Studying an OC Curve of an Acceptance Sampling Plan: A Statistical Quality Control Tool

Abstract:- The research problems under consideration are relationships between sampling risks and other elements inbuilt in a single acceptance sampling plan. Two levels of quality are considered: first, average quality level desired by the consumer AQL, and, second, quality level called lot tolerance percent defective LTPD, or the worst level of quality that the consumer may tolerate. The producer’s risk α is the risk of incorrect rejection is the risk that the sampling plan will fail to verify an acceptable lot’s quality set by AQL and, thus, reject it. The probability of acceptance a lot with LTPD quality is the consumer’s risk β or the risk of incorrect accepting. Operating characteristic (OC) curve describes how well an acceptance plan discriminates between good and bad lots. Acceptance sampling plan consists of a sample size n, and the maximum number of defective items that can be found in the sample c. The OC curve pertains to a specific plan, i.e. to a combination of the sample size n and the acceptance criterion or level c. Using ExcelOM2 software, the following findings were found: (1) with c, AQL and LTPD fixed, the increasing sample size n resulted with the risk α increased and the risk β decreased; and (2) with n, AQL and LTPD fixed, the increasing critical value c implicated that the risk α decreased, but the risk β increased; (3) if AQL is increased, with all other components n, c, and LTPD fixed, then producer’s risk α would increase, but consumer’s risk β would remain the same; and, (4) if LTPD is increased, with all other components n, c and AQL fixed, α would remain the same, while β woul