Analysis of the Operating Characteristic Curve in Acceptance Sampling Schemes for Quality Assurance

Abstract

In modern manufacturing industries, acceptance sampling plans serve as indispensable tools 
for maintaining and verifying product quality. They are employed at various stages—covering 
raw materials, semi-finished products, and finished goods—to determine whether a 
production lot should be accepted or rejected based on the results of sample inspections. 
When a lot fails to meet quality specifications, it is either returned to the supplier or 
subjected to rectifying inspection, during which defective units are identified, replaced, or 
reworked. Although effective, this process often results in high inspection costs, longer 
production cycles, and increased operational inefficiencies. To address these challenges, this 
study proposes an economic model designed to optimize single and double sampling plans for 
improved efficiency and reliability in industrial quality assurance. The model aims to minimize 
the Average Total Inspection (ATI) while maintaining the desired levels of producer’s and 
consumer’s protection. This ensures that high-quality lots are not wrongly rejected and that 
substandard lots are not erroneously accepted. The developed approach provides a 
statistically grounded framework for balancing cost-effectiveness, risk minimization, and 
quality assurance within the production process. A comparative analysis of the optimized 
models for Single Sampling Plans (SSP) and Double Sampling Plans (DSP) demonstrates that 
the ATI generally increases with the fraction defective (p), with SSP yielding slightly higher 
ATI values compared to DSP. The results further revealed that the optimized DSP achieved 
a minimum consumer’s risk of 0.0971, whereas SSP showed a relatively higher consumer’s risk 
of 0.0979, indicating the superior performance and flexibility of the double sampling 
approach. Overall, the study highlights the critical role of optimal acceptance sampling design 
in improving inspection efficiency, reducing production costs, and enhancing decision-making 
across manufacturing and supply chain systems. The proposed economic model provides a 
practical and analytical framework for industries seeking to implement more effective and 
sustainable quality control strategies.