Int J Adv Manuf Technol DOI 10.1007/s00170-015-7304-y
ORIGINAL ARTICLE
Assembly system synthesis using association rule discovery Hoda ElMaraghy 1 & Mohamed Kashkoush 1
Received: 12 February 2015 / Accepted: 11 May 2015 # Springer-Verlag London 2015
Abstract Assembly is the final process for product realization in which various parts, modules, and sub-assemblies are put together to build a product. Designing an assembly system typically involves many issues such as assembly equipment selection, assembly sequence planning, system layout, task assignments, and line balancing. Assembly system synthesis, specifically the choice of assembly resources/equipment, is examined in this paper. An association rule discovery model is employed to extract association relationships between existing and/or previous products and the systems used to assemble them. The extracted knowledge is used to synthesize assembly systems for new products that fall within the scope of their predecessors. The developed method is demonstrated using two examples from the automotive industry. System synthesis results that are consistent with the used assembly data instances are obtained in both examples. The presented systematic system synthesis method supports the utilization of existing legacy data in developing assembly systems for new product generations. This will lead to a significant reduction of time and effort needed to design assembly systems, particularly in applications that feature frequent design changes and updates, as in the automotive industry.
Keyword Assembly . Assembly system synthesis . Association rule discovery . Automotive industry
* Hoda ElMaraghy
[email protected] 1
Intelligent Manufacturing Systems (IMS) Centre, University of Windsor, 401 Sunset Avenue, Windsor, ON N9B 3P4, Canada
1 Introduction Assembly is the capstone of product development phases that accounts for 50 % or more of manufacturing costs [1]. Designing an assembly system involves several issues that the system designer has to address such as assembly equipment selection, assembly sequence planning, number of work stations, level of automation, system layout, tasks assignment, and line balancing. Although many system design aspects are supported by well-developed computer tools, a considerable portion of the design process requires iterations and expert judgment [2]. Significant amount of research has been carried out on each of the mentioned assembly system design aspects at different levels of detail. Webbink and Hu [3] considered the problem of finding the assembly system configuration and assigning of tasks to work stations. They presented an automated method that generates all sets of system configurations and assembly sequences. Feasible solutions, consisting of a matched element from each set, can be obtained accordingly. Boubekri and Nagaraj [4] considered the selection of feasible assembly methods along with the selection of technologies needed to assemble a given product. They developed an integrated methodology that accounts for the following factors: annual volume of the product, number of variants of the product, product life, and number of components in the product. Ozdemir and Ayag [5] considered the problem of allocating various work elements to different work stations, known as assembly line balancing, as well as the proper equipment selection in cases where multiple choices exist. A branch and bound algorithm was used to determine a list of alternatives for the assembly line balancing problem and then generated alternatives are assessed using the AHP (analytic hierarchy process) method to find the best alternative with the least equipment cost. Wang and Liu [6] considered the problem
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of finding the sequence of assembly operations (assembly sequence planning). They developed a search algorithm that searches for the best feasible assembly sequence according to some assembly feasibility constraints (e.g., geometric feasibility) and optimization criteria (e.g., changes of assembly tools). Seleim and ElMaraghy [7] used max-plus algebra [8] to model assembly lines in the form of linear state-space-like equations that could be used for analyzing different assembly system configurations and assessing several what-if scenarios. Hanafy [9] developed a novel model for concurrent design of product families and their corresponding assembly systems where a global product families and platforms formation mathematical model which fully integrates assembly task assignments, assembly sequence, and