Assessment of static complexity in design and

Int. J. Production Economics 169 (2015) 215–232

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Int. J. Production Economics journal homepage: www.elsevier.com/locate/ijpe

Assessment of static complexity in design and manufacturing of a product family and its impact on manufacturing performance Kijung Park a, Gül E. Okudan Kremer a,b,n a b

Department of Industrial and Manufacturing Engineering, The Pennsylvania State University, PA 16802, USA School of Engineering Design, The Pennsylvania State University, PA 16802, USA

art ic l e i nf o

a b s t r a c t

Article history: Received 10 September 2014 Accepted 30 July 2015 Available online 7 August 2015

As products and their manufacturing systems have become more sophisticated and complex, both industry and academia have widely discussed complexity in product design and manufacturing to understand its impact. However, the impact of complexity on manufacturing performance has not been clearly articulated in the previous empirical studies despite the widely expected negative relationship between them. As a response, this paper considers static complexity, which is due to inherent structural characteristics in product design and manufacturing, to elucidate the impact of design and manufacturing complexity on manufacturing performance. Metrics to properly capture design and manufacturing complexity in a product family are proposed and applied to a screwdriver product family case. Then, regression analysis is performed to identify the impact of complexity on manufacturing performance under different demand levels and manufacturing strategies. As a result, the negative impacts of design and manufacturing complexity on lead time and total production cost and their changes commensurate to the increase in demand are observed under the make-to-order policy. On the other hand, similar negative impacts are not statistically significant under the make-to-stock policy. These results indicate that static complexity negatively affects manufacturing performance only in the make-to-order system; and the inventory held of common parts in the make-to-stock system decreases the influence of static complexity on manufacturing performance. & 2015 Elsevier B.V. All rights reserved.

Keywords: Static complexity Design and manufacturing complexity Complexity metrics Product family Manufacturing performance

1. Introduction Nowadays the term “complexity” is frequently used in the manufacturing domain to represent modern manufacturing systems where many uncertainties (e.g., demand and supply variation) and various inter-related components in products and production are considered (Wu et al., 2007). Growing complexity is indeed inevitable for modern companies due to numerous market and business conditions causing an increase in uncertainty (Wiendahl and Scholtissek, 1994; Perona and Miragliotta, 2004). Wiendahl and Scholtissek (1994) observed that the individual departments within a company that used to be hierarchically or sequentially connected have been restructured to functionally integrate and decentralize individual processes to be flexible and responsive to customer demands. This restructuring trend should have reduced the complexity of an entire system, but it resulted in organizational complexity due to the integrated and interactive links. They further mentioned that the coordination between order-related (e.g., make-to-order) and n

Corresponding author at: The Pennsylvania State University, 213T Hammond Building, PA 16802, USA. Tel.: þ 1 814 863 1530. E-mail addresses: [email protected] (K. Park), [email protected] (G.E. Okudan Kremer). http://dx.doi.org/10.1016/j.ijpe.2015.07.036 0925-5273/& 2015 Elsevier B.V. All rights reserved.

customer-independent (e.g., make-to-stock) manufacturing strategies causes complexity in production. Complicating the matter further, most companies are now required to produce multiple product variants to satisfy diverse and frequently changing customer needs, which generally lead to manufacturing additional part variants and assemblies (Schleich et al., 2007). Under the internal and external factors that increase complexity in a manufacturing system, complexity has become an important issue a company must tackle. Despite this fact, there are many obstacles in understanding and measuring complexity. First of all, there is no widely accepted common definition of complexity due to the ambiguity that the term itself has (Klir, 1985; Flood, 1987; Perona and Miragliotta, 2004; Wu et al., 2007; Crespo-Varela et al., 2012). Not surprisingly, complexity concepts introduced in previous literature are also varied depending on the context of their applications (RodríguezToro et al., 2002; Crespo-Varela et al., 2012). Most existing complexity metrics are shown for simple cases, or are very specialized for a certain application area; it is very hard for general manufacturing companies to practically identify their current complexity levels at which they operate. In addition, complexity metrics have been developed mostly from a single perspective, either product design or manufacturing, and with no regard to the relation of complexity in product design and its manufacturing to manufacturing outcomes.

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K. Park, G.E. Okudan Kremer / Int. J. Production Economics 169 (2015) 215–232

Complexity in product designs and manufacturing systems has been investigated to demonstrate its negative impact on manufacturing performance: productivity (Stalk, 1988; MacDuffie et al., 1996; Guimaraes et al., 1999), operational cost (Stalk, 1988; Guimaraes et al., 1999; Wu et al., 2007), profitability (Kekre and Srinivasan, 1990; George and Wilson, 2004), and quality (MacDuffie et al., 1996; Guimaraes et al., 1999). Although the negative impact of complexity on manufacturing performance seems to be expected from a managerial perspective, dynamics between complexity and manufacturing performance under various manufacturing conditions has not been clearly articulated in the literature. For example, MacDuffie et al. (1996) employed different complexity measures associated with products and production systems to statistically justify the negative impact of complexity on manufacturing performance, but not all measures show statistically significant results for the impact of complexity. This paper focuses on static complexity, occurring from the structural configuration of a system, from the perspectives of both product design and manufacturing and scrutinizes the impact of complexity on manufacturing performance under the change in manufacturing policies (make-to-order vs. make-to-stock) and the increase in demand level. This paper firstly proposes informationtheoretic metrics representing static complexity in product design and manufacturing to measure static complexity at a product family level. This is to reflect today's variant-rich manufacturing environments. Manufacturing different products with all different raw materials and subassemblies is a very rare case nowadays; most companies configure product platforms for product families to decrease complexity resulting from the increase in product variety (Ulrich and Eppinger, 2000; Simpson, 2004). Furthermore, analyzing complexity for product variants within the same product family is more appropriate than that for products from different product categories since the sources and changes of complexity can be easily tracked under the same environment. Also, complexity analysis based on each product family not only facilitates comparison of complexity among multiple product families but also informs complexity changes from a product family level to a product portfolio level. The complexity metrics are applied to a screwdriver product family case, adopted from Park (2005) and Artar and Okudan (2008), to observe a relationship between complexity and constituents of a product order. The relationships between the manufacturing performance of the screwdriver product family and the complexity levels derived from the proposed design and

manufacturing complexity metrics are statistically analyzed to confirm the impact of complexity on manufacturing performance. The manufacturing performance variables in the case study are average order lead time and total production cost under a total of six manufacturing conditions, which are obtained from the combinations of manufacturing policies (make-to-order and make-tostock) and demand levels (80,000, 100,000, 120,000 units).

2. A summary of prior research on design and manufacturing complexity In this section, the literature addressing complexity in design and manufacturing contexts is reviewed. Complexity in operations management is generally defined as how the members of a system are varied and interacted (Choi and Krause, 2006). Complexity in industrial manufacturing can be found in both products themselves and their production, and the level of complexity in each of these varies depending on industry, product type, and operational strategies (Wiendahl and Scholtissek, 1994). Complexity for manufacturing systems can be categorized into two broad main areas corresponding to application or focus areas: design complexity (i.e., product design and engineering design process) and manufacturing complexity (i.e., manufacturing and assembly). Each focus area of complexity can be further characterized by its properties: static and dynamic complexity. It should be noted that uncertainty can be seen as a function or outcome of complexity; indeed, following definitions attest to this relationship. Static complexity is the time-independent complexity associated with the structure or physical configuration, and reflects uncertainty resulting from the structural characteristics of a system (Orfi et al., 2011; Park and Kremer, 2013). On the other hand, dynamic complexity is defined as uncertainty caused by the amount of state changes of a system and related to time-dependent activities increasing complexity and unexpected events in a system (Frizelle, 1996; Wu et al., 2007; Park and Kremer, 2013). This section discusses how these types of complexity have been defined beyond ambiguous or ad hoc definitions of complexity and quantified through different approaches. Table 1 shows the literature corresponding to each type of complexity. 2.1. Approaches to design complexity Complexity is a popular term used in many scientific domains such as computer science, biology, and physics (Mitchell, 2009); however, there is no one unique definition to describe complexity

Table 1 Categorization of Complexity Research in Design and Manufacturing. Complexity Focus Areas

Complexity Property Static Complexity

Design Satisfaction of Design Suh (1999), Braha and Maimon (1998), El-Haik and Yang (1999) Complexity Requirements Product Intra-Variety Pahl and Beitz (1996), Griffin (1997), Bashir and Thomson (1999), Gupta and Krishnan (1999), Kaski and Heikkila (2002), Ramdas (2003), Ameri et al. (2008), Crespo-Varela et al. (2012), Orfi et al. (2012), Jacobs (2013) Product Inter-Variety Collier (1981), Wacker and Treleven (1986), Johnson and Kirchain (2010), Roy et al. (2011), Closs et al. (2008), Jacobs and Swink (2011), Orfi et al. (2012), Jacobs (2013) Manufacturing Queuing Information Frizelle and Woodcock (1995) Complexity Process & Assembly Deshmukh et al. (1998), Fujimoto et al. (2003), Zhu et al. (2008), Hu et al. (2008) Information Scheduling Zhang (2012) Supply Chain Operations & Management

Vachon and Klassen (2002), Choi and Krause (2006), Bozarth et al. (2009), Serdarasan (2013)

