Three-stage chain sampling plans

This article outlines the structure of a generalized family of three-stage chain sampling plans, extending the concept of two-stage chain sampling plans of Dodge and Stephens (1966) which is an extension of the original work of Dodge (1955). Expressions are derived for the OC curves for several sets of general sets of three-stage chain sampling plans, with cumulative acceptance numbers of (c₁,c₂,c₃) = (0,1,2), (0,1,3), (0,2,3), (1,2,3),(0,1,4),(0,2,4), (0,3,4), (1,2,4), (1,3,4) and (2,3,4). In the original work of Dodge (1955) only acceptance numbers of 0,1 were used and in the extension work of Dodge and Stephens (1966) acceptance numbers of (c₁,c₂) = (0,1) ,(0,2), (1,2), (0,3), (1,3), (0,4) and (1,4) were used with selected sets of values of k₁,and k₂ (the number of lots considered for cumulation in the first and second stage respectively). In this paper the 0C curves are derived more generally for any k₁, k₂and k₃(the number of lots considered for cumulation in the first, second and third stages respectively) combination and 0C curves of a number of plans are given and comparisons are made with some single sampling, two-stage chain sampling and multiple sampling plans.