Estimated network reliability evaluation for a stochastic flexible flow shop network with different types of jobs

• A flexible flow shop (FFS) with stochastic capacity is studied.
• A stochastic flexible flow shop (SFFSN) network is constructed to model the FFS.
• Propose an index, network reliability, to measure the SFFSN.
• A branch-and-bound approach is involved to evaluate estimated network reliability.
• Two real cases are utilized to demonstrate network reliability evaluation.

In fields such as integrated circuit packaging, printed circuit boards (PCB), and textile fabrication, flexible flow shops (FFSs) are common manufacturing systems and have been studied by several researchers. Previous studies on FFSs assume that the capacity of each station is fixed. However, owing to factors such as maintenance, partial failures, the possibility of failures, and unexpected situations in manufacturing systems, the capacity, i.e., the number of normal machines in a station should have multiple levels and be regarded as a stochastic component. Hence, this study extends the deterministic capacity to the stochastic case for each station. An FFS with stochastic capacity is modeled as a stochastic flexible flow shop network (SFFSN) where each arc denotes a station with stochastic capacity and each node denotes a buffer. To illustrate the ability of a system in satisfying an order in the FFS, this study evaluates the network reliability, which is defined as the probability with which the SFFSN can complete an order within the time constraint. Because the completion time of an order cannot be computed directly, this study proposes an algorithm involving a branch-and-bound approach for the evaluation of the estimated network reliability based on two approximate capacity vectors. Three real cases, IC card, PCB and footwear manufacturing systems, and computational experiments are utilized to demonstrate the proposed algorithm and to discuss the performance of the algorithm, respectively. The experimental results show that the proposed algorithm can acquire the estimated network reliability close to the accurate network reliability.