Dynamic Complexity Suh (1999) El-Haik and Yang (1999) -

Frizelle and Woodcock (1995) Wu et al. (2007) Sivadasan et al. (2006), Zhang (2012) Vachon and Klassen (2002), Bozarth et al. (2009), Serdarasan (2013)


since each domain distinctively interprets complexity from their own perspectives. Despite these varied perspectives, complexity is commonly conceptualized to describe how many dense interactions and how much information a certain system has (Chu, 2011). Complexity can be a useful concept for a company to analyze product design problems; for example, exponentially increasing design details and functions in products that seem to be inevitable to meet diverse customer requirements are frequent concerns. From this point of view, many researchers have tried to apply complexity concepts that are discussed in science fields to product and engineering design contexts. Design complexity can be addressed through the Axiomatic Design framework with two essential design principles: (1) the independence axiom to maintain the independence of the functional requirements, and (2) the information axiom to minimize the information content. The information content in the information axiom is derived by a logarithmic function of the probability of satisfying functional requirements, and complexity is defined as a measure of uncertainty in achieving a set of specified functional requirements (Suh, 1999). Braha and Maimon (1998) divided design complexity into structural complexity and functional design complexity to define complexity in products and design process, depending on the types of the required information. El-Haik and Yang (1999) defined complexity as a quality of an object with various co-existing elements and their properties causing difficulties to understand the object. They derived two components of design complexity in the context of axiomatic design: (1) variability of design parameters, and (2) vulnerability related to the size of the design problem, the interdependency between design parameters, and the sensitivity of functional requirements from design parameter variation. Variety within a product (product intra-variety) is commonly employed to indicate complexity in product design and has been viewed from both structural and functional perspectives. Pahl and Beitz (1996) argued that simple designs dominate complex designs, and proposed qualitatively evaluating simplicity of product designs by considering product shapes (e.g., symmetry) and product design factors (e.g., the number of functions, components, and processes). Bashir and Thomson (1999) created a direct measure of design complexity through the functional tree of a product, which uses the number of functions at the level of decomposition. Griffin (1997) considered complexity as the number of functions in a product, and similarly Gupta and Krishnan (1999) and Ramdas (2003) represented complexity as the number of components in a product. Kaski and Heikkila (2002) regarded the number of physical modules and their interconnectedness as the main components of complexity in a product structure. Ameri et al. (2008) addressed three main perspectives of complexity in product design: (1) structural complexity, considering physical configuration and connectivity among components, (2) functional complexity, indicating the number and connectivity of functions, and (3) behavioral complexity, representing predictability and understandability of a product's behaviors. Crespo-Varela et al. (2012) described design complexity as the degree of difficulty to accomplish expected functional requirements and relationships between components in a product. Product variety in a product family, portfolio, or line (product inter-variety) is also considered as a major source of complexity under the variant-rich business environment that pursues increasing the number of product variants in a cost efficient way to boost profits. Most relevant prior literature has focused on commonality among product variants to identify the degree of product variety and complexity in a product family. Collier (1981) proposed the degree of commonality index (DCI) to evaluate average commonality between different end products. Wacker and Treleven (1986) improved DCI to various types of commonality

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indices (within-product, between-product, and total commonality indices) by changing the original cardinal measure of DCI to the relative measure with absolute boundary (0–1) of the proposed indices. Johnson and Kirchain (2010) stated that non-identical components can be regarded as common components if they share major forming processes and presented four commonality metrics for product families. Focusing on part variants, Roy et al. (2011) developed the design ratio to evaluate commonality of each part in a product family or a group of possible product variants. They claimed that the demand for individual product variants and each part variant used in them, indicating the importance of the variant to the market, should be considered along with benefits from commonality of part variants to determine appropriate product offerings. Closs et al. (2008) defined complexity as a state of processing difficulty resulting from a multiplicity of product architectural design elements and investigated important competencies of complexity at a product portfolio level. Jacobs and Swink (2011) also focused on product portfolio complexity from an architectural view and defined it as a design state reflected by the multiplicity, diversity, and interrelatedness of products within a product portfolio. A generalized approach which combines multiple dimensions of complexity has also emerged recently. Orfi et al. (2012) proposed a complexity measurement and evaluation framework in product family design through qualitative and quantitative measures representing five main dimensions of product complexity indicators (variety, functional index, structural index, design index, and production index). Jacobs (2013) categorized three dimensions of complexity (i.e., multiplicity, diversity, and interconnectedness) and developed the generalized complexity index (GCI) which aggregates these complexity dimensions to quantify complexity in a product, portfolio, or supply chain structure. Most design complexity approaches are based on a structural and static view of complexity and consider the number, diversity, and interrelationships of elements in product design (Choi and Krause, 2006; Closs et al., 2008; Jacobs and Swink, 2011; Jacobs, 2013). Although various approaches have been attempted to characterize design complexity, most studies have focused on complexity within a single product from a narrow view of design complexity or within a product portfolio from a broad view of design complexity. It has not been clearly addressed how the design complexity of each product within a product family, which is widely regarded as a basic unit of product groups in practice, can be practically captured through available product information such as the bill of materials. Commonality is an approach, which can describe complexity within a product family or across product families; however, prior research rarely converted commonality into the context of complexity. Existing commonality measures are mainly based on counting shared elements in product design, but the measurements based on counting complexity elements are not suitable to imply an increase in uncertainty associated with an increase in product variety within a product family. Information theory (Shannon, 2001) effectively links uncertainty and complexity, such that increasing uncertainty in a system makes a system more complex, and thereby more information is required to represent the state of the system (Sivadasan et al., 2006). Thus, an information-theoretic measure of the amount of information required to describe the state of variety in a product family can be helpful to define design complexity in a product family. 2.2. Approaches to manufacturing complexity Complexity in manufacturing can be seen similar to complexity occurring in product design. A manufacturing system is typically

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comprised of multiple manufacturing elements (machines) with different functions and various manufacturing processes. Therefore, a manufacturing system necessarily faces complexity, and it is easily affected by underlying complexity due to the manufacturing constraints and variable states of each machine. At this point, expanding the complexity issues in product design to a manufacturing context is important to properly handle all possible complexity problems arising from the early product design stage to the product manufacturing stage in a company. Manufacturing complexity can be mainly categorized into static and dynamic manufacturing complexity (Frizelle and Woodcock, 1995; Deshmukh et al., 1998): The static complexity is defined as a function of the structure of a manufacturing system, and the dynamic complexity is uncertainty caused by the dynamic properties of a manufacturing system over a time period. In other words, the static complexity is the uncertainty caused due to the structural characteristics of a manufacturing system, and the dynamic complexity is the uncertainty with respect to underlying risks or variability in the operational state of a manufacturing system's elements. A majority of research has discussed manufacturing complexity from an information-theoretic approach. Frizelle and Woodcock (1995) developed static and dynamic complexity measures based on the entropy in a manufacturing system that depends on the inventory queues of each machine at its operational states. Wu et al. (2007) employed the dynamic complexity index developed by Frizelle and Woodcock (1995) to identify a relationship between cost and complexity. Deshmukh et al. (1998) proposed a static complexity measure to quantify the information content existing in a manufacturing system through the processing times of a part mix for each operation at required machines. Fujimoto et al. (2003) proposed an entropy based measure of manufacturing complexity for a product family, considering product variety and its impact on assembly processes. Zhu et al. (2008) focused on manufacturing complexity affected by product variety in mixedmodel assembly lines and proposed the operator choice complexity measure which integrates both product variety and assembly process information to form an information entropy model. Similarly, Hu et al. (2008) developed a unified information theoretic measure of manufacturing complexity aggregating product variety and assembly process information for supply chains as well as assembly systems. Sivadasan et al. (2006) presented variation in information and material flows under both scheduled and non-scheduled states to measure dynamic manufacturing complexity of supplier-customer systems based on an entropy model. Zhang (2012) emulated an entropy model to define static and dynamic manufacturing complexity for job scheduling in a manufacturing system. Manufacturing complexity has been also attempted to be understood and conceptualized at the supply chain level by considering numerous products, processes, stakeholders, and their interactions in a supply chain. Vachon and Klassen (2002) addressed supply chain complexity from the properties of numerousness, interconnectivity, and systems unpredictability. They provided a conceptual framework that represents various sources of complexity in a supply chain with the combinations of two dimensions: (1) technological dimension divided into process/ product structure and infrastructure of management systems, (2) information processing dimension categorized into complicatedness and uncertainty, respectively referred to as the level of interactions and predictability. Focusing on organizational and managerial aspects in a supply chain, Choi and Krause (2006) conceptualized supply chain complexity into (1) the number of suppliers, (2) the degree of differentiation among suppliers, and (3) inter-relationships among suppliers. Bozarth et al. (2009) addressed supply chain complexity from the aspects of detail

