Given a target reliability and confidence, find the minimum number of units that must pass with zero failures to demonstrate that claim.
ANALYZE — What did my completed zero-failure study demonstrate? (Demonstrated Reliability)
Given a sample size already tested with zero failures and a target confidence, find the one-sided lower reliability bound that is demonstrated.
ANALYZE — What did my completed zero-failure study demonstrate? (Achieved Confidence)
Given a sample size already tested with zero failures and a target reliability, find the confidence that claim is supported at.
Assumptions
This calculation assumes independent test units, a common probability of success across the population being evaluated, a binary pre-established pass/fail criterion, representative specimens, zero observed failures, and a stable test method appropriate to the intended claim.
Multiple measurements taken from the same physical unit do not automatically constitute multiple independent test units.
Statistical sample size ≠ engineering coverage
The calculated sample size establishes statistical confidence and reliability only for the population represented by the tested units. It does not determine which device sizes, configurations, manufacturing lots, cavities, machines, operators, materials, aging conditions, or worst-case conditions should be tested. Specimen selection and coverage require separate engineering justification.
Disclaimer
This tool supports statistical planning and education. It does not establish a regulatory-required sample size. Confidence and reliability targets must be selected based on the applicable engineering, quality, risk-management, organizational, and regulatory context.
Methodology & References
Mathematical basis: zero-failure exact binomial ("success-run") relationship, C = 1 − Rn, and its algebraic inverses.
Regulatory context: FDA Quality Management System Regulation (QMSR), 21 CFR Part 820. ASTM F3172-15 (Reapproved 2021) is an FDA-recognized guide for design-verification device-size and sample-size selection for endovascular devices; its zero-failure example illustrates the general binomial methodology but does not establish a universal medical-device sample-size requirement.