## 1 Introduction
It has been a powerful means to ensure product reliability, but it has three defects: (i) the relationship between the different product failures is neglected; (ii) FMEA fails to manage the uncertain product information; and (iii) FMEA regards product failure as a static process rather than a dynamic process, but it is obvious that the generation and propagation of product failure is a typical dynamic and uncertain behavior process. Hence, many extensions to the Petri net (PN) including places, transitions and directed arcs, such as colored PN, timed PN and prioritized PN, fuzzy PN have been successfully developed and applied in analyzing reliability of systems and conducting failure diagnosis [23; 24; 25; 26]. [PERSON] and [PERSON] [27] proposed an approach for analyzing systems reliability using fuzzy stochastic Petri nets (FSPNs) with fuzzy parameters, and their research successfully overcame the difficulties in adopting common software to detect multi-statesystems with high complexity. [PERSON] and [PERSON] [28] put forward an approach to reliability modeling and assessment by the extended object-oriented PN. Its consideration of probability statistics for product failure makes the application scope of the proposed PN become wider than that of the traditional ones. [PERSON] et al. [29] introduced fuzzy reasoning PN (FRPN) into the reliability optimization design for highly sophisticated products, and the case study of a spacecraft solar array demonstrated its rationality and validity by its union with the fuzzy reasoning algorithm which allows it to consider stochastic interconnection between product components. However, researchers expanded the most critical influences on the product reliability optimization design, such as economic cost, state-of-the-art, performance time, and so on [30]. When the reliability design is treated as an optimization problem to solve, it is influenced by a variety of factors that can be converted into different forms of target functions or constraints. It is difficult to process and express the relationship between the various factors and the reliability indicators. The product models related to PN do not take the complexity of the product unit, importance degree, technical level and other factors into account when dealing with the influence of reliability optimization, and they fail to reflect the synthetic situation of product reliability optimization. Modern products consist of so many functional modules and components, but, in reality, reliability optimization design only needs to be conducted at the level of subsystems which consist of modules to save time and cost. These methods based on PN do not consider the subsystem division. The objective of this paper is to develop an approach of reliability optimization design for modern mechanical products, which cannot only use the uncertain evaluation provided by experts for essential factors, subsystem division, but take into account the dynamic propagation of product failure. The interval expert evaluation is combined with the FRPN to build a reliability-based and cost-oriented product optimization model. Then, the cultural-based dynamic multi-objective particle swarm optimization (DMOPSO) using crowding distance sorting method is adopted to solve it so that the best compromise solution can satisfy the reliability constraint of the subsystem composition with minimum cost the on the maximum balance [31]. The remainder of this paper is organized as follows. Section 2 describes the general framework of the proposed method. Section 3 introduces the detail operators, and Section 4 illustrates a numerical case study of the reliability-based and cost-oriented optimization design for a CNC machine tool. Section 5 provides a comparison and analysis of the proposed method, and Section 6 offers the conclusion.