complexity and dynamic complexity, respectively referred to as the distinct number of components or parts in a system and the unpredictability of a system resulting from the interconnectedness of the many parts in the system. With the two complexity aspects, they empirically investigated supply chain complexity at the manufacturing plant level from three major sources, which are (1) complexity occurring within a plant (internal manufacturing complexity) and (2) through the connections with its downstream and upstream partners (downstream and upstream complexity). From the existing literature related to supply chain complexity, Serdarasan (2013) addressed that supply chain complexity consists of three types: (1) static complexity occurring from the structure of a supply chain system, (2) dynamic complexity resulting from the operational behaviors of a supply chain system, and (3) decision making complexity involving both dynamic and static complexity perceived during the decision making process. Serdarasan (2013) further identified various complexity drivers found in the literature according to their origin (i.e., internal, supply/demand interface, external drivers). As reflected in the above provided definitions, multi-directional implications of complexity at the product, the process and the supply chain level have been acknowledged in the literature. More broadly, Fine's (1998) “three dimensional concurrent engineering, 3D –CE” encompassed product, process and supply chain domains, based on which he argued that each of these domains could be represented with an architecture and that matching these architectures is key to success. More specifically, Fixson (2005) suggested that many decisions to arrive at this “matching” across the product, process and supply chain domains “are constrained, or enabled by product characteristics such as the number and complexity of components, component commonality, or product modularity.” (pg. 347). A product family might distinctively affect manufacturing complexity; a product family sharing parts and manufacturing processes on a common product platform can serve to decrease complexity, and the variation on the common platform would become the source of complexity in the product family. From this point of view, the existing complexity measures for individual products and a total manufacturing system, which do not consider the manufacturing system of a product family, may not be applicable to properly capture the complexity of a product family. Although the studies investigating manufacturing complexity for a mixed-model assembly line with part-mix or product-mix might be a useful basis for analyzing complexity in a product familybased manufacturing system (Deshmukh et al., 1998; Fujimoto et al., 2003; Hu et al., 2008; Zhu et al., 2008), the methods included are hard to explicate the linkage between complexity and the variety of products, parts, and manufacturing processes occurring under the commonality of a product family. Also, the information theoretic approach towards complexity has been widely used to effectively quantify and characterize complexity beyond its abstract conceptualization (Sivadasan et al., 2006; Serdarasan, 2013), but a major concern can arise in the availability of a priori information, such as the probability of a system state of interest, to employ information theoretic complexity measures in practice. Beyond theoretical approaches, simpler and more straightforward metrics for design and manufacturing complexity are needed for practical use in company settings. 2.3. Relationship between complexity and manufacturing performance With the efforts to define and quantify complexity in product design and manufacturing, the impact of complexity has been also studied to prove its relationship to performance. Stalk (1988) claimed that a decrease in product variety leads to higher


productivity and lower costs based on empirical evidence. Fagade et al. (1998) reported that increasing complexity decreases the probability of successful product development through observations on empirical cases. George and Wilson (2004) described complexity as a factor detrimental to business profits and growth. Despite the widely held beliefs of the negative impact of complexity, in-depth empirical and experimental studies often failed to clearly adduce the disadvantages of increasing complexity. Kekre and Srinivasan (1990) observed that an increase in product variety is positively linked with market share benefits and profitability; and their empirical results did not support the negative relationship between broader product variety and production costs. MacDuffie et al. (1996) examined 70 international assembly plants in the automotive vehicle industry to identify the impact of product variety on total labor productivity and quality. With four different product complexity measures, they found that only the part complexity measure, which indicates part variation or commonality among vehicle models, consistently shows a statistically significant negative impact on productivity; and the other product complexity measures do not support the negative effect of complexity on manufacturing performance. Perona and Miragliotta (2004) studied 14 Italian companies in the household appliances industry to investigate how complexity can be related to performance of each sample group with three complexity control levers: partnership with suppliers, product modularization, and information systems for production planning. According to their empirical results, complexity only decreases in the group with partnerships despite the fact that all the groups with complexity levers show higher performance than the groups with no complexity levers. Wu et al. (2007) investigated the impact of operational complexity on two types of manufacturing systems: make-to-stock with low product volume, and make-to-order with high product volume. Their simulation results show that a negative relationship between operational cost and complexity are observed only in the make-to-stock system. The investigations to find the relationship between complexity and performance seem to be inconclusive, and it should be also addressed for product family-based manufacturing systems which handle various part and product variants and thereby are exposed to complexity. Moreover, previous works have not explored how complexity can affect the lead time of a product, from an order arrival to a final assembled product in a manufacturing system; instead, most previous studies focused on the impact of complexity on productivity and cost (Stalk, 1988; MacDuffie et al., 1996; Guimaraes et al., 1999; Randall and Ulrich, 2001; Perona and Miragliotta, 2004). Beyond the previous literature focusing on either design or manufacturing complexity, it is also needed to consider how both design and manufacturing complexity can impact on manufacturing performance.

manufacturing (Jiao et al., 2007; Pirmoradi and Wang, 2011). A product family or its manufacturing system, involving higher variety and therefore increasing levels of disorder and uncertainty, can be regarded to require a larger amount of information to describe its state. From this point of view, the informationtheoretic approach can be an effective basis for static design and manufacturing complexity measures for a product family. Information theory basically uses the concept of information content or entropy, which quantifies the amount of information required to represent the state of a system (Shannon, 2001). 3.1. Static design complexity Static design complexity in a product family is defined as a measure of uncertainty in realizing the commonality of a product family design structure. The design structure of a product family is determined by the degree of commonality sharing each component (e.g., part or module). A lower commonality in a product family adds more part-variety to the product family and thus causes an increase in the amount of information required to describe the state of the product family design structure. The amount of information indicating the variety embedded in each part variant can be quantified as information content. That is, the information content of each part variant in a product variant is defined in terms of the commonality of a part variant within a product family, which is given by: I ij ¼ log 2 C ij

Static design and manufacturing complexity measures for a product family are proposed in this section. Since static complexity is based on a function of the structure of a product design or a manufacturing system, it is useful to clearly identify the direct impact of complexity on manufacturing performance. The proposed complexity measures are based on the concept of commonality in products/processes,and information theory. A product family is designed to generate the product variety based on a common platform while responding to customization needs of consumers (Simpson, 2004). From this point of view, the degree of commonality is a major factor to determine the degree of complexity in a product family in relation to its design and

ð1Þ

where Cij is the probability (commonality) of sharing part variant i of product variant j within a product family. The total information content indicating the entire variety inherent to product variant j in a product family is the sum of the individual information content Iij of each part variant i configured in product variant j. Then, the measure of static design complexity (DC j ) in a product variant can be written as: X X DC j ¼ I ij ¼ ð log 2 C ij Þ ð2Þ i

i

where Cij is the probability (commonality) of sharing part variant i of product variant j within a product family. The use of 2as the base for the logarithm in the complexity measure is to make the unit of complexity bit (Frizelle and Woodcock, 1995; Deshmukh et al., 1998; Fujimoto et al., 2003; Hu et al., 2008; Zhang, 2012). Cij can be measured from either a posteriori or a priori way. If a product family has been already designed and constructed, the commonality of each part variant is measured from its structural information. A posteriori part commonality is easily computed by design ratio (Roy et al., 2011), which can be used to compute the commonality of each part variant in a product family: C ij ¼ nij =N

3. Development of static complexity measures for product family

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ð3Þ

where nij is the number of product variants that share part variant i of product variant j, N is the total number of product variants. The design ratio represents the design commonality of each part variant on the bill of materials (BOM) for all possible product variants. Thus, the design ratio of a part variant indicates the probability that the particular part variant is shared by product variants within the product family. If a part variant is used in all product variants, then the design ratio will be 1 indicating the perfect commonality. On the other hand, if a part variant is not applied in any product, the design ratio will be 0 showing no commonality. At the early design stage, before having a physical product family, Cij is estimated by the probability of satisfying a target range of commonality for a given part variant (a priori part commonality). When a given part variant is expected to be shared

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product variants; the process commonality represents how many different part variants used in a product variant are shared in each particular manufacturing process. Thus, the process commonality value reaches to 1, indicating the highest commonality, when all part variants for a product variant can be produced or assembled by one particular manufacturing process. The commonality of each process with respect to each product variant is obtained by: C pj ¼ npj =nj

Fig. 1. Example of Probability Distribution for Expected Commonality.

for product variants in a product family, its desired commonality in a product family is a critical design parameter at the early design stage. This commonality value of the part variant would have a specific range, within which the part variant is expected to have for an effective product family design. If the probability that a part variant is shared by a given number of product variants follows a certain probability mass function (pmf) (See Fig. 1), then the expected commonality of the part variant within the product family is determined as shown in Eq. (4). C ij ðl rn r uÞ ¼

u X

n pij ðnÞ=N

ð4Þ

n¼l

where pij(n) is the probability that part variant i of product variant j is shared by n product variants of all possible N product family members; u is the expected maximum number of product variants sharing part variant i (u r N); l is the expected minimum number of product variants sharing part variant i (0 ol ou). Once the commonality of each part variant is computed, the static design complexity of a product variant can be transformed to the static design complexity of a product order. This transition gives an opportunity to consider the static design complexity in a manufacturing system. The design complexity of a product order has two types: 1) product order consisting of a single product type, and (2) product order consisting of multiple product types. When an order consists of a single product, the static design complexity is computed in the same way for the static design complexity of a product variant. If a product order includes multiple product variants, all different part variants of the product variants in the order and their commonality values in the product family are considered to obtain the static design complexity of the order through Eq. (2). 3.2. Static manufacturing complexity Most existing manufacturing complexity measures are designed for the degree of complexity in an entire manufacturing system rather than the degree of complexity that each product variant in a product family exerts on a manufacturing system. Therefore, a new manufacturing complexity metric is proposed to measure the individual static manufacturing complexity levels of product variants. The proposed static manufacturing complexity measure is also based on commonality and information-theoretic approach to be in line with the properties of the design complexity measure developed in the previous section. Static manufacturing complexity in a product family is defined as a measure of uncertainty embedded in achieving the commonality of manufacturing process to produce a product family. The commonality considered in the proposed manufacturing complexity reflects the process variety that is required to manufacture

ð5Þ

where npj is the number of part variants in product variant j that pass process p, nj is the total number of part variants in product variant j. The amount of information required to describe the commonality of each process is expressed through information content. The information content to describe the commonality of each process for the product variant and the total information content of process variety inherent in each product variant are expressed by Eq. (6) and Eq. (7), respectively. I pj ¼ log 2 C pj

ð6Þ

where Cpj is the probability (commonality) of sharing process p for manufacturing product variant j. X X MC j ¼ I pj ¼ ð log 2 C pj Þ ð7Þ p

p

The total information content of process variety in each product variant is a measure of static manufacturing complexity ðMC j Þ. The static manufacturing complexity measure has the following implication. A manufacturing process, which is specialized only for a few part variants in a product variant, gives additional variety and uncertainty to a manufacturing system than a manufacturing process, which serves as a common process for many different types of part variants. Thus, a manufacturing system only consisting of the former type of manufacturing processes requires more information to describe its operational activities for product variants. Also, the higher number of manufacturing processes product variants need, the higher complexity the system involves because of an increase in the scale of the system. The static manufacturing complexity of product variants can be also transformed to that of product orders for analysis. The static manufacturing complexity of an order consisting of only one product variant can be regarded as that of product variants. If an order has multiple product variants, all part variants of the product variants in the order are considered as part variants of the same product. If the product variants in the same order type share the same part variant passing through the same manufacturing process, then the part variant passing through the process is counted only once for Eq. (5). Then, the static manufacturing complexity of the order is computed by Eq. (7).

