**Method 1.** This tool calculates test sample size required to demonstrate a reliability value at a given confidence level. The calculation is based on the following binomial equation:

where:

C is the test confidence level

R is the reliability to be demonstrated

f is the number of allowable test failures

n is the test sample size

Given inputs of C, R and f, this tool solves the above equation for sample size, n.

**Method 2.** Method 2 makes use of the Weibull distribution to define reliability R for the above equation. Given a reliability requirement R_{rqmt} for a mission time T_{mission}
and a value for the Weibull shape parameter β, the Weibull reliability function
is solved for characteristic life (η). This fully defines the Weibull reliability function and
allows for calculation of any other point on the curve below. R_{test} associated with some available test time T_{test} is then calculated and used in the above
equation to calculate the number of test samples needed. Demonstrating R_{test} at time T_{test} is equivalent to demonstrating R_{rqmt}, provided that
the estimate of β is accurate. Method 2A solves for required sample size. Conversely, given a fixed number of samples, Method 2B solves for test time required.

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**Comments/Questions/Consulting:**

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- http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm.
- MIL-HDBK-338, Electronic Reliability Design Handbook.
- http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval
- http://en.wikipedia.org/wiki/Binomial_distribution
- http://reliabilityanalyticstoolkit.appspot.com/binomial_confidence

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