Dodge-Romig plans revisited

Abstract

Single sampling inspection plans proposed by Dodge and Romig have been critically examined in respect of the distribution of the number of defectives in a sample as and also the requirement of customer’s risk being equal to 0.10. The problem of determining the plan parameters has been formulated as a non-linear integer programming, a non-zero-sum (bi-matrix) game problem between the producer and the customer, and also as problem in (non-statistical) decision analysis. Further, the requirement about a given customer’s risk has been considered as a fuzzy constraint in a fuzzy nonlinear integer programming problem which can be eventually solved in terms of two non-linear integer programming problems, assuming a trapezoidal membership function. Different optimality criteria for determining the plan parameters as constituting the strategies in a decision matrix, where states of nature correspond to various plausible values of lot fraction defective and the pay-off is the average amount of inspection, have been considered. Finally, the author indicates how this analysis is relevant to a wide class of statistical decision problems, particularly many non-parametric tests