# Sample Size Calculator - Binomial Reliability Demonstration Test

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 Rrqmt for a mission time Tmission 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. Rtest associated with some available test time Ttest is then calculated and used in the above equation to calculate the number of test samples needed. Demonstrating Rtest at time Ttest is equivalent to demonstrating Rrqmt, 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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## Calculation Inputs:

1. Select method:
Method 1
Non-Parametric Binomial Reliability Demonstration Test
Method 2A
Parametric Binomial Reliability Demonstration Test
(Calculate Samples)
Method 2B
Parametric Binomial Reliability Demonstration Test
(Calculate Test Time)
2. Number of allowable test failures (f):
3. Reliability requirement (R):
4. Test confidence level (C):
5. Generate test options table:

2. Number of allowable test failures (f):
3a. Reliability requirement at Tmission (Rrqmt):
3b. Mission time (Tmission, hours):
3c. Weibull shape parameter (β):
4. Test confidence level (C):
5. Available test time (Ttest, hours):
6. Generate test options table:
2. Number of allowable test failures (f):
3a. Reliability requirement at Tmission (Rrqmt):
3b. Mission time (Tmission, hours):
3c. Weibull shape parameter (β):
4. Test confidence level (C):
5. Sample size (n):
6. Generate test options table:

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