Value of Increasing Sample Size for Assessing Defect Concentration

Purity and cleanliness are important quality attributes in many products. Foreign contamination or other defects within a product has a detrimental effort on the real performance of the material in end-use applications. Visual evidence of any defects conveys a negative impression to customers with regard to the product quality. Therefore, in many manufacturing or processing facilities, the product is assessed by an on-line inspection system to quantify the concentration of defects for product classification and release. In most cases, the production rate of the facility greatly exceeds the throughput of the available inspection devices so a representative portion of the material produced is inspected. Inspection devices are available with different achievable inspection rates. Optimizing the value of inspection process requires balancing the increased cost of larger inspection rates with the value gained from improved confidence of the results. The concentration of defects is typically on the order of parts per million, and measurements of low count data have inherently large variability. This results in a meaningful amount of Type I and Type II error (incorrect prime/off-grade decision). The impact of increasing the measured throughput was explored using statistics appropriate for discrete data, and the resulting change in Type I/II error determined to assess the value of increasing the inspection rate.