Reliability Sample Size Calculator

Binomial Acceptance Equation

∑i=0f(ni)(1−R)iRn−i=1−CL\sum_{i=0}^{f} \binom{n}{i}(1-R)^i R^{n-i} = 1-CL

n = sample size, f = allowed failures, R = reliability, CL = confidence level.

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How it works

For a reliability demonstration with zero allowed failures (a success-run test), the number of units you must test to prove a reliability R at confidence C is:

n=ln⁡(1−C)ln⁡(R)n = \frac{\ln(1 - C)}{\ln(R)}

Example: To demonstrate R = 90% at 90% confidence (R90C90) with no failures, you need n = ln(0.10)/ln(0.90) ≈ 22 units. Demanding R99C90 instead jumps the requirement to 230 units— a vivid illustration of how expensive high reliability targets become. The calculator also solves for reliability or confidence when the sample size is fixed, and handles cases that allow one or more failures via the binomial form.

Use this early in test planning to trade sample size against confidence and reliability before committing lab resources. To shorten test duration instead of adding units, combine with an acceleration model such as Arrhenius or Coffin-Manson.