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Probability of Sample Acceptance

The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution, not a binomial one. However, for N much larger than n, the binomial distribution is a good approximation, and widely used. Given some number of allowable defects (x) and a probability (p) of randomly selecting a defective item, this tool calculates the probability of lot acceptance. The cumulative probability F of selecting no more than r defective items is:
Cumulative Binomial Equation
For example, given a test sample of n=30 items from a production line that historically produces 5% defective product (p=0.05, q=0.95), there is a 0.21 probability of lot acceptance if zero defects are allowed. This probability increases to 0.81 if two defects (r=2) are allowed.

Binomial Distribution

Calculation Inputs:

1. Test sample size (n):
2. Fraction defective (0 <= p <= 1.0):
3. Maximum allowable defects (x):
4. Decimal places:
5. Bar chart:

Featured Reference:

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  1. MIL-HDBK-338, Electronic Reliability Design Handbook.
  2. Bazovsky, Igor, Reliability Theory and Practice.
  3. O'Connor, Patrick, D. T., Practical Reliability Engineering.