Evaluation of the limit number effects for reduced inspection in ANSI/ASQC Z1.4 using a Markov model Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/bg257j59d

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  • ANSI/ASQC Z1.4 is a widely used attributes acceptance sampling system. A necessary aspect of a scheme, from both a theoretical and psychological viewpoint, is the switching between normal, tightened, and reduced inspection as a function of quality history. In the latest revision of the standard the switching rules were altered to make use of the limit numbers for reduced inspection optional. Furthermore, a statement in the standard suggests that this action will have little effect on operating properties. A Markov model was developed to analyze the effect of the limit numbers. The no limit number model was solved analytically. The resulting closed-form results eliminate the need for matrix inversion and show that the maximum average run length on normal inspection is only 12.7 lots. The results show that use with the limit numbers significantly impacts many performance measures. Averaged across all 152 single sampling schemes and with quality at the AQL, the average run length on normal inspection increases 287% and the percent rejected increases 26% when limit numbers are used. Without limit numbers, the percent inspected on reduced increases 78%, the frequency of transitions between normal and reduced increases 108%, and the number of lots inspected before discontinuation increases 250%. When quality is slightly worse than the AQL (1.25 AQL), the differences are even greater. The average run length on normal increases 452% and the percent rejected increases 36% with limit numbers. Reduced inspection is nearly eliminated when the limit numbers are used. Omission of the limit numbers increases the percent on reduced by 972%, the frequency of transitions between normal and reduced by 776%, and the number of lots inspected by 120%. Contrary to the claim in ANSI/ASQC Z1.4, operating properties are significantly affected. Specifically, use of the limit numbers effectively controls random switching from normal to reduced, and makes reduced inspection truly a reward for exceptional quality rather than an expectation of marginal to poor quality.
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