An optimal plan of zero-defect single-sampling by attributes for incoming inspections in assembly lines

• An optimal sampling plan is developed for incoming inspections in assembly lines.
• Inspection sample sizes are chosen to minimize all quality related costs.
• A three-step procedure is developed to efficiently solve larger size problems.
• The optimization model provides insightful implications for quality management.
• The optimal inspection sampling plan builds a foundation for other advanced plans.

This paper proposes a nonlinear integer program for determining an optimal plan of zero-defect, single-sampling by attributes for incoming inspections in assembly lines. Individual parts coming to an assembly line differ in the non-conforming (NC) risk, NC severity, lot size, and inspection cost-effectiveness. The proposed optimization model is able to determine the inspection sample size for each of the parts in a resource constrained condition where a product’s NC risk is not a linear combination of NC risks of the individual parts. This paper develops a three-step solution procedure that effectively reduces the solution time for larger size problems commonly seen in assembly lines. The proposed optimization model provides insightful implications for quality management. For example, it reveals the principle of sample size decisions for heterogeneous, dependent parts waiting for incoming inspections; as well as provides a tool for quantifying the expected return from investing additional inspection resources. The optimization model builds a foundation for extensions to advanced inspection sampling plans.