Determination of Sample Sizes for Double Sampling Attribute Plans

Abstract

Double sampling plans are generally superior to corresponding single sampling plans from an economic standpoint. That is because the double sampling plans can give an early decision at the first stage whenever lot quality is extremely good or bad. Further, because this method has five parameters (n 1, n 2, c 1, c 2, c 3), double sampling plans can be developed to accord well with required characteristics of the inspection method (e.g. AOQL, producer’s and consumer’s risks). Double sampling attribute plan in MIL-STD 105D[6] adopt some convenient constraints for selecting parameters, for example n 1 = n 2 or 2n 2, and c 2=c 3. Design procedures for single sampling attribute plans with given producer’s and consumer’s risks have been extensively investigated by, among others, PEACH & LITTAURE[9] and HALD [3] [4]. On the other hand, design procedures for double sampling attribute plans with given two risks are not well developed, for it is difficult to determine n 1 and n 2 such that both actual risks close to the specified risks. In this paper, we define two functions λ1 and λ2 with respect to n 1 and n 2, and follow a path that preserves both risks. This is done by describing the changes of λ1 and λ2 with respect to the discrimination ratio (r ≅ p 2/p 1) using a system of differential equations which includes the corresponding single sampling plan as an initial state. Sample sizes (n 1, n 2) of double sampling plans with given acceptance numbers are obtained as numerical solutions of simultaneous differential equations. These double sampling plans have producer’s and consumer’s risks that are almost equal to the specified risks.