4. Methodology The above proposed static design and manufacturing complexity measures are applied to a powered screwdriver product family case in order to investigate how complexity is related to cost and lead time in a product family-based manufacturing system. Furthermore, the investigation covers whether changes in the manufacturing environments (i.e., order demand level and manufacturing strategy) affect the relationship between complexity and manufacturing performance. The product family of five screwdriver types specified by Park (2005) is used within the case study, further details about this product family are introduced in the following section.


4.1. Case study for powered screwdriver product family Park (2005) introduced the product family of five different types of powered screwdrivers with sufficient details, including the bill of materials (BOMs) and costs for inventory management and manufacturing processes. The graphical representation of the screwdriver product family is provided in Fig. 2. Based on the information of the screwdriver product family, our previous work (Artar and Okudan, 2008) modeled a manufacturing system of the product family to analyze the impact of scheduling strategies, resources, demand, and product family size on the manufacturing performances represented by order lead time and the total production cost. Basically, the discrete event simulation model is based on the assumptions that there are incoming orders for 100,000 screwdrivers per year, and 300 working days to produce the screwdrivers. The inter-arrival time of screwdriver orders follows a normal distribution: (μ ¼ 120, σ ¼30) hours. The manufacturing system handles screwdriver orders of five types (P1,…, P5). The orders contain either any one of the five types of the screwdrivers, or a combination of any two of the five types of the screwdrivers to produce. Thus, the modeled screwdriver manufacturing system can accept 5 different single product orders, (P1,…, P5); or 10 different combination product orders, (P1&P2,…, P4&P5). The order quantity of each order type follows a normal distribution with an average of 333 screwdrivers and a variance of 33 for the single product order type and a normal distribution with an average of 166 screwdrivers and a variance of 16 for the multiple product order type. The simulation model

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handles demand level alternatives, including 80,000 and 120,000 products per year with a distribution of Normal (120, 40) hours for the inter-arrival time. When an order arrives at the manufacturing system, each screwdriver in the order is manufactured by assembling its required parts manufactured through in-house processes (i.e., injection, die-casting, powder metallurgy, and stamping) or purchased from outside. The processing time of each part variant on a machine depends on the dimension of the part variant, and random disturbances which can cause failure in production on the machines are not considered. The simulation of the manufacturing system mimics two different scheduling strategies: maketo-order and make-to-stock. i) Make-To-Order Model: this model reflects the make-to-order strategy, which allows orders to immediately enter the manufacturing system whenever they arrive at the system. In this model, one of 15 order types arrives randomly and with equal chance. Once an order type and its pre-defined manufacturing path are identified, an order entity is transformed to represent part entities required to manufacture each screwdriver product variant in the order. Then, all the generated parts are filtered according to their associated machines and placed in queues to be processed through the machines. After the machines process the parts, the part entities are sorted by their part types and located in a queue before they are assembled. When all parts required to produce a screwdriver are available in the queue, the make-to-order model assembles the parts of a screwdriver

Fig. 2. Powered Screwdriver Product Family and Structure Information (Park, 2005).

Fig. 3. Impact of Manufacturing Strategies.

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with pre-defined assembly time. Once a screwdriver in an order is produced, it waits until the other screwdriver is manufactured if the order consists of two screwdrivers. The order leaves system only when all screwdrivers in an order are completed. ii) Make-To-Stock Model: this model describes a manufacturing system under the make-to-stock strategy where the manufacturing system independently produces common parts regardless of order arrivals. Thus, the make-to-stock model continuously processes common parts in the screwdriver product family and stores them in inventory to use them whenever they are needed. The inventory system for the common parts is determined using (s, S) policy, and it is assumed that all parts of the screwdriver product variants can be pulled for each incoming order. The make-to-stock model basically follows the same manufacturing procedures as the make-to-order model, but it results in different average lead times and production costs for product orders due to the independent manufacturing activities and inventory system of the common parts. Fig. 3 shows the difference in the inventory cost, average lead time, and production cost of each order type in the make-to-order and make-to-stock model when the annual demand is 100,000 units. The make-to-stock model maintains more stable inventory level, less lead time, and higher production cost across the order types than the makeorder model due to its inventory holding strategy of common parts.

4.2. Calculation of proposed complexity metrics Based on the proposed complexity measures in Section 3, the static design and manufacturing complexity values for the screwdriver product family are obtained from the bill of materials and manufacturing processes of the product variants. The static design and manufacturing complexity measures are calculated from a product order basis as stated in Sections 3.1 and 3.2 to facilitate comparison between static complexity and manufacturing performance. The following steps are performed to deriveDC j and MC j , where j is the product order type. i) Calculation of Static Design Complexity: All part variants of all product variants on the bill of materials are listed in rows. The part variants of each part type are identified by the different dimensions of the part type (See Appendix A). All order types are listed in columns. There are 15 order types in the screwdriver product family case. After creating the part-order type matrix as seen in Appendix A, the membership of each part variant in the order types is checked. If the product order consisting of one of the five screwdriver variants requires particular part variants, 1 is assigned to the corresponding cells to describe the usage of the part variants. For the case of a multiple product order, the usage of each part variant for the order is derived by ‘OR’ logic between the columns of the single product orders that are associated with the product members of the multiple product order (See Tables 2). Since a single product order can be considered as a product variant, the sum of each row for all single product orders and the number of single product orders become nij and N. Then, the commonality of each part variant of the product variants in the product family C ij can be calculated through Eq. (3). Then, the information content of the part commonality is calculated by Eq. (1), and the calculated results are added to a column in the matrix. The static design complexity of each order type including both single and multiple order types is calculated by

Table 2 Example of Part-Order Type Matrix. Part Name Part Variant (i)

Product Order (j) P1 P2 P3 P4 P5 P1&P2

Length ¼63.5 mm Depth¼ 6.3 mm Bit Storage Length ¼73.4 mm Bit

1

1

1

1

1

1 OR 1¼ 1

0

0

1

0

0

0 OR 0¼ 0

Table 3 Example of Process-Order Type Matrix. # of Required Product Variants (npj)

Injection Powder Metallurgy Stamping Die-Casting

Product Order (j) P1

P2

P3

P4

P5

P1&P2

3 5 0 0

3 5 1 0

3 6 1 0

9 7 1 1

10 7 1 2

6 7 1 0

the sum of the products between each order type's column and the column of the information content. ii) Calculation of Static Manufacturing Complexity: The manufacturing process-order type matrix is created as shown in Appendix B. The number of part variants (npj ) required to pass each manufacturing process (p) for a product order (j) is counted in the matrix (See Table 3). Especially for a multiple product order, if the same part variant is used to produce different product variants in the order, the part variant is counted only once for npj . The part variants purchased from outside to satisfy the product orders are not considered in the matrix for this case study. Then, the process commonality (C pj ) is calculated by each element divided by the sum of all elements in the column where the element exists as expressed in Eq. (5). The process commonality values are converted to information content by Eq. (6), and the static manufacturing complexity of each order type (MC j ) becomes the sum of the information content in the column of the order type by Eq. (7). 4.3. Validation of proposed complexity metrics A structural scale, represented as the number of elements, is a basic factor of the static and structural aspect of complexity (Ameri et al., 2008; Jacobs, 2013). Thus, a proper static complexity measure should be able to reflect the structural scale associated with a related system. Since the proposed design and manufacturing complexity are focused on the structural aspect of complexity in design and manufacturing, the resultant design and manufacturing complexity values are expected to increase when the structural scale in design and manufacturing increases. To validate the proposed static complexity measures, correlation analysis is performed to identify whether the developed complexity metrics properly reflect structural scale changes in design and manufacturing with respect to product orders. The structural scale in design and manufacturing for this particular case study is considered as the number of part variants and manufacturing processes required for each product order. Then, correlation analysis is performed between the number of part variants and static design complexity (DC j ) and between the number of manufacturing processes and static manufacturing complexity (MC j ).


