Application of Fuzzy Theory to Quality Control

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The results of this research can be summarized as follows:1. In the single sampling attribute plans, one would like the producer's and consumer's risks to equal the specified values, respectively, but this is usually not possible since the sample size and the acceptance number must be integers. Therefore, a new design procedure for relaxing the conditions on the risks subjectively the membership functions used in fuzzy methodologies is proposed. The proposed procedure is general because it includes sampling plans based on the minimax criterion and exact sampling plans in the special cases.2. The proposed design procedure, however, includes iterative calculations, then it is rather complex and troublesome. Therefore, a more simplified design procedure based on the fuzzy criterion is proposed.3. In the design for sampling inspection plans, the minimization of sample size is also required. However, the requirement to lessen sample size conflicts with the requirement to lessen the producer's and consumer's risks. Accordingly, the trade- off between the reduction of sample size and the relaxation of the conditions on the risks becomes a serious problem. A new design procedure for the single attribute plan based on fuzzy sets theory is also presented by means of formulating this trade-off problem as a fuzzy mathematical programming.4. On the fixed-number life test plan in which exponerytial life times are assumed, a new design procedure which keeps fuzzy-balance between the producer's risk and the consumer's risk is presented. Furthermore, a closed form formula is also given for the purpose of simplifying the design procedure.5. A fixed-time life test is formulated based on fuzzy sets theory. Acceptable MTBF and rejectable MTBF are represented in terms of,fuzzy concept, and the Bayes' theorem plays an important role in the formulation. The proposed life test takes effect when it is difficult to specify acceptable MTBF and rejectable MTBF strictly.