## 1 Introduction
Machines are a major component of FMS, and often it is not possible to handle machine breakdowns as quickly as the production requirements dictate. In addition, the disturbances caused by these breakdowns lead to scheduling problems, which decrease the productivity of the entire manufacturing operations. This issue points out an important need for the consideration of machine reliability in the performance evaluation process of FMS, especially in light of the increasing complexity of such systems in recent years. Consequently, many researchers have realized the importance of reliability features of the FMS and much work has been contributed. [PERSON] et al. [18] proposed an approach that provides a flexible routing which ensures high overall performance of the cellular manufacturing system (CMS) by minimizing the impact of machine failure through the provision of alternative process routes in case of any machine failure. [PERSON] et al. [19] proposed a Markov-based model for reducing the severity of breakdowns and improving performances of the CMS with unreliable machines. [PERSON] et al. [20] suggested a methodology for availability evaluation of manufacturing systems using semi-Markov model, which considers variable failure or repair rates. [PERSON] and [PERSON] [21] proposed a tool for performance evaluation of general Markovian continuous material flow of two-processing stage production systems with an intermediate finite buffer. [PERSON] [22] developed a semi-Markov model to study the effects of tool failures on the performance of a flexible manufacturing cell (FMC). [PERSON] [23] then developed stochastic models to determine the performance of an FMC under random operational conditions, including random failures of cell components (machine tool and robot) in addition to random processing times, random machine loading and unloading times, and random pallet transfer times. [PERSON] et al. [24] put forward a reliability modeling and evaluating methodology for a repairable, non-series, multistate FMS with finite buffers by using an improved vector universal generation function to satisfy the market demands on capacity and capability of the system. [PERSON] et al. [25] proposed a process performance evaluation chart to examine the manufacturing performance of bearing connectors, which can also be used for multiple evaluations of manufacturing performance in other manufacturing industries. [PERSON] and [PERSON] [26] investigated the innovation process for smart manufacturing in the domain of synthetic rubber and its vulcanization process, as well as a real-time sensing technology to the realization of a smart manufacturing environment by building cloud-based infrastructure and models for the pre-detection of defects. More studies about availability analysis of manufacturing systems can be found in [27; 28; 29; 30; 31]. Although the aforementioned studies have been undertaken, there are very few studies, which consider the influence of production setup activities on availability, and products' output performance of FMS. Moreover, the procedure for overcoming the \"state explosion problem\" in the performance evaluation process of FMS has not been found. Therefore, a system-level FMS performance evaluation method based on the Markov reward approach and Lz-transform method is proposed in the current article to analyze the output performance of different products and availability of the whole FMS, which includes various aging multistate CNC machine tools and non-always available MHS. Section 2 makes a brief introduction of the Markov reward approach and Lz-transform method. An original multistate transition process of CNC machine tools that considers the production flexibility and the performance evaluation procedures of an FMS is presented in Section 3. Numerical results are shown and discussed in Section 4. Finally, concluding remarks and the application of the proposed method are presented.