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Table 4 Manufacturing Performance, Complexity, and Structural Scale of Each Order Type. Product Order Type (j)

MTO (80,000)

MTO (100,000)

Lead Time (min)

Total Lead Cost ($) Time (min)





Total DCj Cost ($) (bit)

MCj (bit)

# of Part Variants

# of Processes

P1 P2 P3 P4 P5 P1&P2 P1&P3 P1&P4 P1&P5 P2&P3 P2&P4 P2&P5 P3&P4 P3&P5 P4&P5

321.4 193.0 261.4 558.2 634.0 333.9 228.7 517.8 398.3 247.1 563.2 442.7 382.3 447.3 544.1

26.5 23.3 27.7 53.8 64.8 28.5 24.3 43.1 48.4 26.5 47.5 43.3 38.2 44.3 55.7

34.1 26.6 30.6 73.3 96.5 35.6 30.0 53.3 67.4 36.1 70.0 74.8 70.8 43.2 82.6

61.6 58.7 45.6 81.8 103.1 42.7 70.2 65.6 103.7 57.1 110.8 80.0 92.3 74.9 111.3

86.1 89.7 89.1 87.8 91.6 89.3 87.3 86.7 92.5 90.4 91.3 88.6 88.8 91.0 88.6

87.8 89.1 91.0 89.4 93.0 89.6 89.5 88.0 94.7 90.0 93.8 91.4 89.9 90.6 91.4

88.9 91.9 92.8 89.8 95.3 91.8 89.7 90.0 99.4 92.6 94.3 90.7 93.9 94.4 93.6

2.1 5.6 5.8 10.7 10.2 6.0 6.1 11.6 10.9 6.0 10.8 10.1 10.9 10.2 10.4

17 22 24 41 42 32 35 55 57 29 61 61 64 64 48

2 3 3 4 4 3 3 4 4 3 4 4 4 4 4

500.9 262.8 322.4 867.4 1088.7 493.6 353.3 710.8 670.7 449.8 972.8 982.4 964.7 428.4 949.5

MTO (120,000)

1144.3 939.6 624.2 1004.8 1187.6 648.8 1227.0 944.8 1195.4 881.1 1715.1 1072.0 1347.9 961.9 1385.8

MTS (80,000)

146.3 180.6 145.7 96.3 125.8 198.3 137.4 112.2 143.5 186.2 194.7 107.8 128.0 149.2 91.7

Table 5 Pearson's Correlation between Static Complexity and Structural Scale Cases

Design Complexity & # of Part Manufacturing Complexity & # of Variants Processes

All Types Single Types Multiple Types

0.992 0.991

0.990 0.995

0.992

0.983

MTS (100,000)

190.2 167.0 186.9 132.1 153.6 205.5 190.7 144.6 185.5 175.8 249.1 167.0 152.9 140.3 147.5

MTS (120,000)

219.6 233.4 228.3 139.3 196.6 259.8 196.1 190.6 275.3 236.0 262.0 152.9 238.7 219.3 190.3

Complexity Structural Scale

26.2 27.3 33.9 56.9 58.6 49.5 56.4 81.5 84.5 43.5 83.8 84.8 90.8 91.8 71.5

grows in a manufacturing system, total production cost and order lead time also increase. ii) The different types of manufacturing systems can manage static complexity in different ways; therefore, the impact of static complexity on manufacturing performance will vary in response to implemented manufacturing strategies (i.e., maketo-stock vs. make-to-order). iii) An increase in order demand causes a more negative impact of static complexity on the manufacturing performance. 5. Results

4.4. Analysis of complexity on manufacturing performance From the computed design and manufacturing complexity values of the 15 order types, regression analysis is conducted to analyze the impacts of design and manufacturing complexity on the performance measures. This is addressed by finding the statistically significance and coefficient value of each complexity measure variable in each regression model. The manufacturing performance data in Table 4 is adopted from our simulation results (Artar and Okudan, 2008) for the same screwdriver product family. As seen in the table, the manufacturing performances (i.e., average order lead time and total production cost) per each order type are given according to the manufacturing strategies and demand quantities. There are six different lead times and total production costs, for the cases of the make-to-order (MTO) and the make-tostock (MTS) manufacturing systems matching the demand quantities of 80,000, 100,000, and 120,000 units. These manufacturing performance measures under different scenarios make it possible to find how the impacts of design and manufacturing complexity on the manufacturing performances change. In order to compare the impact potentially changing subject to order demand levels, the 80,000 and 120,000 casesare compared only; since the 80,000 and 120,000 demand conditions were simulated with the same variance of the inter-arrival order time, but the 100,000 demand case followed a smaller variance of the inter-arrival order time than these two demand levels. Using regression analyses, the following hypotheses are tested: i) Both static design and manufacturing complexity negatively affect manufacturing performance. That is, as complexity

Table 4 shows the computed complexity values. The static design and manufacturing complexity of each product order type are calculated by the proposed static complexity measures in Sections 3.1 and 3.2. Additionally, the number of part variants and processes with respect to each product order type are also specified in Table 4 to provide the structural information. 5.1. Validation of static complexity measures The correlations between the static complexity and structural scale in static design and manufacturing are evaluated for three cases: (1) all 15 product order types, (2) 5 single product order types, and (3) 10 combinatorial orders of the multiple product order types (See Table 5). The correlation results show that the proposed design and manufacturing complexity measures are highly correlated with the structure scale of static design and manufacturing regardless of the order types. These results indicate that those measures are able to appropriately reflect the complexity of the screwdriver product family that is directly linked to the structural scale of its design and manufacturing system. Thus, the static design and manufacturing complexity measures based on information theory and commonality are also suitable to capture static complexity in design and manufacturing occurring from their scale. 5.2. Relationships between static complexity and manufacturing performance The single linear regression models between the static complexity measures and the manufacturing performances are built to

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explore the relationships between them. From the screwdriver product family case, six manufacturing performance results (i.e., total production cost and average order lead time) obtained under all combinations of the manufacturing strategies (i.e., make-toorder and make-to-stock) and the demand assumptions (80,000, 100,000, and 120,000 units) are used to represent the response values of each single linear regression model. Then, the static design and manufacturing complexity measures are separately considered as an independent variable in each single linear regression model. All data used to build each regression model are specified in Table 4. Additionally, Appendix C shows the multiple linear regression analyses considering both static and dynamic complexity on the manufacturing performances. 5.2.1. Make-to-order case In the case of the make-to-order system (See Table 6), the static design complexity is a significant linear predictor of the order lead time and the total production cost in all the scenarios at the 90% confidence level, and each regression model except the make-to-order lead time for the 120,000 demand case has the static design complexity as a significant linear predictor at the 95% confidence level. The positive coefficients of the statistically significant design complexity in all the regression models confirm the negative impact of the static design complexity on the manufacturing performances. This finding supports the hypothesis that static design complexity negatively affects manufacturing performance. The coefficient of the static design complexity for the order lead time and total production cost tends to increase under the make-to-order setting when the order demand increases from 80,000 to 120,000. This shows that the impact of the static design complexity rises as the order demand level increases. However, the single regression results show modest R2 values (ranging between 23.5% and 39.8%), indicating that a small portion of the variation in each manufacturing performance can be explained by the measured static design complexity. Therefore, it cannot be concluded that the manufacturing performances can be predicted from the static design complexity only. As we can be followed from the results in Table 6, all the single regression models with the static manufacturing complexity show higher R2 values than the regression models using the static design complexity except for the make-to-order lead time (120,000) case. The static manufacturing complexity is a significant linear predictor at the 95% confidence level in the regression models except for the make-toorder lead time (120,000) case. Notably, the coefficient of the static

manufacturing complexity in the regression models in Table 6 is all positive, supporting the initially stated assertion relevant to the negative impact of static manufacturing complexity on manufacturing performance. The statistically significant static manufacturing complexity coefficient in the single regressions for both the make-to-order manufacturing performances becomes larger as the demand increases from 80,000 units to 120,000 units. This fact supports that an increase in the demand quantities causes increases in the negative impact of the static manufacturing complexity on the manufacturing performances. 5.2.2. Make-to-stock case None of the regression models in the make-to-stock case seems to be suitable to predict the manufacturing performances (See Table 7); in all the scenarios, the R2 values are less than 30%. In addition, the coefficient values of the static design and manufacturing complexity are not statistically significant at the 95% confidence level for all the manufacturing performances. Thus, the impacts of the static design and manufacturing complexity are not certainly identified from the coefficient values. At the 90% confidence level, several regression models have a significant coefficient, but the consistent negative impact of static complexity cannot be confirmed from those coefficients. For example, the negative coefficient of the static manufacturing complexity for the regression model of the make-to-stock lead time (demand ¼ 80,000 units) can be inferred that the manufacturing complexity positively affects the make-to-stock lead time; the lead time decreases when both design and manufacturing complexity increase. This result is in contrast with the consistent negative impacts of static design and manufacturing complexity on the manufacturing performances under the make-to-order case. Overall, it seems that neither the static design and nor manufacturing complexity can explain the make-to-stock manufacturing performances. The Post Hoc Power (PHP) is also calculated for each regression model. G*Power 3.1 (Faul et al., 2009), the power analysis package, was used for the calculation of PHP as shown below. As seen in the results from Tables 8 and 9, the regression models under make-toorder achieve enough powers (4 0.8, except for the order lead time at 120,000 demand case), but the regression models under make-to-stock fail to achieve such strong power. Thus, the power analysis confirms the p-value analysis, and the manufacturing performances under make-to-stock cannot be explained by static design and manufacturing complexity.

