Reliability evaluation for an intermittent production system with stochastic number of normal machines

In an intermittent production system (IPS), a number of normal machines in a workstation may present multiple levels owing to maintenance, possibility of failure, etc. It means that the number of machines in each workstation is stochastic. This paper proposes a key performance index (KPI), which reflects the probability that an IPS can complete demand d within time constraint T. Such a probability is defined as system reliability. The IPS is modeled as a stochastic network, in which each arc is regarded as a workstation with stochastic number of normal machines, and each node is represented as a buffer. The concept of minimal machine vector (MMV), which indicates the minimal capacity required at each workstation to satisfy the demand and time constraints, is presented for evaluating the system reliability. In particular, a novel algorithm based on depth-first search is proposed to derive all MMVs. This algorithm avoids searching for unnecessary child nodes, and thus increases efficiency. Two practical examples, a printed circuit board and a footwear manufacturing systems, are used to illustrate the proposed algorithm. Such a KPI can provide information to production managers to understand the probability that an order can be completed on time.