# Zero Acceptance (c=0) Sampling Plan Calculator

> Source: https://netray.co/tools/aerospace-zero-acceptance-sampling-plan-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Find the sample size that gives a chosen consumer risk at your limiting defect rate, then see the probability of accepting lots at any defect level.

## Category

quality

## Industry

Aerospace

## Audience

- Quality engineer
- Receiving inspector
- Supplier quality engineer

## Tool

**Kind:** calculator

**Currency:** $

**Inputs:**

#### Lot size

**Key:** lot_size

**Type:** number

**Default:** 500

**Min:** 1

**Step:** 10

**Unit:** units

#### Limiting quality (LTPD)

**Key:** ltpd

**Type:** number

**Default:** 10

**Min:** 0.1

**Max:** 50

**Step:** 0.5

**Unit:** % defective

**Help:** Defect rate you want to reject with high probability.

#### Consumer risk

**Key:** risk

**Type:** select

**Default:** 0.1

**Options:**

##### 10% (typical)

**Value:** 0.1

##### 5%

**Value:** 0.05

##### 1%

**Value:** 0.01

#### Sample size you plan to use

**Key:** sample_size

**Type:** number

**Default:** 22

**Min:** 1

**Step:** 1

**Unit:** units

**Help:** Compare your current sample size with the calculated minimum.

#### Actual lot defect rate

**Key:** lot_defect

**Type:** slider

**Default:** 2

**Min:** 0

**Max:** 20

**Step:** 0.5

**Unit:** % defective

**Outputs:**

#### Sample size, large lot basis

**Key:** n_inf

**Expr:** ceil(ln(risk) / ln(1 - ltpd / 100))

**Format:** integer

**Description:** Smallest n with (1 - LTPD)^n <= consumer risk.

#### Sample size adjusted for lot size

**Key:** n_fin

**Expr:** min(lot_size, ceil(n_inf / (1 + n_inf / lot_size)))

**Format:** integer

**Primary:** true

**Description:** Approximate finite-lot adjustment. Exact values come from the hypergeometric distribution.

#### Fraction of lot inspected

**Key:** frac

**Expr:** sample_size / lot_size * 100

**Format:** percent

#### Consumer risk at your sample size

**Key:** cr

**Expr:** pow(1 - ltpd / 100, sample_size) * 100

**Format:** percent

**Description:** Probability of accepting a lot that is exactly at the LTPD.

#### Probability of acceptance at actual defect rate

**Key:** pa

**Expr:** pow(1 - lot_defect / 100, sample_size) * 100

**Format:** percent

**Primary:** true

#### Probability of rejection

**Key:** reject

**Expr:** 100 - pa

**Format:** percent

**Chart:**

#### OC curve: acceptance probability vs lot defect rate

**Type:** line

**X:** lot_defect

**From:** 0

**To:** 20

**Steps:** 41

**Series:**

- pa

**Disclaimer:** Uses the binomial model with acceptance number c=0, which is accurate for large lots and a good approximation otherwise. For small lots the hypergeometric distribution is exact. Follow the sampling plan required by your customer or contract.

## Content

**Intro:** Zero acceptance number sampling plans, written c=0, accept a lot only if no defects are found in the sample. They are common in aerospace receiving inspection because they are simple and give a clear rejection rule. This calculator finds the sample size and shows the OC curve.

**Sections:**

#### How to use the calculator

**Body:** Enter the lot size and the limiting quality, which is the defect rate you want to catch with high probability. Pick the consumer risk, the chance you are willing to accept a lot at that bad level. The calculator returns the smallest sample size and adjusts it for finite lots. Then enter the sample size you currently use and the real defect rate you expect to see. The calculator shows your consumer risk, the probability of accepting a lot at the actual defect rate, and the chart traces the whole OC curve from zero to twenty percent defective.

#### The math

**Body:** With acceptance number zero, a lot is accepted only when every sampled unit is good. Under the binomial model, probability of acceptance equals (1 minus p) to the power n, where p is the lot defect fraction and n the sample size. The smallest n that holds consumer risk at beta for a limiting quality LTPD is the natural log of beta divided by the natural log of (1 minus LTPD), rounded up. For example, a 10 percent LTPD and 10 percent consumer risk needs 22 units. The finite-lot adjustment scales n down for small lots but remains an approximation.

**Bullets:**

- Pa = (1 - p)^n for c = 0
- n = ceil(ln(beta) / ln(1 - LTPD))
- Finite lot approximation: n / (1 + n / N)

#### Reading the OC curve

**Body:** The OC curve falls steeply for c=0 plans. At a defect rate of 2 percent with 22 units, the probability of acceptance is about 64 percent, which means a lot with a real defect rate that low will often still be rejected. This is the price of zero acceptance: it protects the consumer strongly but penalizes good lots with small defect rates. If your supplier has a real defect rate well below the LTPD, a larger sample with c greater than zero can offer a better balance, but only if the contract allows it.

#### Common mistakes

**Body:** A common error is quoting an AQL when using c=0 plans, since AQL and LTPD describe different points on the curve. Another is applying the calculated sample size to attribute checks of multiple characteristics without defining what counts as a defective unit. Finally, remember that sampling does not improve the lot: rejected lots need a defined disposition such as 100 percent sort or return, and the supplier needs corrective action.

**Cta:** If you want sample size and lot disposition suggested automatically at receiving from supplier history in your ERP, we can help design that.

**Faq:**

#### What does c=0 mean?

**Answer:** It means the acceptance number is zero. If any defective unit is found in the sample, the lot is rejected. If none are found, the lot is accepted. It is easy to apply and common in aerospace and defense.

#### How is this different from ANSI/ASQ Z1.4?

**Answer:** Z1.4 is indexed by AQL and lot size and typically allows an acceptance number above zero. A c=0 plan is designed from a limiting quality and consumer risk. Use whichever your customer or procedure requires.

#### Why is the finite lot value only approximate?

**Answer:** Sampling without replacement from a small lot follows the hypergeometric distribution, not the binomial. The adjustment here is a standard approximation. For small lots, use hypergeometric tables or software to confirm.

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

**Answer:** No. This plan counts defective units, which is attribute data. For measured data, use a variables sampling plan or monitor the characteristic with capability analysis.

## Search terms

c=0 sampling plan calculator, zero acceptance number sampling plan, LTPD sample size calculator, acceptance sampling OC curve calculator, aerospace receiving inspection sample size, consumer risk sample size, lot tolerance percent defective calculator, attribute sampling zero defects

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