Table 6 Regression Results under Make-To-Order. x ¼Design Complexity

Make to Order Lead Time (80,000)



Make to Order Total Cost (80,000)


MTO Total Cost (120,000)

1. Regression Equation 2. R-sq 3. Basic Test -Test for β0 (Intercept) -Test for β1 (Slope)

y¼ 189 þ3.44x

y¼ 217þ 7.19x

y¼ 716þ 5.89x

y¼ 19.3 þ0.33x

y¼19.1 þ0.57x

y ¼38.3 þ 0.62x

33.0%

34.6%

23.5%

33.4%

34.3%

39.8%

t¼ 2.08 p ¼0.058 t¼ 2.53 nn p ¼0.025 Make to Order Lead Time (80,000) y¼ 95.8 þ36.4x

t¼ 1.19 p ¼0.256 t¼ 2.62 p ¼0.021nn Make to Order Lead Time (100,000) y¼ 75þ 69.8x

t¼ 3.65 p ¼0.003nn t¼ 2.00 p ¼0.067n Make to Order Lead Time (120,000) y¼ 741þ 40.6x

t ¼2.27 p ¼ 0.041nn t ¼2.55 p ¼ 0.024nn Make to Order Total Cost (80,000) y¼ 9.11þ 3.60x

t¼ 1.31 p ¼0.215 t¼ 2.61 p ¼0.022nn Make to Order Total Cost (100,000) y¼4.0 þ6.01x

t ¼2.72 p ¼ 0.018nn t ¼2.93 p ¼ 0.012nn MTO Total Cost (120,000) y ¼30.4 þ 5.53x

57.9%

51.3%

17.5%

64.1%

59.4%

49.5%

t¼ 1.24 p ¼0.236 t¼ 4.22 p ¼0.001nn

t¼ 0.44 p ¼0.666 t¼ 3.70 p ¼0.003nn

t¼ 3.39 p ¼0.005nn t¼ 1.66 p ¼0.120

t ¼1.36 p ¼ 0.196 t ¼4.82 p ¼ 0.000nn

t¼ 0.32 p ¼0.752 t¼ 4.36 p ¼0.001nn

t ¼2.19 p ¼ 0.047nn t ¼3.57 p ¼ 0.003nn

x ¼Manufacturing Complexity 1. Regression Equation 2. R-sq 3. Basic Test -Test for β0 (Intercept) -Test for β1 (Slope)

α ¼0.05nn, 0.1n


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Table 7 Regression Results under Make-To-Stock x ¼ Design Complexity

Make to Stock Lead Time (80,000)



Make to Stock Total Cost (80,000)



1. Regression Equation 2. R-sq 3. Basic Test -Test for β0 (Intercept) -Test for β1 (Slope)

y¼ 173–0.49x

y¼186–0.22x

y¼ 220–0.07x

y¼ 87.8 þ 0.02x

y¼ 88.2 þ0.04x

y¼89.4 þ 0.05x

10.7%

2.7%

0.2%

8.5%

19.5%

18.4%

t ¼6.68 p ¼ 0.000nn t ¼ 1.25 p ¼ 0.234 Make to Stock Lead Time (80,000) y¼ 190–5.56x

t¼ 7.81 p¼ 0.000nn t¼ 0.60 p¼ 0.557 Make to Stock Lead Time (100,000) y¼203–3.63x

t ¼7.16 p ¼0.000nn t ¼ 0.15 p ¼0.884 Make to Stock Lead Time (120,000) y¼ 240–2.88x

t¼ 62.02 p ¼0.000nn t¼ 1.10 p ¼0.291 Make to Stock Total Cost (80,000) y¼ 87.4 þ 0.22x

t¼ 61.92 p ¼0.000nn t¼ 1.77 p ¼0.099n Make to Stock Total Cost (100,000) y¼ 87.8 þ 0.34x

t¼ 46.39 p¼ 0.000nn t¼ 1.71 p¼ 0.110 Make to Stock Total Cost (120,000) y¼89.0 þ 0.42x

22%

12.1%

4.7%

11.8%

23.8%

20.2%

t ¼7.32 p ¼ 0.000nn t ¼ 1.91 p ¼ 0.078n

t¼ 8.38 p¼ 0.000nn t¼ 1.34 p¼ 0.204

t ¼7.46 p ¼0.000nn t ¼ 0.80 p ¼0.438

t¼ 58.68 p ¼0.000nn t¼ 1.32 p ¼0.209

t¼ 59.07 p ¼0.000nn t¼ 2.01 p ¼0.065n

t¼ 42.85 p¼ 0.000nn t¼ 1.81 n p¼ 0.093

x ¼ Manufacturing Complexity 1. Regression Equation 2. R-sq 3. Basic Test -Test for β0 (Intercept) -Test for β1 (Slope)

α ¼0.05nn, 0.1n

Table 8 Achieved Power (PHP) Values of Regression Models under Make-To-Order. DC¼ Design Complexity Make to Order Lead MC¼Manufacturing Complexity Time (80,000)



Make to Order Total Make to Order Total Cost (80,000) Cost (100,000)

Achieved Power for DC (1-β error probability) Achieved Power for MC (1-β error probability)

P¼ 0.82

P¼ 0.84

P ¼0.65

P¼ 0.84

P ¼0.84

P ¼0.91

P¼ 0.99

P¼ 0.98

P ¼0.52

P¼ 0.99

P ¼0.99

P ¼0.98

6. Discussion & conclusions In this paper, static complexity measures for both design and manufacturing complexity were proposed based on the commonality and information-theoretic approaches. Furthermore, the complexity measures were applied to a screwdriver product family case to show how a product family's degree of static complexity can be measured from both design and manufacturing perspectives by employing available resources (i.e., the bill of materials and manufacturing processes). The correlation results between the static complexity measures and the structural scale of the product family system confirmed that the proposed measures focusing on structural variety also properly reflect structural scale, which is the basic property of static complexity. Then, a series of regression analyses was conducted to identify the impacts of the static design and manufacturing complexity on the manufacturing performance measures (i.e., leadtime, total production cost) of the screwdriver product family manufacturing system under different manufacturing conditions of the demand (i.e., 80,000 units, 100,000 units, 120,000 units) and the manufacturing strategy (i.e., make-to-order, make-to-stock). From the regression results, it is observed that the impacts of the static design and manufacturing complexity on the lead-time and total production cost were consistently negative under the make-to-order system; and such consistent statically significant results were not obtained in the make-to-stock system. The statistically insignificant impacts of the static design and manufacturing complexity in the make-to-stock case could be explained by the effect of inventory in the make-to-stock system. The make-to-stock system independently manufactures the common parts of the screwdriver products regardless of their order arrivals and stocks them in the inventory to use whenever they are needed. Thus, the make-to-stock system can offset the impact of the static design and manufacturing complexity inherent in incoming orders and thereby leads to the distinct manufacturing


performances due to the reduced lead time and additional cost resulting from the inventory management. That is, the characteristics of the make-to-stock would make the system involve a much smaller scale of the impact of the static design and manufacturing complexity than the make-to-order system has. The statistically significant coefficients of the static design and manufacturing complexity in the single regression models of the make-to-order scenario become greater as the order demand increases, supporting that an increase in the demand causes increasing the negative impacts of the static design and manufacturing complexity on the manufacturing performances in the make-to-order system. However, our power analysis presented in Table 9 shows the insufficiency of achieved power to make conclusive interpretations for the make-to-stock scenario. In summary, the negative impacts of the static design and manufacturing complexity on the lead time and total production cost and their worsened impacts according to the increase in the demand are clearly identified in the make-to-order system. However, such an obvious relationship was not observed in the make-to-stock system. This result contradicts with the experimental results observed by Wu et al. (2007). They examined the relationship between operational costs and operational complexity by comparing the two types of supply chain systems: (1) the make-to-stock with low product variety but high volume, and (2) the make-to-order with high variety but low volume. They applied the operational (dynamic) complexity index developed by Frizelle and Woodcock (1995) to those two cases and concluded that the operational complexity index is only associated with the operational costs in the make-to-stock case. The different results from this paper and Wu et al. (2007)'s paper seem to come from the different perspective of complexity. The design and manufacturing complexity metrics employed in this paper reflect the static aspects of complexity caused by the structure and configuration of product design and manufacturing under scheduled manufacturing environment, but the operational

226


Table 9 Achieved Power (PHP) Values of Regression Models under Make-To-Stock DC ¼Design Complexity MC¼ Manufacturing Complexity


Achieved Power for DC (1-β error P¼ 0.36 probability) Achieved Power for MC (1-β P¼ 0.62 error probability)



Make to Stock Total Make to Stock Total Cost (80,000) Cost (100,000)


P ¼0.17

P¼ 0.10

P¼ 0.25

P ¼0.61

P¼ 0.53

P ¼0.10

P¼ 0.21

P¼ 0.38

P ¼0.67

P¼ 0.58

Fig. 5. Expected Complexity Dynamics in Flexible Manufacturing.

