Binomial Calculator

Enter p:    Proportion Defective
Enter n:    Sample Size
Enter r:    Number Defective
Enter CL:   % Confidence Level
     
 

This calculator calculates the confidence level, number of samples, or number rejects allowed to satisfy a set of given conditions for a one shot device. The calculations are based on the Binomial Distribution and the following formula:

 
Confidence Level (CL) = 
where:
n= sample size
p= proportion defective
r= number defective
=probability of k or fewer failures occurring in a test of n units

 

Example use of the Calculator:
Assume that you need to be 95% confident that your product is no more than 10% defective. You tested 60 samples and 3 were found to be defective. Did you meet the goal of 95% confidence? Using the calculator, input p = .1, n = 60, r = 3, and calculate for CL. You would only be 86.26% confident that your product is no more than 10% defective.
Enter: p = 0.10
  n = 60
  r = 3
Press Calculate
Solves for: CL = 86.26%
What is the maximum number of defects in a sample size of 60 that would yield a 95% confidence level that the product was no more than 10% defective? Using the calculator, input p = .1, n = 60, CL = 95, and calculate for r. The number of defectives allowed would have been 1.
Enter: p = 0.10
  n = 60
  CL = 95
Press Calculate
Solves for: r = 1
Knowing that you had 3 defects, what minimum sample size is needed to be 95% confident that the product is no more than 10% defective? Calculator inputs are p =.1, r = 3, CL = 95, and calculate n. The minimum sample size will be 76.
Enter: p = 0.10
  r = 3
  CL = 95
Press Calculate
Solves for: n = 76

 

CAUTION:
The calculator is capable of handling large sample sizes (n) and number defective (r) values. If n is greater than (>) 1,500 and r is greater than (>) 100, the calculation may take an excessive amount of time.