Practical screening and monitoring tools for out-of-specification risk in biological products under finite sample sizes.

Evaluating the risk of out-of-specification (OOS) occurrence before it happens is essential to prevent delays or interruptions in the supply of biological products. This study proposes a practical and quantitative evaluation approach using two indices, S1 and S2, as OOS risk screening and monitoring tools under finite-sample conditions. S1 evaluates whether the variability of data points in a dataset satisfies a low OOS risk criterion, defined as an acceptable level of inherent variability. S2 evaluates whether the observed data range remains within the specification limits with a range-proportional safety margin. Monte Carlo simulations based on normal distributions with sample sizes up to 500 demonstrated that S1 > 1 effectively identified datasets that deviated from the low OOS risk criterion, whereas S2 > 1 functioned as an early alert indicator that predicted or coincided with OOS occurrences. Regardless of the distribution type, both indices increase by definition as the spread of data points increases, suggesting their potential applicability as practical monitoring tools even for non-normal datasets. The combined use of S1 and S2 provides complementary and early warning insights into potential quality deviations and supports proactive quality risk management of biological products.