Research on Defective Rate Control in Production Processes Based on Hypothesis Testing and Cost Optimization

Abstract

In modern manufacturing, delivering high-quality products at minimal cost is essential for maintaining competitive advantage. This study combines statistical hypothesis testing with cost-strategy optimization to design a low-cost sampling and testing scheme that effectively controls defect rates at multiple production stages. First, under the null hypothesis that the defect rate does not exceed the nominal value, In this article,calculate required sample sizes of 98 at 95 % confidence and 59 at 90 % confidence. In this article,then apply normal distribution theory to determine appropriate sampling frequencies, ensuring test accuracy across confidence levels. Second, by constructing a cost matrix and sampling-quantity vector, In this article,evaluate inspection strategies at both the procurement (spare parts) and production (finished product) stages. In this article,find that foregoing spare-parts inspection in favor of finished-product testing significantly reduces inspection costs and market-exchange losses while maintaining quality standards. Specifically, this approach minimizes the number of original-parts inspections yet preserves finished-product integrity, yielding substantial cost savings and lower risk exposure. Overall, our framework offers manufacturers a theoretically grounded, practically feasible method for defect-rate control and inspection-cost optimization.