Application of Fuzzy Theory to Quality Control

本研究的结果可概括如下：1.在单一抽样属性方案中，希望生产者和消费者的风险分别等于指定值，但这通常是不可能的，因为样本量和接受数量必须是整数。为此，提出了一种新的设计方法，以放宽模糊方法中对风险隶属度函数的主观条件。该方法包括基于极大极小准则的抽样方案和特殊情况下的精确抽样方案，具有通用性。然而，所提出的设计过程包括迭代计算，因此相当复杂和麻烦。因此，提出了一种更加简化的基于模糊准则的设计方法。在抽样检验方案的设计中，也要求样本量最小。然而，减少样本量的要求与降低生产者和消费者的风险的要求相冲突。因此，减少样本量和放宽风险条件之间的权衡成为一个严重的问题。将该权衡问题转化为模糊数学规划问题，提出了一种基于模糊集理论的单属性方案设计方法。在假设指数寿命的定数寿命试验方案中，提出了一种在生产者风险和消费者风险之间保持模糊平衡的设计方法。此外，为了简化设计过程，还给出了闭合形式的公式。基于模糊集理论，提出了一种固定时间寿命试验方法。可接受的MTBF和可拒绝的MTBF用模糊概念表示，贝叶斯定理在公式中起着重要的作用。建议的寿命试验在难以严格指定可接受的MTBF和拒绝的MTBF的情况下生效。

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.