Abstract

Quality control in manufacturing often requires precise estimation of the probability of defective items in a production batch to make informed decisions on product acceptance or rejection. While statistical models such as the binomial or Poisson distributions are widely used, they assume infinite or large populations, which may lead to inaccurate results when dealing with finite production lots. The hypergeometric distribution, by contrast, provides a more accurate framework by considering sampling without replacement, making it ideal for analyzing defects in small or finite batches.

This study investigates the application of the hypergeometric distribution in quality sampling for finite production lots. A mathematical model is developed to estimate the probability of obtaining a specific number of defective products in a given sample size. Realistic case data from a manufacturing scenario are used to illustrate the calculation process, and results are compared to those obtained using the binomial model. Findings reveal that the hypergeometric distribution offers greater precision, especially in cases where the sample size is a significant proportion of the total lot size. The difference in probability estimates, although sometimes marginal, can be critical for high-stakes quality decisions.

The research highlights the importance of selecting the correct statistical model in quality control sampling. Practical recommendations are provided for implementing hypergeometric distribution calculations in quality inspection processes, with emphasis on industries dealing with limited or costly production runs. Future research may explore integration with software-based quality monitoring tools for real-time defect probability assessment.