# Influence of Manufacturing Process Modularity on Lead Time Performances and Complexity
## 2 Related Works  
Modular approaches are increasingly being used as an integral part of design methods as many systems, including products and processes, evolve toward increasing modularity [9]. [PERSON] and [PERSON] [10] classify modular design methods into Design Structure Matrix (DSM), Modular Function Deployment (MFD), and Function Structure Heuristics (FSH). DSM methods aim to structurally describe system elements to cluster them into modules [11]. MFD approach consists of five stages that are aptly characterized, e.g., in the work of [PERSON] et al. [12]. FSH techniques developed by [PERSON] et al. [13] include three strategies aimed at identifying modules for product architectures at the functional level. Modularity in system property can be studied from many diverse perspectives. In contrast to specific views on modularity, generic insights attract more attention. One of these insights is that tweaking this system property appears as a possible way in the course of system evolution as it slows its atrophy [14], but this effort should not be endless and ineffectual. The effectiveness of such an effort also depends on the appropriateness of the modularity metrics used. There are several possible approaches for how to evaluate product and process modularity as a relative measure of the degree of granularity, i.e., the level of detailization of the system element before or after its decomposition [15]. In other words, relative modularity can be defined as a measure quantifying the tendency of the network to be organized in network modules [16]. Such metrics (see, e.g., [17; 18; 19; 20]) are used to compare this property among multiple designs. Several independent authors pointed out in their works [21; 22; 23; 24; 25] that over-modularization is as undesirable as under-modularization. They came to this conclusion by assessing the advantages and disadvantages of these two contradictory solutions. [PERSON] et al. [26] stated that low system modularity in general can cause a higher number of unwanted effects than the same system of high modularity. Moreover, in the case of under-modularization, there are difficulties maintaining the large system elements or modules. On the other hand, a disadvantage of over-modularization is that a large number of linkages need to be managed. A possible solution to overcome this issue is to accurately identify the level of system granularity by an exact formula for quantifying this measure. According to [PERSON] and [PERSON] [27], OM can be achieved 'through balanced modularization as structural symmetry in the distribution of the sizes of modules'. [PERSON] and [PERSON] [28] proposed the optimal product modularity measure to obtain a product structure tree which ensures OM at all hierarchical levels. When talking about optimal modularity, it is important to mention the well-known optimal network modularity indicator developed by [PERSON] and [PERSON] [29], whose formula is described in Section 4 of this paper. Process modularity issues are often investigated in the context of process complexity (see, e.g., works of [30; 31; 32]). Process modularity is considered as the degree to which a system is composed of relatively independent interacting elements encapsulated into modules that can be combined in variations to provide different functions [33]. Process complexity can be defined as the degree to which a process is complicated to analyze, study, or understand [34]. It is apparent that both process modularity and process complexity are important inherent system properties. It is also known that process modularity is primarily used to reduce its complexity by decomposing processes into modules, as they are easier to manage than as a whole [35]. The related problems were explored, e.g., in work [36], where authors identified a strong negative correlation between complexity and system modularity which confirms that lower complexity implies higher modularity.