Binomial Probability of Success

Given a random sample of n items and a probability of failure/defect rate p, this tool calculates the probability that exactly x failures will occur in the sample. The probability that exactly x failures will occur in a random sample of n items is given by:

The tool also calculates the cumulative probability that not more than r failures will occur in a sample of n items. The cumulative probability that r or fewer failures will occur in a sample of n items is given by:

where q = 1 - p.

For example, a manufacturing process creates defects at a rate of 2.5% (p=0.025). A sample of 20 parts is randomly selected (n=20). What is the probability that the sample contains 3 or fewer defective parts (r=3)? The probability of finding 3 or fewer defects in 20 samples is 0.9986.

Calculation Inputs:

1. Number of samples (n):
2. Probability of failure/defect rate (p):
3. Maximum allowable defects (r):
4. Decimal places:
5. Chart options:

f(x) chart
F(r) chart

Title:

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References:

1. MIL-HDBK-338, Electronic Reliability Design Handbook.
2. Bazovsky, Igor, Reliability Theory and Practice.
3. O'Connor, Patrick, D. T., Practical Reliability Engineering.
4. http://en.wikipedia.org/wiki/Binomial_distribution
5. Khan Academy, Binomial Distribution 1.
6. Khan Academy, Binomial Distribution 2.
7. Khan Academy, Binomial Distribution 3.
8. Khan Academy, Binomial Distribution 4.