Standalone closed-form formula for the throughput rate of asynchronous normally distributed serial flow lines

Flexible flow lines use flexible entities to generate multiple product variants using the same serial routing. Evaluative analytical models for the throughput rate of asynchronous serial flow lines were mainly developed for the Markovian case where processing times, arrival rates, failure rates and setup times follow deterministic, exponential or phase-type distributions. Models for non-Markovian processes are non-standalone and were obtained by extending the exponential case. This limits the suitability of existing models for real-world human-dependent flow lines, which are typically represented by a normal distribution. We exploit data mining and simulation modelling to derive a standalone closed-form formula for the throughput rate of normally distributed asynchronous human-dependent serial flow lines. Our formula gave steady results that are more accurate than those obtained with existing models across a wide range of discrete data sets.