Binomial Distribution in Quality Control Testing of Pharmaceutical Products in Kaduna Industrial Zone

This study applies the binomial probability distribution to quality control testing protocols for pharmaceutical product batches manufactured in the Kaduna Industrial Zone, North West Nigeria, home to several of Nigeria's largest indigenous pharmaceutical manufacturers. Quality assurance in pharmaceutical production is governed by stringent national and international regulatory standards, and the design of statistically defensible acceptance sampling plans is essential for detecting defective product batches before distribution. The study reviews the theoretical basis of acceptance sampling under the binomial model, deriving operating characteristic curves, average outgoing quality curves, and average sample number functions for sampling plans of varying sample sizes and acceptance numbers. Working with anonymised batch testing records supplied by two cooperating manufacturers in the Kaduna Industrial Zone over a three-year period, the study evaluates the performance of currently deployed sampling plans against the computed operating characteristic curves, identifying acceptance quality limits and lot tolerance percent defective thresholds. Comparisons are made with alternative plans specified under the ISO 2859-1 and ANSI/ASQ Z1.4 standard series. Results reveal that existing sampling plans in use at the sampled facilities provide inadequate protection against lots with defect rates between 3 and 7 percent, a range that corresponds to sporadic manufacturing non-conformances documented in the historical records. Revised sampling plans offering stronger discrimination at this critical defect rate range are proposed. Keywords: binomial distribution, acceptance sampling, quality control, pharmaceutical manufacturing, Kaduna