Fuzzy design procedure for single attribute sampling plan : decision-making in a fuzzy environment

This paper presents an alternative design procedure for solving single attribute sampling plans using fuzzy set theory. This design attempts to properly represent risk conditions (traditionally given in a classical mathematical model) using a fuzzy mathematical model in an attempt to illustrate the value of fuzzy set theory to Industrial Engineering applications. This proposed design utilizes, as its base conditions, a conventional single attribute sampling plan developed by A. Hald [11,12]. Specifically, the proposed design attempts to generate sample size requirements (which can be compared to sample size requirements by Hald) to determine the value of applying fuzzy set theory to single attribute sampling plans similar to sampling plans introduced by H. Ohta and H. Ichihashi [13] (which is based on fuzzy set membership functions). However, the proposed design modifies Ohta & Ichihashi's membership functions of the producer's and the consumer's risks to be more representative of membership functions intended by Hald. This research involves developing a computer program to ease the implementation of the design procedure by performing most of the tedious and iterative calculations involved in obtaining the solution. The proposed design procedure is applied to a range of problems which are then presented and compared to results obtained by applying Raid's conventional design. This illustrates an alternative approach in obtaining a comparable qualitative-based solution to Raid's conventional, quantitative-based solution, in terms of the number of samples required. The research illustrates that all solution space in Raid's solution are equal, if not superior, to the proposed design. However, further research is needed to estimate membership functions for upper tolerance limits for both risk conditions and the means of interpreting the results of fuzzy analysis.