Research Article

ESD Reports Summer 2005

Measuring Modularity

from an Engineering Systems Perspective

By Katja Hölttä-Otto, Research Affiliate
Eun Suk Suh, ESD Ph.D. Candidate
and Olivier de Weck, Robert N. Noyce Career Development Assistant Professor of Aeronautics and Astronautics and Engineering Systems

INTRODUCTION
Modularity has become a pervasive theme in product development. Modular architecture, defined as having a one-to-one mapping from functional elements to the physical components of the product, and uncoupled design, has many benefits. They include cost savings due to commonality and the ability to design modules independently in parallel within a company or at suppliers.

However, a fully modular design may not always be achievable in designing engineering systems and products. There appears to be a potential trade-off between the desire for modularity from a “business” or lifecycle engineering standpoint and the desire for high performance and efficiency in the technical domain. As a consequence we can formulate the following hypothesis that, if proven correct, might be considered an important principle of System and Product Architecture: Technical constraints in terms of mass, volumetric and power efficiency imposed on the design of engineering systems leads to a higher degree of coupling between elements of form and functional elements (= integral architectures) relative to systems of equivalent functionality where such constraints are substantially relaxed.

SYSTEM ARCHITECTURE AND PERFORMANCE ANALYSIS
We include two pairs of products in the analysis: a cellular and desk telephone as well as a laptop and desktop computer. We decompose these selected systems and form component-to-component Design Structure Matrices (DSM) for each system (Figures 1 and 2).

Figure 1. Component-to-component DSM for the two phones
click here to view a larger image

Figure 2. Component-to-component DSM for the two computers
click here to view a larger image

First we analyzed existing modularity metrics but found that they were not usable for various reasons. Generally, they measured modularity based on a subjective definition of module boundaries, whereas our goal is to look at the fundamental degree of coupling of a product independent of where the module boundaries are set. Therefore we developed a new index, the Singular Value Modularity Index (SMI,) based on the decay pattern (Fig. 3) of the DSM singular values:

Steps:

1. Form a binary component-component DSM of the product (enter a 1 for components that are connected, a 0 when two components are not connected, set the diagonal to 0)

2. Perform a singular value decomposition of the DSM

(1)

The singular values are the diagonal elements of the middle matrix

(2)

3. Compute the SMI, which is the inverse of rate at which the singular values decay in the system. If all singular values are equal, then the SMI is equal to 1 (fully modular), if there is only one non-zero singular value, then the SMI is closer to 0 (more integral).

(3)

are the singular values of the DSM arranged in a descending order, and N is the number of components (rows/columns in a DSM). The singular values describe the principal components of the interconnectivity of the product. If a few large singular values dominate, it suggests that the connectivity of the system is concentrated in a few major components making the product more integral. The system can be understood almost entirely by focusing on those few key components. Many products that feature a bus-modular architecture appear to have this feature. If on the other hand the singular values decay in a more gradual fashion (see desk phone and desktop PC in Fig.3) it is an indication that connectivity is more decentralized in the system and that the product in inherently more decoupled, i.e. more modular.

We calculated two modularity indices for each product:

1. functions to modules ratio and

2. the new metric SMI (Eq. 3)

The decay pattern for the four case products is shown in Figure 3 and the metrics are in Table 1.

Table 1. Module index summary for desktop PC-laptop and desk phone-cellular phone pairs. A larger SMI (closer to 1) indicates a more modular system. More functions per module indicates a more integral system.

Figure 3. Singular value decay patterns for the pair of phones (left) and computers (right)

CONCLUSIONS
We found support for our hypothesis that design of engineering systems subject to strong technical performance constraints in terms of packaging, light weighting and power efficiency leads to more integral architectures. This result is significant, since the metrics we used measure modularity from a different perspective. Moreover, in both cases we noticed that the product with more stringent technical constraints (vs. the product with relaxed technical constraints) is more integral in terms of more functions per module and in terms of connectivity both within and between modules.

We observed a significant difference in the interaction profiles in the DSM matrix of these two classes of systems. We found that the higher a system’s performance requirement or constraint, the higher the coupling among system elements. We showed this through examples with two functionally equivalent product pairs that were subjected to a physical teardown inspection and by using two different metrics to measure modularity and coupling in design. The weight and power constrained laptop computer and cellular phone are more coupled and more integral than the desktop PC and desk phone, respectively. This has profound implications on how products are sourced, assembled and upgraded. The SMI metric is able to quantify the degree of modularity without introducing arbitrary module boundaries.

The result is an apparent violation of the independence axiom in Axiomatic Design (which states, that un-coupled or decoupled designs are preferred over coupled designs), as well as the idea of perfect modularity being always achievable. While a high degree of modularity might always be desirable, we showed that, at least in certain cases it is not always achievable, because the axiomatic or modular design has to be compromised by technical concerns such as efficiency of weight, packaging, and/or power.

The insight is that in performance-critical design, considerations other than pure axiomatic or modular design must be considered. But it is as important to note that modular and axiomatic approaches have their place in design when business drivers are more important than technical drivers. This is also why it is easier to modularize industrial machinery and buildings, compared to mobile digital devices and vehicles.

Published as:
Holtta K., Suh E.S., de Weck O. L., “Trade-off between Modularity and Performance for Engineered Systems and Products”, ICED 2005: The 15th International Conference on Engineering Design , Melbourne , Australia , August 15-18, 2005