Designing a variables two-plan sampling system of type TNTVSS-(nT, nN; k) for controlling process fraction nonconforming with unilateral specification limit

This paper proposes a variables two-plan sampling system involving normal and tightened inspections, denoted as TNTVSS-(nT,nN;k)$ (n_{\text{T}}, \, n_{\text{N}}; \, k) $, for controlling process fraction nonconforming with a unilateral specification limit based on one-sided capability indices. The system utilises two single variables sampling plans with different sample sizes (nT,nN)$ (n_{\text{T}} , \, n_{\text{N}} ) $ and the same critical acceptance value k$ k $, where nT$ n_{\text{T}} $ and nN$ n_N $ are sample sizes required for tightened inspection and normal inspection, respectively. The tightened inspection plan is used when the quality deteriorates and the normal inspection plan is used when the quality is found to be good. The operating characteristic (OC) function of the proposed sampling system is developed based on the exact sampling distribution. The plan parameters under various settings are determined by solving two non-linear equations simultaneously, which satisfy the required quality levels and allowable risks given by the producer and the consumer. The behaviour of the proposed sampling system in terms of the OC curve and the average sample number are also examined, discussed and compared with the traditional single variables sampling plan.