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Series-parallel systems with intermediate buffers widely exist in reality. For example, a production line can have multiple production phases connected in series. Each phase can have several production units organised in parallel to enhance the performance of the system. Between these phases, some intermediate buffers are allocated to store work in process (WIP). These buffers can reduce the influence of the breakdown and maintenance of a subsystem on the production rate of the whole system. However, the effects of intermediate buffers also make the degradation process of the system more difficult to model. Some existing papers developed methods to evaluate the performance of the series-parallel or series system with intermediate buffers. Tan and Gershwin [20] investigated the steady-state of a general Markovian two-stage continuous-flow system by solving a system of differential equations that describes the dynamics of the system. After that, Tan and Gershwin [19] further applied their model to the steadystate analysis of more general situations, e.g. systems with multiple components in series or parallel in each subsystem. Alexandros and Chrissoleon[1] analysed the steady-state of a two-workstation onebuffer follow line by using the Markovian property of the system. Liu et al. [13] investigated a system similar to that in Ref. [1], which considers the asynchronous operations of independent parallel units. The system was modelled by a Quasi-Birth-Death (QBD) process that can be solved efficiently. When there are more than two subsystems (components) in a series-parallel (series) system, the above-mentioned performance evaluation approaches based on steady-state analysis become impractical. Besides methods using the Monte Carlo simulation [9], some approximate approaches e.g., the aggregation method [4, 8, 21] and the decomposition method [5, 12], are developed to evaluate the performance of the system analytically. Although the above papers addressed the performance evaluation of a series-parallel system, these papers assumed a predetermined maintenance strategy, while the maintenance strategy optimisation is not considered. Yifan Zhou Zhisheng ZhAng

Optimal maintenance of a series production system with two multi-component subsystems and an intermediate buffer