# Cp and Cpk Calculator for SAP QM Inspection Characteristics

> Source: https://netray.co/tools/sap-qm-cpk-capability-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Enter the mean, standard deviation and specification limits of a quantitative characteristic and get Cp, Cpk and the expected parts per million out of tolerance.

## Category

quality

## Erp

SAP S/4HANA

## Industry

Discrete Manufacturing

## Audience

- Quality engineer
- SAP QM consultant
- Supplier quality

## Tool

**Kind:** calculator

**Inputs:**

#### Process mean

**Key:** mean

**Type:** number

**Default:** 10

**Step:** 0.001

**Help:** Average of the recorded results for the characteristic.

#### Standard deviation

**Key:** sigma

**Type:** number

**Default:** 0.012

**Min:** 0.0001

**Step:** 0.001

**Help:** Within-subgroup sigma for Cp and Cpk, overall sigma for Pp and Ppk.

#### Upper specification limit

**Key:** usl

**Type:** number

**Default:** 10.05

**Step:** 0.001

#### Lower specification limit

**Key:** lsl

**Type:** number

**Default:** 9.95

**Step:** 0.001

**Outputs:**

#### Cp

**Key:** cp

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

**Format:** decimal

**Description:** Potential capability if the process were centred.

#### Cpu

**Key:** cpu

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

**Format:** decimal

#### Cpl

**Key:** cpl

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

**Format:** decimal

#### Cpk

**Key:** cpk

**Expr:** min(cpu, cpl)

**Format:** decimal

**Primary:** true

**Description:** Actual capability, penalises an off-centre process.

#### Expected ppm out of spec

**Key:** ppm

**Expr:** (normsdist(0 - 3 * cpu) + normsdist(0 - 3 * cpl)) * 1000000

**Format:** integer

**Primary:** true

**Description:** Assumes a stable, normally distributed process.

#### Mean offset from centre

**Key:** offset

**Expr:** mean - (usl + lsl) / 2

**Format:** decimal

**Chart:**

#### Cpk as the mean drifts across the tolerance

**Type:** line

**X:** mean

**From:** 9.95

**To:** 10.05

**Steps:** 21

**Series:**

- cpk

**Disclaimer:** Valid for a stable process with normally distributed data. Check control charts and normality first. Many customers require Cpk of 1.33 or higher and 1.67 for critical characteristics, but follow your own customer requirement.

## Content

**Intro:** Quantitative characteristics recorded in SAP QM give you the data for capability studies. This calculator turns the mean, standard deviation and limits of a characteristic into Cp, Cpk and the expected rate of parts out of tolerance.

**Sections:**

#### How to use the calculator

**Body:** Export the results for one characteristic and one period, for example from the results recording or an analysis report, and compute the mean and standard deviation in a spreadsheet. Enter them with the upper and lower specification limits from the inspection plan. Cp compares the tolerance width to six sigma, and Cpk takes the nearer limit into account. The chart shows how Cpk falls as the mean drifts toward either limit, which helps explain why centring matters.

#### The formulas

**Body:** Cp is the tolerance width divided by six times sigma. Cpu is the upper limit minus the mean, divided by three sigma, and Cpl is the mean minus the lower limit, divided by three sigma. Cpk is the smaller of the two. The expected out-of-spec rate uses the normal distribution tail beyond each limit, converted to parts per million. For a one sided specification enter only the relevant limit logic in your own calculation, since this tool assumes two limits.

**Bullets:**

- Cp = (USL - LSL) / (6 sigma)
- Cpk = min((USL - mean) / 3 sigma, (mean - LSL) / 3 sigma)
- Cpk 1.00 is about 2,700 ppm; 1.33 is about 63 ppm if centred
- Use at least 25 subgroups of 4 or 5 for a reliable study

#### Worked example

**Body:** A bore has a tolerance of 10.00 plus or minus 0.05 and the recorded results have a mean of 10.000 and sigma of 0.012. Cp is 0.10 divided by 0.072, about 1.39. The process is centred, so Cpk is also about 1.39 and the expected out-of-spec rate is a few ppm. Move the mean to 10.02 and Cpk drops to about 0.83, even though Cp is unchanged. That is the point of the chart: a capable but off-centre process still makes scrap.

#### Common mistakes

**Body:** Calculating capability on an unstable process gives a number that means nothing, so look at a control chart first. Using overall sigma and calling it Cpk mixes Cpk with Ppk. Rounded or truncated measurements, mixed machines in one sample, and small samples all distort the result. In SAP QM, make sure the results come from one characteristic with one specification, not a mix of plan versions.

**Cta:** If you want capability figures calculated straight from the results in your SAP system, with the query shown and no manual exports, we can build that on-premises.

**Faq:**

#### What is a good Cpk value?

**Answer:** Many customers ask for at least 1.33 on normal characteristics and 1.67 on critical ones, and some automotive and aerospace programs set their own limits. A Cpk below 1.00 means the process produces out-of-tolerance parts. Always use the requirement in your contract or customer standard.

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

**Answer:** Cp compares tolerance width with process spread and ignores where the mean sits. Cpk uses the distance from the mean to the nearer limit, so it drops when the process is off-centre. If Cp is high and Cpk is low, centre the process.

#### Does SAP QM calculate Cpk itself?

**Answer:** SAP QM supports statistical process control with control charts and can evaluate results, and capability indices are available in the evaluation functions of the QM component in many setups. Details depend on your release and configuration, so verify what your system reports before you rely on a spreadsheet.

#### Can I use this for attribute data?

**Answer:** No. Cp and Cpk apply to continuous measurements with limits. For pass or fail attribute data, use a proportion defective or ppm measure, and the sampling plan from your inspection plan to decide acceptance.

## Search terms

Cpk calculator, Cp Cpk formula, SAP QM process capability, process capability index calculator, ppm out of spec calculator, Cpk from inspection results, SAP QM quality score capability, capability index Excel

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