Complexity in Manufacturing

Synonyms

Complexness

Definition

The original Latin word “complexus” signifies “entwined” or “twisted together.” The Oxford Dictionary defines “complex” as something that is “made of (usually several) closely connected parts.” A system would be more complex if more parts or components exist and with more connections in between them (EIMaraghy et al. 2012).

Several different measures defining complexity have been proposed within the scientific disciplines. Such measures of complexity are generally context dependent. Colwell (2005) defines 32 complexity types in 12 different disciplines and domains such as projects, structural, technical, computational, functional, and operational complexity. Engineered system complexity is invariably multidimensional. A complex system usually consists of a large number of members, elements, or agents, which interact with one another and with the environment. They may generate new collective behavior, the manifestation of which can be in one or more of the following domains: functional, structural, spatial, or temporal.

A complex system is an “open” system, in the thermodynamics sense, involving entropy principles as well as involving nonlinear interactions among its subsystems which can exhibit, under certain conditions, a degree of disorderly behavior. In particular, the future progression of events may become very sensitive to conditions at any given point of time and “chaotic behavior” may emerge.

Extended Definition

Complicatedness, Complexity, and Chaos

In simple terms for now, a simple system or artifact is easily knowable. A complicated system or product is not simple but is knowable, e.g., a car is a complicated product/system. A complex system is one where uncertainty exists. For instance, the development of a car is complex; it requires engineering business knowledge in several disciplines and collaborative work in teams. Details are not fully knowable to each development engineer. A complicated system could refer to a system having many parts, making it somewhat harder to understand, perhaps by virtue of its size, whereas complex refers to a system containing uncertainty during the development process or intrinsically in its design, the outcome not being fully predictable or controlled. Complexity may also be at the operational level such as during the manufacturing process itself. What is complicated is not necessarily complex and vice versa, and what is complicated for one person may be complex for another less knowledgeable individual or a group with less technological tools (Fig. 1). The word technology comes from Greek (technología) meaning “art, skill, craft.” Technology is the knowledge, scientific methods, engineering techniques, and tools that help analyze, solve problems, and mitigate against the negative effects of complexity.

Complexity in Manufacturing, Fig. 1

The spectrum of process complexity (EIMaraghy et al. 2012)

While researchers adopting the axiomatic complexity theory argue that engineers should constantly be working to reduce the complexity of engineered systems to make them more robust, others disagree with this approach and argue that the engineered system design should advocate complexity as a way to generate novelty and nurture creativity. Indeed, chaos and bifurcation theories have been proposed as means for qualitative, structural changes in mathematics and social sciences and creativity in engineering.

Sources of Complexity

Modern complex products or equipment may have many thousands of parts and take hundreds of manufacturing and assembly steps to be produced. Most complex products and equipment now incorporate not only mechanical and electrical components but also software, control modules, and human-machine interfaces. Some equipment are connected online to the World Wide Web and “the Internet of things” for real-time reporting and diagnostics. Although these additions have made equipment more versatile and dependable, significant complexity has been introduced to the product design.

The state of the art and the research literature in complexity are reviewed for the world of manufacturing from three perspectives: (i) complexity of engineering design and the product development process, (ii) complexity of manufacturing processes and systems, and (iii) complexity of the global supply chain and managing the entire business, as well as their intersections.

Perspectives on Complexity in Engineering

The research publications on complexity in engineering are divided into two groups: the first treats engineering complexity in the functional domain, e.g., the axiomatic design complexity theory, and the second treats complexity in the physical domain. The former (Suh 2005) promotes the idea that complexity must be defined in the functional domain as a measure of uncertainty in achieving a set of tasks defined by functional requirements. This complexity theory aims to reduce the complexity of any system by taking the following actions: (i) minimizing the number of dependencies, (ii) eliminating the time-independent real complexity and the time-independent imaginary complexity, and (iii) transforming a system with time-dependent combinatorial complexity into one with time-dependent periodic complexity by introducing functional periodicity and by reinitializing the system at the beginning of each period. This theory has been successfully applied in the design of engineered systems including in manufacturing.

Theory and Application

Engineering Complexity in the Functional Domain

The theory of complexity in the functional domain is based on the axiomatic design theory, which is useful when looking at design as the transformation from the functional requirements (FRs) to the design parameters (DPs) in the physical domain at the conceptual and embodiment design levels (EIMaraghy et al. 2012). In this complexity is defined as the measure of uncertainty in achieving the functional requirements of a system within their specified design range.

Kim (2004) illustrated the four causalities of complexity with respect to the design axioms (Fig. 2). Type I complexity is a result of heavy coupling of the functional requirements, which is a violation of the independence axiom. Time-independent complexity is a type II complexity and is a result of the information axiom violation, resulting in real complexity due to uncertainty. Time-independent imaginary complexity is a type III complexity, or “difficulty,” which is a result of lack of understanding about the system. Type IV complexity is due to non-equilibrium. If an engineered system is at an equilibrium state with its surroundings, it is going to be stable until its equilibrium state is disturbed by the application of external energy. Some engineered systems are not at an equilibrium state at all times. However, they are stable if they possess a functional periodicity. For instance, modern physics such as quantum mechanics and superstring theory assumes the existence of a functional periodicity in natural matter such as atoms, electrons, and subatomic particles.

