Reliability evaluation for a multistate network with time attribute and periodical maintenance

In a hybrid flow shop (HFS), each machine at a workstation may fail due to unexpected failure, human negligence, etc. As a result, the number of available machines at a workstation should be multistate. From a decision-making viewpoint, it is a practical issue whether the HFS with a stochastic capacity could complete a given demand or not. System reliability is one of the performance indexes to assess the system performance. It is defined as a probability that the HFS with multistate capacity can satisfy demand successfully. The HFS is firstly modeled as a multistate hybrid flow shop network (MHFSN). In real-world systems, the reliability of each machine may change as time elapses. Hence, machine reliability is considered in the MHFSN, and thus it is important to evaluate time-dependent system reliability. To consider a time attribute in the MHFSN, Weibull distribution is adopted to represent each machine reliability that will degrade as time passes. To prevent decreasing machine reliability and system reliability, managers need to maintain machines periodically to retain system capability. Hence, an algorithm is proposed to evaluate system reliability with periodical maintenance. Note that system reliability is provided in a time period, and thus managers are able to make a maintenance decision in time based on the changes of the system reliability.