A comparison of sample size calculation algorithms

When a sample is taken without replacement from a finite population which is suspected to have defects, the probability that sample will have defects or not is described by the hypergeometric density function. Usually a hypergeometric density function is approximated by two binomial density functions depending on the approximation condition, and which one satisfies approximation condition is not known always before sample size calculation. Therefore simultaneous application of two binomial density functions is often required. This paper compares three kinds of binomial approximation and a hypergeometric algorithm when applied to sample size calculation for various values of q, the over-all classification probability of classifying a defect as a defect when measured with up to three verification methods of the International Atomic Energy Agency (IAEA). The first approximation is the simply applied standard binomial approximation which is currently used by the IAEA. The second one is the correctly applied standard binomial approximation with simultaneous application of two binomial density functions. The third one is the improved binomial approximation developed by Mr. J. L. Jaech.