Statistical Quality Control: Acceptance Sampling Plans in the Light of Fuzzy Mathematics

Abstract

Abstract Statistical quality control is a productivity enhancing and regulatory technique with three factors––Management, Methods and Mathematics. More precisely, if we want to properly design a self-regulating system for quality, we have to look to the field of cybernetics for design information. Quality improvement management aims to decrease variability, which leads to decrease the costs, the production time, the number of defects, scrap, rework,––and increase the customer satisfaction. Many problems in these scientific investigations generate non-precise data incorporating non-statistical uncertainty. A non-precise observation of a qualitative variable can be described by a special type of membership function defined on the set of all real numbers called a fuzzy number. In this paper, I have thoroughly discussed Acceptance sampling plans (Single, Double, Chain and Sequential) by attributes with the help of fuzzy parameters (mainly by fuzzy Poisson distribution and hypotheses testing). Finally many examples have been used and at last the paper ends with a comparative study.

Keywords

• Acceptance sampling plans
• Fuzzy numbers
• Fuzzy probability of acceptance
• Lot tolerance percent defective
• SPRT