Applying the Fuzzy Parameters to the Sequential Sampling Plan by Attributes

Abstract

Acceptance sampling is one of the major fields in statistical quality control. The most important tool of acceptance sampling is the probability theory, the reason is that more samples’ information was generated from process quality control; in some situations, it is treated as infinite. The definition of acceptance sampling refers that the specific sampling plans are applied on a designated lot or the sequence lots. In this study, the rectifying inspection for sequential-sampling plan possesses higher reliability and economic values in various fields. Under some circumstances, however, it may not be possible to define the acceptance sampling parameters as the crisp values. For solving the problem of uncertainty, this paper employs the membership functions to express relative variable in the fuzzy sense. Meanwhile, the triangular fuzzy number-one of the most popular membership function is used to represent the parameters of sampling inspection. By using the fuzzy parameters to deal with the parameters of binomial distributions, the acceptance probability functions are derived. Both the methods of signed distance and centroid are applied for defuzzification, then these estimates under different defuzzification methods are obtained and can be compared. After comparison, the better defuzzification method can be found.

Keywords:

• Acceptance Sampling Plan
• Rectifying Inspection Programs
• Triangular Fuzzy Number
• Centroid
• Signed Distance
• Defuzzification