# OC Curve and Acceptance Probability Calculator for SAP QM Sampling

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

## Short answer

See how a sampling plan behaves: acceptance probability and average outgoing quality across incoming defect rates.

## Category

sap

## Erp

SAP S/4HANA

## Audience

- SAP QM consultant
- Quality engineer
- Supplier quality

## Tool

**Kind:** calculator

**Inputs:**

#### Sample size

**Key:** n

**Type:** number

**Default:** 50

**Min:** 2

**Max:** 2000

**Step:** 1

**Unit:** units

#### Acceptance number

**Key:** c

**Type:** select

**Default:** 1

**Options:**

##### 0 (accept on zero defects)

**Value:** 0

##### 1

**Value:** 1

##### 2

**Value:** 2

#### Incoming lot defect rate

**Key:** defect_pct

**Type:** slider

**Default:** 2

**Min:** 0

**Max:** 10

**Step:** 0.1

**Unit:** %

**Outputs:**

#### Defect fraction

**Key:** p

**Expr:** defect_pct / 100

**Format:** decimal

#### P(0 defects in sample)

**Key:** p0

**Expr:** pow(1 - p, n)

**Format:** decimal

#### P(1 defect in sample)

**Key:** p1

**Expr:** n * p * pow(1 - p, n - 1)

**Format:** decimal

#### P(2 defects in sample)

**Key:** p2

**Expr:** n * (n - 1) / 2 * p * p * pow(1 - p, n - 2)

**Format:** decimal

#### Probability of accepting the lot

**Key:** pa_pct

**Expr:** (p0 + if(gte(c, 1), p1, 0) + if(gte(c, 2), p2, 0)) * 100

**Format:** percent

**Primary:** true

#### Probability of rejecting the lot

**Key:** reject_pct

**Expr:** 100 - pa_pct

**Format:** percent

#### Average outgoing quality (rejected lots screened)

**Key:** aoq

**Expr:** defect_pct * pa_pct / 100

**Format:** percent

**Primary:** true

**Description:** Large-lot approximation, assumes rejected lots are 100 percent inspected and defects replaced.

**Chart:**

#### OC curve and AOQ across incoming defect rate

**Type:** line

**X:** defect_pct

**From:** 0

**To:** 10

**Steps:** 40

**Series:**

- pa_pct
- aoq

**Disclaimer:** Binomial model, valid for lots much larger than the sample (rule of thumb: lot at least 10 times the sample).

## Content

**Intro:** The operating characteristic (OC) curve answers a practical question: if a supplier ships lots at a given defect rate, how often will your inspection plan accept them? Use it before you maintain a sampling procedure in SAP QM, or when a supplier challenges a rejection.

**Sections:**

#### How to use it

**Body:** Set the sample size and acceptance number of the plan you are evaluating, then slide the incoming defect rate. The result shows the probability of acceptance and the average outgoing quality (AOQ). The chart sweeps defect rate from 0 to 10 percent so you can read the whole curve at once. Compare two plans by running each and noting the acceptance probability at your AQL and at your LTPD.

#### Formulas

**Body:** Acceptance probability is the cumulative binomial: Pa = sum for k = 0..c of C(n,k) x p^k x (1-p)^(n-k). The calculator evaluates the terms explicitly for c up to 2. AOQ is approximately p x Pa, assuming rejected lots are fully screened and corrected. The peak of the AOQ curve is the average outgoing quality limit (AOQL), the worst long-run quality the plan lets through.

#### Reading the curve

**Body:** A steep curve discriminates well between good and bad lots. A shallow curve, typical of small samples, accepts poor lots often and rejects good ones. If a plan accepts 90 percent of lots at your AQL but still accepts 20 percent at your LTPD, increase the sample size, not the acceptance number alone, because raising c at the same n makes the curve more lenient.

#### Common mistakes

**Body:** Do not mix up the lot defect rate with the sample defect rate. Do not use this model for tiny lots, where the hypergeometric distribution is correct. And remember that an SAP dynamic modification rule changes the plan over time, so the curve you evaluate is only valid for the current inspection stage.

**Cta:** We can summarise lot acceptance history and rejection reasons from your SAP QM data so you can compare real performance with these curves.

**Faq:**

#### What is a good probability of acceptance at the AQL?

**Answer:** Many plans target 90 to 95 percent acceptance at the AQL. That is the producer risk, so the lower it is, the more good lots get rejected.

#### What does AOQ tell me?

**Answer:** It estimates the defect rate in product after inspection, when rejected lots are screened. Its maximum, the AOQL, is the worst average outgoing quality over all possible incoming rates.

#### Why limit c to 2?

**Answer:** The tool writes out the binomial terms directly. That covers the usual receiving inspection plans, and larger acceptance numbers should use a spreadsheet or statistics package.

#### Is this valid for variables sampling?

**Answer:** No. The OC curve of a variables plan has a different form and depends on the standard deviation and k value used.

## Search terms

OC curve calculator, operating characteristic curve calculator, probability of acceptance sampling plan, average outgoing quality calculator, AOQ calculator, SAP QM sampling plan evaluation, acceptance sampling binomial calculator

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