# Zero Acceptance (c=0) Sample Size Calculator for Confidence and Reliability

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

## Short answer

Success-run sample size for c=0 plans: how many conforming pieces prove a reliability at a given confidence, with inspection time.

## Category

quality

## Audience

- Quality engineer
- Validation engineer
- Supplier quality

## Tool

**Kind:** calculator

**Inputs:**

#### Confidence level

**Key:** conf

**Type:** select

**Default:** 0.95

**Options:**

##### 90%

**Value:** 0.9

##### 95%

**Value:** 0.95

##### 99%

**Value:** 0.99

#### Required conformance (reliability)

**Key:** rel

**Type:** slider

**Default:** 95

**Min:** 80

**Max:** 99.9

**Step:** 0.1

**Unit:** %

**Help:** The minimum share of good parts you want to demonstrate.

#### Inspection time per piece

**Key:** min_each

**Type:** number

**Default:** 4

**Min:** 0

**Step:** 0.5

**Unit:** min

#### Inspection labor rate

**Key:** labor_rate

**Type:** number

**Default:** 36

**Min:** 0

**Step:** 1

**Unit:** $/hr

**Outputs:**

#### Sample size with zero failures allowed

**Key:** n

**Expr:** ceil(ln(1 - conf) / ln(rel / 100))

**Format:** integer

**Primary:** true

**Description:** If all n pieces conform, you demonstrate the stated reliability at the stated confidence.

#### Maximum defective rate demonstrated

**Key:** ltpd

**Expr:** 100 - rel

**Format:** percent

#### Inspection time

**Key:** hours

**Expr:** n * min_each / 60

**Format:** hours

#### Inspection labor cost

**Key:** cost

**Expr:** hours * labor_rate

**Format:** currency

**Primary:** true

**Chart:**

#### Sample size vs required reliability

**Type:** line

**X:** rel

**From:** 80

**To:** 99.5

**Steps:** 40

**Series:**

- n

**Disclaimer:** Assumes a large lot or an ongoing process (binomial model). For small lots, use a hypergeometric or published c=0 table.

## Content

**Intro:** When a corrective action closes, someone has to prove the fix worked. A c=0 plan answers how many consecutive good pieces are enough. This calculator gives the success-run sample size for your chosen confidence and reliability, plus the inspection time to get it.

**Sections:**

#### How to use it

**Body:** Pick a confidence level, usually 95 percent, and the reliability you want to demonstrate, such as 95, 99 or 99.9 percent conformance. The tool returns the number of pieces that must all pass. A single failure means the plan fails and you have not shown the claimed reliability. Enter inspection time and labor rate to see what the verification costs.

#### The success-run formula

**Body:** With zero allowed failures, the probability that a process with conformance R passes n pieces in a row is R to the power n. For confidence C, you require R to the n to be no more than 1 minus C. Solving gives n equals the natural log of 1 minus C divided by the natural log of R, rounded up. For 95 percent confidence at 95 percent reliability, n is 59. At 99 percent reliability it is 299.

**Bullets:**

- n = ln(1 - C) / ln(R), rounded up
- 95/95 gives 59 pieces
- 95/99 gives 299 pieces
- Higher reliability grows n quickly

#### How to read the result

**Body:** The curve shows why demanding 99.9 percent from a small sample is unrealistic: it needs thousands of pieces. If the number is too large, change the question. Use process capability data, a control chart showing stability, or a risk-based reliability target agreed with the customer instead of brute-force sampling.

#### Common mistakes

**Body:** Applying a c=0 result to a different process condition than the one tested, sampling from one shift or one machine and claiming the whole process, and treating the plan as proof of a variable characteristic when a capability study is the right tool. Randomize or stratify the sample across the conditions that matter.

**Cta:** If verification of effectiveness sampling is currently tracked in spreadsheets, we can help connect inspection results from the ERP or MES to your CAPA records.

**Faq:**

#### What does 95/95 mean?

**Answer:** It means 95 percent confidence that at least 95 percent of the population conforms. With zero failures, 59 consecutive conforming pieces demonstrate it under the binomial model.

#### Can I allow one failure?

**Answer:** Yes, but the sample size rises. This tool covers c=0 only. For c=1 or more, use the binomial or a published plan and state the acceptance number in your procedure.

#### Is it valid for small lots?

**Answer:** For small lots the binomial is conservative. A hypergeometric calculation needs fewer pieces. If your lot is under a few hundred, use the exact method.

#### Is this the same as AQL sampling?

**Answer:** No. AQL plans protect against a producer risk at a stated quality level. A c=0 reliability plan is a demonstration of a minimum conformance, and is often used for validation and CAPA checks.

## Search terms

success run theorem sample size, c=0 sampling plan calculator, zero failure sample size, confidence reliability sample size, 95/95 sample size, verification of corrective action sample size, attribute sample size calculator, ncr verification sampling

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