Optimal skip-lot sampling plan based on the yield index for auto-correlated data

Acceptance sampling is one of the most important tools in quality control, and it has been extensively used in the industry for inspecting received lots. As different situations and purposes could be encountered in real life, numerous approaches for sampling plans have been established. When the quality of the process is good and stable, Skip-lot sampling plans (SkSPs) are useful strategies of sampling and could be an advantageous examination scheme. Therefore, this paper aims to incorporate the process yield index for a first-order autoregressive process S-pk;AR(1) and the SkSP, when the quality characteristic follows a normal distribution with bilateral specification limits, to produce a variables Skip lot sampling plan of type 2 (SkSP-2) with a single sampling plan (SSP) based on S-pk;AR(1) as the reference plan. A non-linear optimization model is solved to decide the plan parameters, by fulfiling the quality and risk obligations identified by the manufacturer and buyer and minimizing the average sample number (ASN). We investigated the efficiency and performance of the suggested SkSP-2 S-pk;AR(1)-based, associated with the variables SSP in terms of average sample number curves and the operating characteristic. Furthermore, the plan parameters with particular conditions are delivered for reference as tables, and an industrial application is offered to prove the applicability of the proposed plan.