Optimal Designing of Variables Sampling Plan for Resubmitted Lots

Abstract

This article proposes a variables sampling plan that can be applied for sampling inspection of resubmitted lots when the quality characteristic of interest follows the normal distribution. Resubmission of lots for inspection is allowed in some situations where the original inspection results are suspected or when the supplier or producer is allowed to opt for resampling as per the provisions of the contract, etc. The advantages of this proposed variables sampling plan over the existing single sampling variables plan are discussed. Tables are also constructed for the selection of optimal parameters of known and unknown standard deviation variables resampling scheme for specified two points on the operating characteristic curve, namely, the acceptable quality level and the limiting quality level along with the producer and consumer's risks. The optimization problem is formulated as a nonlinear programming where the objective function to be minimized is the average sample number and the constraints are related to lot acceptance probabilities at acceptable quality level and limiting quality level under the operating characteristic curve.

Keywords:

• Application
• Decision making
• Lot resubmission
• Nonlinear programming
• Quadratic programming
• Quality characteristics
• Resampling scheme
• Sampling by variables

Mathematics Subject Classification:

• 62P30
• 90C30
• 90C90

Acknowledgments

The authors thank the anonymous reviewers and the editor for their valuable comments and suggestions, which significantly improved the presentation of this manuscript.