# Zero Failure Success Run Sample Size Calculator

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

## Short answer

Compute the zero-failure sample size n = ln(1 - confidence) / ln(reliability) for design validation and PPAP test planning.

## Category

quality

## Industry

Automotive

## Audience

- Reliability engineer
- Design engineer
- Supplier quality engineer

## Tool

**Kind:** calculator

**Currency:** $

**Inputs:**

#### Reliability to demonstrate

**Key:** rel

**Type:** slider

**Default:** 95

**Min:** 50

**Max:** 99.9

**Step:** 0.1

**Unit:** %

**Help:** Share of units expected to survive the test.

#### Confidence level

**Key:** conf

**Type:** select

**Default:** 90

**Options:**

##### 80%

**Value:** 80

##### 90%

**Value:** 90

##### 95%

**Value:** 95

##### 99%

**Value:** 99

#### Cost per tested sample

**Key:** cost

**Type:** number

**Default:** 350

**Min:** 0

**Step:** 10

**Unit:** $

**Help:** Part cost plus fixture, lab time and handling.

#### Test stations available

**Key:** slots

**Type:** number

**Default:** 12

**Min:** 1

**Step:** 1

**Help:** How many parts can be tested at the same time.

#### Duration of one test cycle

**Key:** test_days

**Type:** number

**Default:** 5

**Min:** 0

**Step:** 0.5

**Unit:** days

**Outputs:**

#### Samples required, zero failures

**Key:** n

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

**Format:** integer

**Primary:** true

**Description:** All must pass for the claim to hold.

#### Total test cost

**Key:** tot_cost

**Expr:** n * cost

**Format:** currency

**Primary:** true

#### Test batches needed

**Key:** batches

**Expr:** ceil(n / slots)

**Format:** integer

#### Calendar test time

**Key:** lead

**Expr:** batches * test_days

**Format:** days

#### Rule of three check (n = 3 / (1 - R))

**Key:** rule3

**Expr:** ceil(3 / (1 - rel / 100))

**Format:** integer

**Description:** Approximation valid near 95 percent confidence.

**Chart:**

#### Samples required vs reliability target

**Type:** line

**X:** rel

**From:** 80

**To:** 99

**Steps:** 40

**Series:**

- n

**Disclaimer:** Binomial success-run method: assumes identical, independent samples and a test that represents field stress. Failure of any sample invalidates the zero-failure claim.

## Content

**Intro:** How many parts must you test, with no failures, to say a product is 95 percent reliable with 90 percent confidence? This calculator applies the success run theorem to answer that, and prices the answer in samples, money and weeks of test time.

**Sections:**

#### How to use it

**Body:** Set the reliability you must demonstrate and the confidence level. Typical pairs are 90/90, 95/90 and 95/95, and your design validation plan or customer test specification should state which applies. Enter the cost of each tested sample, your parallel test stations and the length of one cycle. The tool returns the sample count, total cost and the calendar time. Use the chart to see how quickly the sample size grows as the reliability target approaches 100 percent.

#### The formula

**Body:** If every one of n samples survives, the probability of that happening when true reliability is R equals R to the power n. Setting that equal to one minus confidence C gives n = ln(1 - C) / ln(R), rounded up. For 95 percent reliability at 90 percent confidence this yields 45 samples, at 95 percent confidence 59 samples. The rule of three, n about 3 / (1 - R), is the quick version at 95 percent confidence.

#### What a pass means

**Body:** A pass says you have statistical grounds to claim at least R reliability at confidence C for the tested conditions and life. It does not say the product will last longer than the test, and it does not cover failure modes not stressed in the test. If a failure occurs, you can still use success-run variants that allow one or more failures, but they need more samples, and the test plan should say so in advance.

#### Common mistakes

**Body:** Treating a short test as proof of a long field life is the biggest one. Another is testing samples from a single lot, which cannot reflect lot-to-lot variation, so draw from several lots or setups. Others include changing the test mid-run, dropping a failed sample as an outlier without root cause, and quoting reliability with no confidence level.

**Cta:** Netray can help tie validation test results to part numbers, lots and revisions in your ERP or quality system, so evidence survives engineering changes.

**Faq:**

#### Why are 59 samples used so often?

**Answer:** 59 samples with zero failures demonstrates 95 percent reliability at 95 percent confidence, since 0.95 to the power 59 is about 0.05. It is a common sample size in validation plans.

#### What if one sample fails?

**Answer:** The zero-failure claim no longer holds. You must either find a root cause and restart, or use a larger sample plan that allows failures, which needs a different formula and more parts.

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

**Answer:** No. AQL plans accept or reject lots based on defect counts. Success-run testing demonstrates reliability for design or process validation at a chosen confidence level.

#### Can I reduce the sample size?

**Answer:** Only by lowering reliability or confidence, by testing to a more severe stress with a validated acceleration factor, or by using prior data through Bayesian methods that your customer accepts.

## Search terms

success run theorem calculator, zero failure sample size, reliability demonstration sample size, 90/90 sample size, 95/95 sample size 59, bogey test sample size, reliability confidence sample size, ppap testing sample size

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