Complexity in Manufacturing, Fig. 2

Complexity in the functional domain – causality-based complexity radar chart (Kim 2004)

Time-dependent combinatorial complexity is a combined result of type I, II, and IV complexities. Time-dependent periodic complexity is a smaller-scale complexity.

According to this complexity theory, complexity of any system can be reduced by taking the following actions: (1) minimize the number of functional requirements (FRs), (2) eliminate the time-independent real complexity, (3) eliminate the time-independent imaginary complexity, and (4) transform a system with time-dependent combinatorial complexity into a system with time-dependent periodic complexity by introducing functional periodicity and by reinitializing the system at the beginning of each period. The importance of the functional periodicity in reducing time-dependent combinatorial complexity is illustrated using several examples by Suh (2005). The main objective of this complexity theory is to reduce complexity while designing and operating engineering systems such as products and manufacturing systems so as to make the system robust, guarantee their long-term stability, make the system reliable, and minimize the cost.

Real Complexity

There are two kinds of time-independent complexity: real and imaginary. Time-independent real complexity is defined as a measure of uncertainty when the probability of achieving the FR is less than 1.0 because the system range does not lie inside the design range. The real complexity arises for many different reasons: (i) coupling of FRs, (ii) decrease in the allowable tolerance due to the presence of coupling terms, (iii) lack of robustness (increase in entropy), (vi) wrong choice of DPs, or (v) wrong decomposition of FRs and DPs. To eliminate the real complexity, we must come up with a design that satisfies the independence axiom in which the FRs are maintained independent and then make the design robust so that the system range is always in the design range.

In design and manufacturing of mechanical parts, it is commonly assumed that a system with a large number of parts is more complicated than that with smaller number of parts. This assumption is true only if the interface between the interconnected parts adds additional uncertainty in satisfying the FRs. However, the mere presence of many interconnected parts does not necessarily make a system more complex, if the interconnected parts do not add any additional uncertainty.

Imaginary Complexity

Imaginary complexity is defined as uncertainty that is not real uncertainty but arises because of the designer’s lack of knowledge and understanding of a specific design itself. Even when the design is a good design, consistent with both the independence axiom and the information axiom, imaginary uncertainty can exist when we are ignorant of what we have. An example is the combination lock which is easy to open once we know the sequence of numbers we have to activate it, but in the absence of the information on the combination, it would appear to be complex (Suh 2005).

The time-independent imaginary complexity and time-dependent periodic complexity can occur only when we must satisfy many FRs at the same time, whereas the time-independent real complexity and the time-dependent combinatorial complexity can exist regardless of the number of FRs that must be satisfied at the same time.

Time-Dependent Complexity

Time-dependent complexity occurs because future events affect the system in unpredictable ways. Often this results in a time-varying system range, i.e., the system range moves away from the design range (change in “information content” or entropy) as shown in Fig. 3. Ideally, the design range should be much below the system range to avoid this type of complexity.

Complexity in Manufacturing, Fig. 3

The spectrum of process complexity (Suh 2005)

There are two types of time-dependent complexity, which are defined as follows: (i) the periodic complexity is defined as the complexity that only exists in a finite time period, resulting in a finite and limited number of probable combinations, and (ii) the combinatorial complexity is defined as the complexity that increases as a function of time due to a continued expansion in the number of possible combinations with time, which may eventually lead to a chaotic state or a system failure. To reduce combinatorial complexity, we have to devise a means of preventing the system range from moving out of the design range (Suh 2005).

Application in Multidiscipline Complexity of Engineered Systems

Multidisciplinarity (Tomiyama et al. 2007) causes problems that were nonexisting when products were mono-disciplinary, because multidisciplinarity significantly increases not only the complexity of products but also that of the product development process. Complexity resulting from multidisciplinarity is different from other types of complexity such as computational complexity and uncertainty complexity, because it results from how our knowledge itself is formulated. Simpler design problems can be first decomposed into simpler mono-disciplinary subproblems with the classic divide-and-conquer strategy. These mono-disciplinary problems can be easily attacked and solutions for the entire problem can be synthesized. In contrast, multidisciplinary problems cannot be solved in a straightforward manner. When a design problem involves multiple domains, unless there is a uniform theory that can attack the problem as a whole, we are forced to use a set of theories, each of which is valid only in one domain. While in principle these theories are independent from each other, they can have intrinsic interactions for a variety of reasons. These interactions among theories indicate the existence of cross-disciplinary problems. The complexity involving multiple disciplines is explained by examining the structure of knowledge represented by relationships among theories. Tomiyama et al. (2007) identified “complexity by design” and “intrinsic complexity of multidisciplinarity.” Due to size (computational complexity) and multidisciplinarity, we apply the “divide-and-conquer” approach. However, due to very high “functional density,” the approach can fail because it is almost impossible to decompose the whole system (particularly with high functional density) into subsystems that have the least interactions among them. Often, systems designers are surprised by “unpredicted” interactions that are hard to solve, somewhat similar to the “imaginary complexity” in the functional complexity theory. This type of “no-fault” failure has been on the increase in many complex multidisciplinary products and deserves more attention from designers and industrial enterprises. A detailed example application in the design and operation of an AGV (automatic guided vehicle) system is discussed in EIMaraghy et al. (2012).

