Analysis of production systems when run length influences product quality

Proponents of the Just-In-Time philosophy contend that smaller run lengths result in improved product quality through the prompt identification of defects and due to learning curve effects. Others argue that smaller run lengths result in excessive interruptions and disruptive environments that impair learning and increase defects. We formulate appropriate models to account for either positive or negative learning effects in production processes. The defect rate of the process is modelled as a function of the run length, and closed-form solutions are derived. From a JIT perspective, the results of our analysis indicate that considerably smaller lot sizes are appropriate – even without reductions in setup costs – when there is a significant inverse relationship between run length and product quality.