ARIMA modeling for sequential pharmaceutical assay monitoring acrossproduction lots: Raw and Box-Cox sensitivity analyses

Abstract

This preliminary short communication evaluates whether chronological production-lot assay results can support short-term next-lot forecasting using non-seasonal ARIMA models. A lot-level assay series was used to evaluate short-term forecasting of 9-deoxy-9alphaaza- 9alpha-methyl-9alpha- homoerythromycin A assay results. The dataset contained 199 valid chronological production-lot observations. The first 179 observations were used for model fitting, and the final 20 real assay results were held out for validation. Calendar aggregation was assessed but was not selected because monthly, quarterly, and semiannual series contained missing intervals, while annual aggregation yielded only 18 observations. The final analysis therefore used chronological production-lot order as the time index and targeted next-lot assay forecasting rather than equal-calendar stability prediction. Non-seasonal ARIMA models were compared using AICc, parameter significance, Ljung-Box residual diagnostics, model parsimony, and holdout validation. Raw ARIMA(0,1,1) with one regular difference and a constant was selected as the primary model after screening using statistical software. Box-Cox transformation with lambda = 2 produced the same ARIMA(0,1,1) structure but did not improve validation accuracy. The primary raw model gave ME = 0.75, RMSE = 1.01, MAE = 0.80, and MAPE = 0.79% on the 20-result validation set. The raw model was therefore retained as the most interpretable and scientifically reasonable model for next-lot assay monitoring.

Bangladesh J. Sci. Ind. Res. 61(3), 111-118, 2026