ANSI/ASQC Z1.4 is a widely used attributes acceptance sampling system. The latest revision of the standard makes optional the use of limit numbers for reduced inspection. This paper presents a Markov model of the sampling system without limit numbers. The model is valid for all single, double and multiple sampling schemes. Closed form, analytical results are developed for various performance measures. The maximum average run length on normal inspection is found to be only 12.7 lots, which leads to excessive switching between plans when quality is worse than the AQL.