Lemma 1.
∀ and di and ∈ . That is, if the inspection sample size does not exceed Ni−di,the incoming inspection has a chance of failing to detect the NC items. This chance declines with the increase in di. h(0|Ni,di,ni)=0, ∀ . That is, the incoming inspection is able to prevent all NC items of part i from entering the assembly line if the sample size niexceeds Ni−di.
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.