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Attribute-Data Sample Size

Find how many parts you must inspect to detect a defect at a target rate with a chosen confidence — the zero-acceptance sizing behind LTPD sampling.

Inputc = 0: n = ln(1−C) / ln(1−p) , C = confidence , general c: solve Σₖ₌₀ᶜ e⁻ⁿᵖ(np)ᵏ/k! = 1−C

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The engineering

This sizes an attribute (go/no-go) inspection: how many units to pull so that a lot running at defect rate p has only a (1−C) chance of slipping through with c or fewer observed defects. Reach for it when you're setting up incoming inspection, a first-article check, or defending a sampling plan against a customer spec.

The zero-acceptance case (c = 0) is the workhorse — reject the lot on the first defect — and it gives the smallest sample for a given protection. A handy sanity check: for c = 0 and 95% confidence, n ≈ 3/p, so a 1% defect target needs about 300 parts. Bumping the acceptance number up buys you tolerance to random escapes but costs a lot more inspection.

The math here is the operating-characteristic point at the defect rate you name — it is not the full Z1.4 switching scheme (normal/tightened/reduced). Use it to reason about a single plan's protection, then pin the actual plan to the standard's tables when a contract requires them.

Where this math comes from

Acceptance sampling grew out of Bell Labs in the late 1920s, where Harold Dodge and Harry Romig built the first practical plans so inspectors could pass or fail lots without checking every piece. Their double-sampling and LTPD tables turned quality from 100% sorting into a statistical bet with known odds — a necessity once telephone hardware was being made by the millions.

World War II forced standardization: the military needed one language for buying munitions and electronics from thousands of vendors. That effort produced MIL-STD-105, which after decades of revision was handed to civilian standards bodies and reissued as ANSI/ASQ Z1.4. The zero-acceptance c = 0 plans this card favors were popularized by Nicholas Squeglia, whose compact tables became a shop-floor staple.

  1. 1928Harold Dodge & Harry RomigDevelop acceptance sampling and LTPD tables at Bell Labs.
  2. 1950U.S. Department of DefenseIssues MIL-STD-105A to standardize attribute sampling across suppliers.
  3. 1961Nicholas SquegliaPublishes zero-acceptance-number (c=0) sampling plans.
  4. 1995MIL-STD-105 cancelledStandard transferred to civilian bodies as ANSI/ASQ Z1.4.
  5. 2018ASQReaffirms ANSI/ASQ Z1.4-2003 (R2018) as the current attribute-sampling standard.

See the full timeline of the math behind every calculator →

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