assembly cost was developed. Samy and ElMaraghy [10] introduced and implemented a method for defining and mapping products and their corresponding assembly systems in order to help system designers develop less complex assembly system. Bukchin et al. [11] addressed the design of an assembly system facility involving multiple assembly lines of different layouts in which it is required to find the minimum area of the facility and to maximize the efficiency of the material handling system using a mixed integer programming. A recent comprehensive survey for the state of the art research on the design and operations of assembly systems with particular focus on product variety was presented by Hu et al. [12]. This research focuses on assembly system synthesis, specifically the problem concerned with the selection of the set of assembly system components (i.e., resources or equipment) needed to assemble a given product. The resulting initial system synthesis would subsequently be analyzed, configured, and fine tuned by the system designer. Synthesizing assembly systems for new products is done in industry based on experience which does not guarantee optimality, and the research on this topic remains limited. Making use of available historical assembly data in planning for new products saves a lot of development time and effort and results in more responsive and cost-effective product/system development. Knowledge discovery models and particularly association rules discovery techniques were used successfully in many industrial applications [13–23]. For instance, in quality control, Da Cunha et al. [13] studied the association between the assembly sequence and the likelihood of having defective products and utilized it in sequencing of modules and forming product families which minimizes the cost of production faults. In product design, Song and Kusiak [16] developed a method for optimizing product configuration based on extracted association rules among the product features provided to the customers. In manufacturing process control, Sodyan et al. [24] introduced an algorithm for manufacturing process control based on association relationships between the process input and output parameters and demonstrated it through an
industrial example of spray-forming process. For the facility layout problem, Altuntas and Selim [25] proposed five weighted association rule-based data mining algorithms to address the facility layout problem, which is concerned with the optimal arrangement of a given number of system components (i.e., machines) within a given area. Demand, part handling factor and efficiency of material handling equipment were used as weighting criteria. In this paper, a mathematical model is used to synthesize assembly system components for a new product through the discovery of implicit knowledge accumulated over time in the assembly facility records. Given the data related to a set of current and/or legacy products and their corresponding assembly systems, an Integer Programming (IP) association rule discovery model [26], recently developed by the authors, is used to reveal association rules between assembly system components and product features. The discovered rules are utilized in synthesizing the assembly system components required for future products containing new combinations of features. The assembly system synthesis problem studied in this research has been recently addressed by few researchers. Using classical statistical-based association rule discovery algorithms, Jiao et al. [27] presented a process planning decision support tool to correlate product features and process elements based on historical data and applied it to a case study of vibration motors used in cell phones. AlGeddawy and ElMaraghy [28] modeled the co-evolution of products and their corresponding assembly systems based on historical data using cladistic analysis which is a hierarchical classification method commonly used in biology [29] and demonstrated the developed model using a case study of automotive belt tensioners/idlers. The association rule discovery model employed in this paper offers an alternative Integer Programming-based method requiring significantly less implementation and rule extraction and filtering effort than those found in literature. The assembly system synthesis application presented in this research is tested using two examples from the automotive industry: the belt tensioners/idlers case study introduced by AlGeddawy and ElMaraghy [28] as well as a new case study for automobile engine block assembly.
