How does variability in input load relate to the probability of critically delayed delivery in a simple multipart re-entrant flow-line problem?

Aspects of the computation of tail-probabilities by simulation in the context of a generic job/flow-shop model are discussed. The job/flow-shop model consists of structural elements such as bottlenecks, re-entrance as well as a mixture of these two fundamental types of production complexity and is operated as a multi-part production set-up. Standard simulation methodology relies heavily on the Central Limit Theorem, but as powerful as this statistical concept might be, it has its pitfalls. As is shown, it can be quite deceptive and consequently harmful. Given a certain production batch size, the discussion will focus on the estimation of the probability of critically delayed delivery beyond a specified threshold and try to establish a relation to certain parameters that can be linked to the degree of regularity of the arrival stream of parts to the job/flow-shop. This last aspect relates remotely to the Lean Thinking philosophy that praises the smooth and uninterrupted production flow as being beneficial to the overall operation of productive points in general, and the findings will also be linked to this discussion.