Binomial Confidence Intervals

This tool calculates one-sided and two-sided confidence intervals for discrete reliability test data (i.e., go/no-go testing). Given a risk (α), confidence is calculated at the 1-α level for the true proportion defective p, where N_d defects are found in a sample size of N. For additional details, click here.

The tool is prefilled with example data from the NIST Engineering Statistics Handbook. See the example shown at the bottom of this page.

Calculation Inputs:

1. Sample size (N):

2. Number of defects found (N_d):

3. Confidence: 90% (Default) 99% 98% 95% 90% 85% 75% 70% 65% 60% 55% 50%

4. Decimal places: 3 0 1 2 3 4 5 6 7 8 9 10 15 20

5. Output: Proportion defective, two-sided confidence Proportion defective, single-sided lower confidence level Proportion defective, single-sided upper confidence level Reliability, two-sided confidence Reliability, single-sided lower confidence level Table of all reliability values (Nd = 0 to N), two-sided confidence

6. Chart:

Featured Reference:

An Introduction to Reliability and Maintainability Engineering

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Comments/Questions:


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References:

1. http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm.
2. MIL-HDBK-338, Electronic Reliability Design Handbook.
3. http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval
4. http://en.wikipedia.org/wiki/Binomial_distribution
5. O'Connor, Patrick, D. T., Practical Reliability Engineering.
6. Bazovsky, Igor, Reliability Theory and Practice.
7. Khan Academy, Margin of Error 1.
8. Khan Academy, Margin of Error 2.
9. Khan Academy, Confidence Interval Example.
10. O'Connor, Patrick, D. T., Practical Reliability Engineering.
11. Birolini, Alessandro, Reliability Engineering: Theory and Practice.
12. Collani, E. von; Drager, Klaus Binomial Distribution Handbook for Scientists and Engineers.

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