2 Scope The association rule discovery model [26] employed in this research is a general model that can extract association relationships between any two corresponding groups of data (e.g., input and output parameters of a given manufacturing process). The model was used before by the authors for discovering association relationships between manufacturing system capabilities (manufacturing domain) and product features
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(product domain). In assembly systems, various types of system components such as material handling equipment (e.g., automated-guided vehicle (AGV) or gantry transportation systems) or robot (e.g., SCARA or articulated robots) are used to represent different assembly systems. For the products, the part name or code is used to represent different products (e.g., frame variant x or spring variant y). Different assembly applications most likely have different forms of representation as will be demonstrated in the examples in Section 4. The problem studied in this research could be defined as follows: for a given number of old and/or existing assembly data instances where each instance includes data about a given product (P) and the corresponding assembly system (AS) used to produce it, it is required to find association rules associating assembly system components with product feature and vice versa. As illustrated in Fig. 1, it is required to build a mapping between the product or design domain, in terms of product
features (F), and the assembly domain, in terms of assembly system components (C). The term “data instances” mentioned in the problem definition is not necessarily limited to the same assembly facility; data from multiple facilities that produce the same type of products could be employed as along as a consistent description and encoding of products and assembly systems is maintained. It should be pointed out that having an association between a certain product feature F and an assembly system component C does not mean that C is capable by itself of assembling F. For example, if an association relationship is discovered between a certain type of fixtures and a certain type of bearings, this absolutely does not mean that such a fixture is the only piece of equipment required to assemble that bearing. In fact, the applicability and significance of association relationships are best realized in combination. Thus, when a new combination of product features are considered, the
Product or Design Domain
Assembly System Domain
P2
AS 3
P3 F5
P6
F10 F3
C16
AS 2
F14
F8
C4
P1
F12
C2 C14
F4
F9
AS 6
C3
AS 1 C11
C12
C6
C9
C13
C5
F1 F2
F13
F11 F7
F15
C1
P5
C7
C8
C10
AS 5
F6
P4
C15
AS 4
F5
C16 C3
F10
C4 C2
F12 F9
C6
C11 F13
F3
C14
C5
F4
F8
C12 C15
F14 F1 F11
F2 F7
F15
C1
C13 C9
C10 C8 C7
F6
Fig. 1 Schematic illustration of association rule discovery (reproduced from [26])
Int J Adv Manuf Technol
corresponding assembly system that should be capable of producing that product is synthesized by combining the system components associated with the features of the new product.
Table 2
Association matrix obtainable by the IP model Product feature (F)
Sys. comp. (C)
C1 C2 C3 C4 C5 C6
3 Association rule discovery IP model This section summarizes the utilized association rule discovery model [26] and illustrates its application in the assembly context. It is an Integer Programming (IP) model consisting of three main sets of constraints. The model is inspired by a classical problem in computer science and complexity theory known as the set covering problem [30]. Given a number of tasks to be carried out, and the group of alternative resources available for performing each task, the set covering problem, therefore, looks for the minimum number of resources that can carry out all tasks. Hence, the used IP model looks for the minimum number of association relationships that satisfy all given assembly data instances. Vehicle routing, facility location, airline crew scheduling, and assembly line balancing are some of the common applications that can be modeled as a set covering problem [31]. Unlike conventional statistical-based association rule discovery methods (e.g., Apriori algorithm [32]), the used IP model does not search for the top-ranked association rules that satisfy some minimum statistical thresholds. It considers every data instance as a manufacturing solution that has been successfully implemented, and thus, the model takes into account all sets of rules that satisfy every instance of the given data. The input data to the model have to be first encoded in a binary matrix format. Two groups of data, as shown in Table 1, are involved: a group for assembly systems and a corresponding group for products. Each instance of the data is represented by one row that encodes the set of assembly system components and the product features it produced. The model parameters are defined as follows: n u v cik
