Performance modelling of serial production lines with inspection/repair stations

The authors derived a set of analytical models for serial production lines with multiple operation stations and multiple inspection/repair stations. Multiple defect types may be acquired by the production units from the raw stock as well as during processing at operation stations. The analytical models are steady-state equations for outgoing quality level, throughput rate and scrap rates. The analytical models are based on (1) traffic rate equations of the flow through a production line when represented as a directed flow network and (2) probabilistic models of changes in defect attributes of the production units as they flow. The formulas may be used for evaluating inspection configuration designs including the formulation of optimal cost models.