Engineering Complexity in the Physical and Operational Domains

Complexity in the physical and the operational domains is represented by models that capture the three elements of complexity: absolute quantity of information, diversity of information, and information content (effort). Figure 4 shows the classification of the various types of complexity in the physical domain (EIMaraghy et al. 2012).

Complexity in Manufacturing, Fig. 4

Classification of engineering design and manufacturing complexity in the physical domain (EIMaraghy et al. 2012)

EIMaraghy and Urbanic (2004) developed metrics and applications for product, process, and operational complexity. In these metrics, an important factor is considered: the human operators and their perception of the tasks’ complexity (cognitive complexity). The complexity of manufacturing systems, products, processes, and operations is related to the information to be processed in the system, including the physical and the cognitive aspects as illustrated in Fig. 5. Increasing system size and variety leads to more information and higher complexity.

Complexity in Manufacturing, Fig. 5

Physical and cognitive complexity (EIMaraghy and Urbanic 2004)

Another application using both functional and physical complexity theories was presented by Kim (1999). He found that in lean manufacturing, the system complexity, which is affected by increased product variety, is much less than in an equivalent mass production system. He proposed a series of system complexity metrics based on a complexity model developed using systems theory. These measures are (1) relationships between system components (number of flow paths, number of crossings in the flow paths, total travel distance by a part, and number of combinations of product and machine assignments) and (2) number of elementary system components. These metrics include a mix of structure (static time-independent) and operation (dynamic and time-dependent) factors. No suggestion regarding their relative importance or how they may be combined into one system complexity metrics was offered.

Engineering Complexity Using Heuristics and Indices

Kuzgunkaya and EIMaraghy (2006) introduced a metric to measure the structural complexity of manufacturing systems based on the complexity inherent in the structure of its components: machines, buffers, and Material Handling Systems (MHS). It includes quantity of information (using the entropy) and diversity of information. Classification and coding systems were originally developed for manufactured parts. However, equivalent coding and classification systems for manufacturing systems did not exist until the development of the structural classification and coding system (SCC) by EIMaraghy (2006) to classify the various types of equipment in a manufacturing system, such as machines, buffers, and transporters, as well as their layout. They used this classification code to assess the structural complexity of manufacturing systems configurations. The original equipment has been extended (EIMaraghy et al. 2010) to include the assembly-specific structural features of typical equipment used in products assembly systems. It accounts for the number, diversity, and information content within each class of the assembly system modules caused by the assembled products variety. The chain-type structure of the SCC coding scheme facilitated its extension (Fig. 6). The code characterizes the complexity of the various equipment within the assembly system such as machines, transporters, buffers, feeders, and handling equipment. Equipment controls, programming, operation, power source, and sensors are common fields.

Complexity in Manufacturing, Fig. 6

Structural classification and coding system (SCC) (EIMaraghy 2006)

Graph and Network Complexity Theories

Topological complexity is used by the graph and network theories. The complexity of such structures can be described by symmetry-based measures frequently applying the concept of entropy or by other measures including average- or normalized-edge complexity, subgraph count, overall connectivity, total walk count, and others based on adjacency and distance (EIMaraghy et al. 2012).

Computational and Information Complexity

Computational complexity is measured by the quantity of computational resources (e.g., time, storage, program, communication) which is required for solving a particular task. Here, the Turing machines are used as a fundamental tool for analyzing algorithms and combinatorial optimization problems. The complexity of a structure is defined in the Kolmogorov’s complexity (Li and Vitányi 2008) as its minimal description length, e.g., by a program on a universal Turing machine. Some other complexity measures, e.g., time complexity, space complexity, and, for distributed systems, communication complexity, are associated with algorithms (EIMaraghy et al. 2012).

Computational complexity comes from the number of elements (subsystems, components, or parts). This complexity becomes problematic, when the number of elements (N) grows, because the same algorithm that was able to solve a problem for a smaller N cannot solve one for a larger N′ in a reasonable time (or with using reasonable memory). For example, assume every element in a system has a direct relationship with all other elements. The computational complexity in terms of the number of relationships in this case is O (N (N − 1)) = O (N2), which is called polynomial complexity (O (Na), in which a is a positive constant). Practically, it is well known that computational complexity grows very quickly, when the complexity is O (aN) (exponential), O (N!) (factorial), or O (NN) (double exponential). These are called non-polynomial (NP) complexity as opposed to polynomial cases (P). Some NP complexity classes (NP-complete or NP-hard) are known to be difficult or even impossible to manage and solve. In manufacturing, NP-complete problems can be found, for instance, in production planning problems and logistics problems.

Cross-References

• Logistics

• Manufacturing System

• Production Planning

• System