Fig. 4. Impact of Static and Dynamic Manufacturing Complexity in the Case Study.

complexity in Wu et al. (2007) considers the uncertainties occurring from dynamic and unscheduled state changes (e.g., breakdown of machines, the queue length of a machines representing the stock of inventory). Consequently, the complexity levels in the manufacturing system scenarios where the operational uncertainties are eliminated show zero in Wu et al. (2007). Therefore, Wu et al. (2007)'s results might be due to the fact that the operational complexity index is not designed to capture static complexity inherent in products and their manufacturing processes. Thus, the impact of the operational complexity is not clearly observed in the make-to-order manufacturing system which has more stable and static environment than the defect-prone and make-to-stock system. In contrast to Wu et al. (2007)'s work, no clear impacts of the static design and manufacturing complexity on the manufacturing performances under the make-to-stock condition could be inferred; there are several reasons for this. First, the make-to-stock system for the screwdriver product family, which consistently produces common parts, would have lessened the effects of the inherent static design and manufacturing complexity. Regardless of the static design and manufacturing complexity hold in the product variants of orders, any product order in the make-to-stock system can freely use common components in the inventory without additional lead time and production cost affected by the static complexity. Second, the insignificant negative impact of the static complexity in the make-tostock system might not be true as the complexity existing in the make-to-stock system could have been captured by dynamic complexity measures. These statements are supported by changes in the impact of manufacturing complexity according to the manufacturing strategies of the screwdriver manufacturing system (See Fig. 4.). The impact of dynamic manufacturing complexity in the screwdriver product family case may be indirectly estimated by the resultant inventory costs since dynamic complexity reflecting the queuing status of a manufacturing system affects inventory costs (Wu et al., 2007). From the inventory cost results of the screwdriver product family simulation models (Artar and Okudan, 2008), the impacts of dynamic manufacturing complexity on the make-to-order

system and the make-to-stock system are estimated from their average total inventory cost of all order types for the demand case of 100,000 units. This result is compared with the cost impact of static manufacturing complexity on the make-to-order system and the make-to-stock system, which can be inferred from the coefficients of the single regression models of the total production cost on the static manufacturing complexity under the 100,000 demand in Tables 6 and 7. Fig. 4 suggests both static and dynamic complexity should be considered altogether for both make-to-order and maketo-stock cases to obtain conclusive results. The total complexity impact of a manufacturing system could be obtained from the aggregation of both static and dynamic complexity perspectives (See Fig. 5). The optimal point at which the impact of complexity is minimized might be observed by implementing a flexible manufacturing management, with appropriate transitions from the make-to-order to the make-to-stock of individual parts or products and vice versa. Although we have considered static design and manufacturing complexity across the variants of a product family, we readily acknowledge that similar investigation needs to be replicated where products are more diverse. Our proposed static complexity measures would be flexibly applied to product variants in multiple product families or product portfolio if the bill of materials and manufacturing processes for considered product variants can be aggregated for analysis. Also, the relationship between static and dynamic complexity under the flexible manufacturing management environment needs to be thoroughly investigated in future research. Finally, the impacts of design and manufacturing complexity on manufacturing performance should be further investigated with scenarios where a higher number of observations can be used to generated sufficient power for generalizable results, specifically for the make-to-stock case.

Acknowledgments The authors would like to acknowledge the support of Design Society and ICED 2013, which provided an opportunity to discuss and improve the preliminary work of this research (Park and Kremer, 2013).

Appendix A Calculation of static design complexity

Part Type

Part Name

Bit

Bit Bit Storage Housing Lower Housing

Screw

Lock

Snap Ring Side Cap Hinge Ring Long Screw Hand Cover Lock Outside Torque Inside Torque Roller

P1

P2

P3

P4

P5

P1&P2 P1&P3 P1&P4 P1&P5 P2&P3 P2&P4 P2&P5 P3&P4 P3&P5 P4&P5 Commonality Information (Ci) Content (Ii)

L ¼63.5 /D ¼6.3 L ¼73.4 L ¼231 L ¼229 L ¼244.6 L ¼148 L ¼172 L ¼231 L ¼229 L ¼244.6 L ¼148 L ¼172 L ¼14.9 / D ¼2.131 L ¼14.5 / D¼ 3.0 – – D ¼20 D ¼9.9 D ¼2.85 T ¼2 L ¼40 D ¼25.4 H ¼7.6 H ¼6 L ¼15.5

1 0 1 0 0 0 0 1 0 0 0 0 1

1 0 0 1 0 0 0 0 1 0 0 0 0

1 1 0 0 1 0 0 0 0 1 0 0 0

1 0 0 0 0 1 0 0 0 0 1 0 0

1 0 0 0 0 0 1 0 0 0 0 1 0

1 0 1 1 0 0 0 1 1 0 0 0 1

1 1 1 0 1 0 0 1 0 1 0 0 1

1 0 1 0 0 1 0 1 0 0 1 0 1

1 0 1 0 0 0 1 1 0 0 0 1 1

1 1 0 1 1 0 0 0 1 1 0 0 0

1 0 0 1 0 1 0 0 1 0 1 0 0

1 0 0 1 0 0 1 0 1 0 0 1 0

1 1 0 0 1 1 0 0 0 1 1 0 0

1 1 0 0 1 0 1 0 0 1 0 1 0

1 0 0 0 0 1 1 0 0 0 1 1 0

1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

0 2.32 2.32 2.32 2.32 2.32 2.32 2.32 2.32 2.32 2.32 2.32 2.32

0 0 0 0 0 0 0 1 0 0 0 0

1 0 0 0 0 0 0 0 1 0 0 0

1 0 0 0 0 0 0 0 0 1 0 0

0 1 0 1 1 1 0 0 0 0 1 1

0 0 1 1 1 1 1 0 0 0 1 1

1 0 0 0 0 0 0 1 1 0 0 0

1 0 0 0 0 0 0 1 0 1 0 0

0 1 0 1 1 1 0 1 0 0 1 1

0 0 1 1 1 1 1 1 0 0 1 1

1 0 0 0 0 0 0 0 1 1 0 0

1 1 0 1 1 1 0 0 1 0 1 1

1 0 1 1 1 1 1 0 1 0 1 1

1 1 0 1 1 1 0 0 0 1 1 1

1 0 1 1 1 1 1 0 0 1 1 1

0 1 1 1 1 1 1 0 0 0 1 1

0.4 0.2 0.2 0.4 0.4 0.4 0.2 0.2 0.2 0.2 0.4 0.4

1.32 2.32 2.32 1.32 1.32 1.32 2.32 2.32 2.32 2.32 1.32 1.32

0 0 0 0 0 0

0 0 0 0 0 0

1 0 0 0 0 0

0 1 1 1 1 1

0 1 1 1 1 1

0 0 0 0 0 0

1 0 0 0 0 0

0 1 1 1 1 1

0 1 1 1 1 1

1 0 0 0 0 0

0 1 1 1 1 1

0 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1

0 1 1 1 1 1

0.2 0.4 0.4 0.4 0.4 0.4

2.32 1.32 1.32 1.32 1.32 1.32

0

0

0

1

1

0

0

1

1

0

1

1

1

1

1

0.4

1.32

0

0

0

1

1

0

0

1

1

0

1

1

1

1

1

0.4

1.32

0

0

0

1

1

0

0

1

1

0

1

1

1

1

1

0.4

1.32

H ¼6.3, D¼ 4 – Position Lock Handle L ¼28 Wedge L ¼25 Spring D ¼4.9 Position L ¼19.2 Gear Front Lower L ¼71 End Housing Upper L ¼71 Housing Snap Ring 2 legs ¼ 25


Upper Housing

Part Variant

227

Electric

Head

0

0

0

1

1

0

0

1

1

0

1

1

1

1

1

0.4

1.32

0 1 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0

0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1

0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 1 1

1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 0 0

1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 0 0

0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 1 0 1 1 1

0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1

1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 0

1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 0

0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1

1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1

1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1

1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1

1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1

1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 0 0

0.4 0.2 0.4 0.4 0.6 0.4 0.6 0.4 0.6 0.4 0.6 0.4 0.4 0.4 0.6 0.4 0.2 0.2 0.2 0.4 0.2 0.4 0.4 0.4 0.4 0.4

1.32 2.32 1.32 1.32 0.74 1.32 0.74 1.32 0.74 1.32 0.74 1.32 1.32 1.32 0.74 1.32 2.32 2.32 2.32 1.32 2.32 1.32 1.32 1.32 1.32 1.32

1 0 0 1 0 0 0 1 0 0 0 1 0 0

0 1 0 0 1 0 0 0 1 1 0 1 0 0

0 1 0 0 1 0 0 0 1 1 0 0 1 0

0 0 1 0 0 1 0 1 0 0 0 1 0 1

0 0 1 0 0 0 1 0 1 0 1 1 0 0

1 1 0 1 1 0 0 1 1 1 0 1 0 0

1 1 0 1 1 0 0 1 1 1 0 1 1 0

1 0 1 1 0 1 0 1 0 0 0 1 0 1

1 0 1 1 0 0 1 1 1 0 1 1 0 0

0 1 0 0 1 0 0 0 1 1 0 1 1 0

0 1 1 0 1 1 0 1 1 1 0 1 0 1

0 1 1 0 1 0 1 0 1 1 1 1 0 0

0 1 1 0 1 1 0 1 1 1 0 1 1 1

0 1 1 0 1 0 1 0 1 1 1 1 1 0

0 0 1 0 0 1 1 1 1 0 1 1 0 1

0.2 0.4 0.4 0.2 0.4 0.2 0.2 0.4 0.6 0.4 0.2 0.8 0.2 0.2

2.32 1.32 1.32 2.32 1.32 2.32 2.32 1.32 0.74 1.32 2.32 0.32 2.32 2.32

0 0 0

0 0 0

0 0 0

1 1 1

1 1 1

0 0 0

0 0 0

1 1 1

1 1 1

0 0 0

1 1 1

1 1 1

1 1 1

1 1 1

1 1 1

0.4 0.4 0.4

1.32 1.32 1.32

0

0

0

1

1

0

0

1

1

0

1

1

1

1

1

0.4

1.32


Shaft

Gear L ¼62 Housing Housing Pin L ¼40 Ring Gear L ¼24, D ¼35.5 L ¼25, D¼30.5 L ¼20 Planetary L ¼20.2 / T ¼4 Arm L ¼44 Planetary D ¼11.8 D ¼14.6 Intermediate L ¼20.2 / T ¼4 L ¼25 Planetary D ¼11.8 D ¼14.6 Cover H ¼10.8, D ¼30 D ¼37 Motor H ¼10.9, D ¼8 Coupling D ¼5.6 Gear Train L ¼40.5 To L ¼12.7 L ¼11.6 D ¼6.9 Chunk L ¼55 L ¼5.3 D ¼10 Bushing D ¼16 Shaft – Spring – Washer Switch L ¼36.7 L ¼41.8 – Switch L ¼27 Button L ¼25.5 L ¼32 L ¼30 Battery 2.4v 3.6v Battery Cap L ¼20 L ¼45.6 Motor L ¼51 L ¼27.5 Charger – Inlet Wire L ¼10 Light – Head – Housing Head Middle –

