The proof of Lemma 1 is in Appendix A. Lemma 1 shows that the zero-defect, single-sampling plan with a sample size of ni eliminates the chance of more than Ni−ni NC items of part i entering the assembly line.
When the choice of inspection sample size ni impacts the effectiveness of incoming inspection because the probability h(0|Ni, di, ni) is positive. Lemma 2 in the following summarizes this impact.