Optimal and economic design of variables resampling scheme based on double specification limits

In this manuscript, designing methodologies of a variables sampling plan (VSP) for resubmitted lots are proposed for the application of measurable quality characteristics having double specification limits. The optimal plan parameters of the proposed variables resampling scheme (VRS) are obtained for both known and unknown sigma (standard deviation) cases and satisfy both the producer’s risk and consumer’s risk simultaneously at their respective quality levels. Two types of fraction nonconforming levels namely symmetric fraction nonconforming and asymmetric fraction nonconforming based on the double specification limits are also considered for determining the optimal plan parameters. A nonlinear optimization problem is formulated to design the optimal plan parameters. Merits of the proposed VRS are also investigated. A real-life application of the proposed sampling scheme is explained. In addition, an economic aspect of design of the VRS based on double specification limits is investigated.