228

Gear

Head Cap Electri Snap Ring Washer

– – – – # of Part Variants Design Complexity (DCj)

0 0 0 0 17

0 0 0 0 22

0 0 0 0 24

1 1 1 1 41

1 1 1 1 42

0 0 0 0 32

26.2 27.3 33.9 56.9 58.6 49.5

0 0 0 0 35

1 1 1 1 55

1 1 1 1 57

0 0 0 0 29

1 1 1 1 61

1 1 1 1 61

1 1 1 1 64

1 1 1 1 64

1 1 1 1 48

0.4 0.4 0.4 0.4

56.4

81.5

84.5

43.5

83.8

84.8

90.8

91.7

71.5

1.32 1.32 1.32 1.32

Appendix B

# of product variants passing (npj)

Product order (j) P1

Injection Powder Metallurgy Stamping Die-Casting nj (sum) # of required manufacturing processes Process Commonality (Cpj) Injection Powder Metallurgy Stamping Die-Casting Information Content (Ipj) Injection Powder Metallurgy Stamping Die-Casting Manufacturing Complexity (MCj)

P2

P3

3 3 3 5 5 6 0 1 1 0 0 0 8 9 10 2 3 3 Product order (j) P1 P2 P3 0.375 0.333 0.300 0.625 0.556 0.600 0.000 0.111 0.100 0.000 0.000 0.000 Product order (j) P1 P2 P3 1.42 1.58 1.74 0.68 0.85 0.74 0 3.17 3.32 0 0 0 2.09 5.60 5.80

P4

P5

P1& P2

P1& P3

P1& P4

P1& P5

P2& P3

P2& P4

P2& P5

P3& P4

P3& P5

P4& P5

9 7 1 1 18 4

10 7 1 2 20 4

6 7 1 0 14 3

6 8 1 0 15 3

12 12 1 1 26 4

13 12 1 2 28 4

5 7 1 0 13 3

12 12 2 1 27 4

13 12 2 2 29 4

12 13 2 1 28 4

13 13 2 2 30 4

12 7 1 2 22 4

P4 0.500 0.389 0.056 0.056

P5 0.500 0.350 0.050 0.100

P1& P2 0.429 0.500 0.071 0.000

P1& P3 0.400 0.533 0.067 0.000

P1& P4 0.462 0.462 0.038 0.038

P1& P5 0.464 0.429 0.036 0.071

P2& P3 0.385 0.538 0.077 0.000

P2& P4 0.444 0.444 0.074 0.037

P2& P5 0.448 0.414 0.069 0.069

P3& P4 0.429 0.464 0.071 0.036

P3& P5 0.433 0.433 0.067 0.067

P4& P5 0.545 0.318 0.045 0.091

P4 1.00 1.36 4.17 4.17 10.70

P5 1.00 1.51 4.32 3.32 10.16

P1& P2 1.22 1.00 3.81 0 6.03

P1& P3 1.32 0.91 3.91 0 6.14

P1& P4 1.12 1.12 4.70 4.70 11.63

P1& P5 1.11 1.22 4.81 3.81 10.94

P2& P3 1.38 0.89 3.70 0 5.97

P2& P4 1.17 1.17 3.75 4.75 10.85

P2& P5 1.16 1.27 3.86 3.86 10.15

P3& P4 1.22 1.11 3.81 4.81 10.94

P3& P5 1.21 1.21 3.91 3.91 10.23

P4& P5 0.87 1.65 4.46 3.46 10.45


Calculation of static manufacturing complexity

Appendix C Multiple regression analysis between complexity and manufacturing performance

229

Multiple regression models with both static design and manufacturing complexity are created to additionally observe how the manufacturing performances are affected by both static design and manufacturing complexity. From the multiple regression models in the make-to-order case (See Table C1), each R2 value becomes greater than the R2 values in the simple regression models using design or manufacturing complexity in the same scenarios. In the case of the 120,000 order demand, both the regression models for the lead time and total production cost have lower R2values

230

Table C1 Multiple Regression Results under Make-to-Order Make to Order Lead Time (80,000)





MTO Total Cost (120,000)

1. Regression Equation

y¼ 104–2.09x1 þ 50.9x2

y¼ 81–1.67x1 þ 81.4x2

y¼ 717 þ5.98x1–0.8x2

y¼ 10.2–0.27x1 þ 5.47x2

y¼ 5.3–0.329x1 þ8.29x2

2. R-sq 3. Basic Test Test for β0 (Intercept)

60.9%

51.8%

23.5%

69.8%

62.2%

y¼ 30 þ0.082x1 þ 4.96x2 49.7%

t ¼1.34 p ¼ 0.206 t ¼ 0.96 p ¼ 0.356 t ¼2.92 n p ¼ 0.013 n f ¼9.33 n p ¼ 0.004 n

t¼ 0.46 p ¼0.653 t¼ 0.34 p ¼0.741 t¼ 2.07 p ¼0.061 f¼ 6.44 n p ¼0.013 n

t ¼3.26 n p ¼ 0.007 n t ¼0.97 p ¼ 0.352 t ¼ 0.02 p ¼ 0.987 f ¼1.84 p ¼ 0.200

t¼ 1.58 p ¼0.140 t¼ 1.49 p ¼0.161 t¼ 3.80 n p ¼0.003 n f¼ 13.84 n p ¼0.001 n

t¼ 0.42 p ¼0.681 t¼ 0.94 p ¼0.365 t¼ 2.97 n p ¼0.012 n f¼ 9.86 n p ¼0.003 n

t¼ 2.08 p ¼0.060 t¼ 0.20 p ¼0.844 t¼ 1.53 p ¼0.152 f¼ 5.92 n p ¼0.016 n

Test for β1 Test for β2 Test for all β (Test for the Model)

α ¼0.05nn

Table C2 Multiple Regression Results under Make-to-Stock. x1 ¼ Design Complexity, x2 ¼Manufacturing Complexity







1. Regression Equation 2. R-sq 3. Basic Test Test for β0 (Intercept)

y¼ 188þ 0.48x1-8.90x2 24.6%

y¼201þ 0.73x1-8.68x2 19.7%

y¼ 236 þ 0.996x1-9.78x2 13.5%

y¼ 87.4-0.002x1 þ0.235x2 11.8%

y¼ 87.7 þ 0.006x1 þ 0.291x2 23.9%

y¼ 89þ 0.0184x1 þ 0.294x2 20.8%

t¼ 7.04 p ¼0.000nn t¼ 0.64 p ¼0.534 t¼ 1.48 p ¼0.164 f¼ 1.95 p ¼0.184

t¼ 8.26 p¼ 0.000nn t¼ 1.07 p¼ 0.306 t¼ 1.60 p¼ 0.137 f¼ 1.48 p¼ 0.267

t ¼7.36 p ¼ 0.000nn t ¼1.10 p ¼ 0.291 t ¼ 1.36 p ¼ 0.199 f ¼0.94 p ¼ 0.419

t¼ 56.05 p ¼0.000nn t¼ 0.05 p ¼0.962 t¼ 0.67 p ¼0.514 f¼ 0.81 p ¼0.469

t¼ 56.45 p ¼0.000nn t¼ 0.14 p ¼0.887 t¼ 0.84 p ¼0.420 f¼ 1.89 p ¼0.194

t¼ 41.05 p ¼0.000nn t¼ 0.30 p ¼0.767 t¼ 0.60 p ¼0.557 f¼ 1.58 p ¼0.247

Test for β1 Test for β2 Test for all β (Test for the Model)

α ¼0.05nn


x1¼Design Complexity, x2¼ Manufacturing Complexity


than the other demand cases. In all regression models, static design complexity turns out to be not a significant linear predictor at the 95% confidence level when it is added to the model with static manufacturing complexity. However, static manufacturing complexity is significant at the 90% confidence level in the maketo-order lead time (80,000, 100,000) and the make-to-order total production cost (80,000, 100,000). It can be inferred that the impact of static design complexity is negligible in comparison to the impact of static manufacturing complexity. The coefficients of static manufacturing complexity consistently show plus signs except in the make-to-order lead time (120,000) model, where static manufacturing complexity is not significant. These results indicate that the coefficients of the statistically significant static manufacturing complexity in the multiple regression models also corroborate the negative impact on the manufacturing performances in the make-to-order system. As seen in Table C2, the multiple regression models are not appropriate to predict the manufacturing performances in the make-to-stock manufacturing system. In all the cases, neither the entire models nor the static design and manufacturing complexity variables are significant at the confidence level of 95%; and the R2 values are very low. Similar to the multiple regressions for the make-to-order case, all the signs of the design complexity coefficients vary in the multiple regression models for the make-tostock case. Moreover, all the coefficients of static design and manufacturing complexity are not statistically significant at the 95% confidence level. Thus, the impact of complexity is not directly associated with the manufacturing performances in the make-tostock system.

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