Analysis of the use of limit numbers in ANSI ZI-4 using a simulation model

Abstract

ANSI Zl-4 is a set of sampling plans and procedures for sampling inspection by attributes which includes provisions for switching between normal, tightened, and reduced inspections as a function of the quality history. In the latest version of ANSI Zl-4 (American National Standard 1981), the switching rules were revised to simplify its use. Specifically, the use of the limit numbers in switching between normal and reduced inspections was made optional. Moreover, a statement in the standard suggests that the use of limit numbers will have little impact on the performance of the scheme. This paper describes the use of a simulation model to explore the effect of using the limit number criterion on the scheme's performance. The use of the limit numbers significantly impacted all seven of the performance measures across the 36 levels of sample size, acceptance number, And quality level examined in this study. The use of the optional limit numbers reduced the lots inspected prior to termination by 21%, the transitions between normal and reduced inspections by 55%, and fraction of lots inspected under reduced inspection by 51%, Using the limit numbers increased the fraction of lots rejected by 30%, the average run length on normal inspection by 37%, and the lots inspected on normal inspection by 36%. The results show that the limit numbers are effective in eliminating random switching between normal and reduced inspection.