of spec (overall)

**Key:** ppm

**Expr:** (normsdist(0 - 3 * ppu) + normsdist(0 - 3 * ppl)) * 1000000

**Format:** integer

**Disclaimer:** Assumes normally distributed data. Estimated PPM is a model prediction, not a count of observed rejects.

## Content

**Intro:** Pp and Ppk describe how a process actually performed over the whole study, drift included. Cp and Cpk describe how well it could perform if only short-term variation were present. The gap between them tells you whether your problem is centering and stability or inherent spread.

**Sections:**

#### How to use the calculator

**Body:** Enter your specification limits, the mean of all readings, the overall sample standard deviation and, if you have a control chart, the within-subgroup sigma estimated as R-bar divided by d2. The tool returns Pp, Ppu, Ppl and Ppk using the overall sigma, and Cp and Cpk using the within sigma. It also predicts the parts per million falling outside the specification limits under a normal model.

**Bullets:**

- Overall sigma uses every reading in one standard deviation.
- Within sigma comes from subgroup ranges or moving ranges.
- For one-sided specs enter a far-away dummy limit and read the matching Ppu or Ppl.

#### Formulas and meaning

**Body:** Pp is (USL minus LSL) divided by six overall standard deviations. Ppu is (USL minus mean) over three overall sigma and Ppl is (mean minus LSL) over three overall sigma. Ppk is the smaller of the two. Cp and Cpk have the same form but use the within-subgroup sigma. Pp ignores centering, while Ppk penalises an off-center mean. Automotive PPAP usually asks for Ppk of 1.67 or better on initial studies and Cpk of 1.33 or better in ongoing production.

#### Reading the gap between Cpk and Ppk

**Body:** If Cpk and Ppk are close, the process is stable and subgroup averages are not wandering. If Ppk is much lower than Cpk, there is shift or drift between subgroups, caused by tool wear, material lots, temperature or operators. Fix that with control charting and root cause work, not by tightening spread. If both are low, the inherent variation is too large for the tolerance and you need a process change or a tolerance review. A Pp well above Ppk means the mean is off target.

#### Common mistakes

**Body:** Using the within-subgroup sigma and calling it Ppk is the classic error, as is using Ppk on data from a process that has not been brought into control. Another is calculating from too few parts, so see the confidence interval tool for how much a small sample can mislead. Finally, check normality before trusting the PPM estimate, since tails matter most for it.

**Cta:** If you pull measurement data out of your ERP or MES into spreadsheets for Ppk reporting, we can help set up a private, read-only report that does it automatically.

**Faq:**

#### What is the difference between Ppk and Cpk?

**Answer:** Cpk uses within-subgroup variation, which is the short-term, best-case spread. Ppk uses the overall standard deviation of all data, which includes shifts and drift between subgroups. Ppk is therefore usually equal to or lower than Cpk on a real process.

#### What Ppk is acceptable?

**Answer:** Common targets are 1.33 minimum and 1.67 for critical characteristics at initial process studies, such as PPAP. Your customer requirements govern. Always state the sample size and the confidence in the result with the number.

#### Which standard deviation do I use for Ppk?

**Answer:** Use the ordinary sample standard deviation of every individual reading in the study, with n minus 1 in the denominator. Do not use R-bar over d2 for Ppk, because that estimates only the within-subgroup component.

#### Can Ppk be higher than Cpk?

**Answer:** Rarely, and usually it is a sign of too little data, a non-random sample or mixed measurement systems. Under normal conditions the overall sigma is at least as large as the within sigma, so Ppk should not exceed Cpk by much.

## Search terms

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