Analytical approximations to predict performance measures of manufacturing systems with general distributions, job failures and parallel processing

Parallel processing is prevalent in many manufacturing and service systems (i.e. some components may have to wait for other components before the assembly can begin). It is also common to observe manufacturing systems that deal with multiple products, resources shared between different products, and circulation due to random part failures. An example of such a system configuration is observed at a facility equipped to assemble and test web servers. The primary objective of this research was to develop analytical approximations to predict performance measures of a system with the above characteristics and evaluate its accuracy. Manufacturing systems with general distributions, multiple products, job circulation due to failures, resource sharing, and a fork and join system (to model parallel processing of some assembly operations) were studied using the parametric decomposition approach. The different work centers (or stations) in the manufacturing system is modeled as a network of queues and the parametric decomposition approach is applied to decompose the network of queues into individual queues to estimate the performance measure of the system. Existing analytical formulations were modified and appropriate correction terms were added to the approximations to bridge the gap in the error between the analytical approximation and the simulation models. Random instances were generated and the flow times from the approximations and simulation models were compared. The experimental study conducted indicates that the analytical approximations along with the correction terms can serve as a good estimate for the flow times of the manufacturing systems with the above characteristics.