Evaluate the system reliability for a manufacturing network with reworking actions

To measure the system reliability of a manufacturing system with reworking actions is a crucial issue in industry, in which the system reliability could be one of the essential performance indicators to evaluate whether the manufacturing system is capable or not. In a manufacturing system, the input flow (raw materials/WIP) processed by each machine might be defective and thus the output flow (WIP/products) would be less than the input amount. Moreover, defective WIP/products are usually incentive to be reworked for reducing wasting and increasing output. Therefore, reworking actions are necessary to be considered in the manufacturing system. Based on the path concept, we revise such a manufacturing system as a stochastic-flow network in which the capacity of each machine is stochastic (i.e., multistate) due to the failure, partial failure, and maintenance. We decompose the network into one general processing path and several reworking paths. Subsequently, three algorithms for different network models are proposed to generate the lower boundary vector which affords to produce enough products satisfying the demand d. In terms of such a vector, the system reliability can be derived afterwards.