Number of available data instances Number of product features Number of assembly system components A binary (0–1) parameter that takes value of “1” if component k exists in assembly system i, otherwise it is “0” (e.g., an element in the left-hand side of Table 1)
Table 1 Assembly system
AS 1 AS 2 AS 3
C1
C2
1 0 1
0 0 1
…
Product
Cv 1 1 1
Prod. 1 Prod. 2 Prod. n
F2
1 1 0
0 1 0
…
Fu 0 0 1
F3
F4
F5
1 0 1 0 0 1
0 0 0 0 1 1
0 0 1 0 0 0
0 1 0 0 0 0
1 0 0 1 0 0
A binary (0–1) parameter that takes value of “1” if product feature j exists in product i, otherwise it is “0” (e.g., an element of the right-hand side of Table 1) dkm A binary (0–1) parameter that takes the value “1” if the two system components k and m should not be associated together with the same feature. The model involves one main set of decision variables (x), where xkj is a binary element in the matrix shown in Table 2 (association matrix); xkj takes the value “1” if the assembly system component k is associated with product feature j and “0,” otherwise. Table 2 shows an example of an association matrix for a data set involving six assembly system components and five product features. The model objective function (Eq. 1) minimizes the total sum of the x variables in the association matrix. This is equivalent to finding the minimum number of association rules which are sufficient to explain the given data. Obtaining the optimal values of all the x variables (association matrix) is the ultimate objective of the model. Min
Xv Xu k¼1
Xv
c x k¼1 ik k j
Xu
f x j¼1 i j k j
Table 3
ð1Þ
x j¼1 k j
≥ f ij
ð2Þ
≥ cik
ð3Þ
Matrix defining alternatives of each system component Sys. comp. (C)
Product features
F1
F2
fij
Sample input data for the association rule discovery model Assembly system components
F1
Sys. comp. (C)
C1 C2 C3 C4 C5
C1
C2
C3
C4
C5
0 0 0 0 0
1 0 0 0 0
0 0 0 0 0
0 0 1 0 0
0 0 0 0 0
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A
Bolt Pulley
B
Bolt Bushing Pulley
C
Bolt Pulley U-arm
D
Alignment liner
Pivot
Pulley
U-arm
E
Symmetric damper
Alignment liner
N-arm
Spring Pulley Bolt
F
Asymmetric damper Spring
Bolt Pulley
U-arm
G
Asymmetric damper Spring
Pivot Pulley
U-arm
Fig. 2 Existing tensioner/idler variants (reproduced from [28])
In addition to the binary constraint (Eq. 5) on the association matrix values, the IP model has three main sets of constraints. The first two (Eqs. 2 and 3) guarantee that the values
Table 4
to be assigned by the model to each x variable do satisfy the relations between the product features and assembly system components present in the data. In other words, if the discovered association matrix is used along with the alreadyavailable product features set of data, the corresponding assembly system component set of data can be obtained and vice versa (referred to as re-generation of data). The third set of constraints (Eq. 4) does not allow any two assembly system components that are mutually exclusive or any two system components where one includes the other, to be both associated with the same product feature. This is how the model recognizes alternatives of the same type of assembly system component. An automatic welding robotic arm and a manually operated welding gun should not be both associated with the same part of a given product as they are two different alternatives (e.g., solutions) for performing the same function (i.e., redundant). Table 3 shows an example of the matrix used to encode assembly system components that are not allowed to be associated together with the same product feature (d matrix). In this example, C1 and C2 are two mutually exclusive alternatives of a same type of assembly system component (two different alternatives that each of them can perform the same function); hence, they constitute one group, and accordingly, they should not be jointly associated with the same product feature. C3 and C4 in this example also constitute one group of assembly system components. In addition to the main decision variable x, two sets of auxiliary decision variables y and w are used to relax, when needed, the first and the second sets of constraints, respectively, in order to assure feasible solutions for cases where inconsistent data is used. The sum of each of the two sets of variables is added to the objective function to minimize their values as well. Moreover, a weighted objective function is used so as to assign higher significance to the original term given by Eq. 1. Accordingly, y and w are assigned non-zero values by the model only when inconsistent data is present.
Belt tensioners/idlers features (extracted from [28])
Product variant Product features 1. Spring 2. Damper
3. Arm
4. Fastening element
5. Alignment element
Symmetric Asymmetric U-shaped N-shaped Bolt
Pivot
Fixed alignment Self alignment
6. Bushing
A-idler 1 B-idler 2 C-idler 3 D-idler 4 E-tens. 1 F-tens. 3
0 0 0 0 1 1
0 0 0 0 1 0
0 0 0 0 0 1
0 0 1 1 0 1
0 0 0 0 1 0
1 0 1 0 1 1
0 1 0 1 0 0
0 0 1 0 0 1
0 0 0 1 1 0
0 1 0 0 0 0
G-tens. 4
1
0
1
1
0
0
1
1
0
0
Int J Adv Manuf Technol Belt tensioners/idlers system components (extracted from [28])
Table 5
System Assembly system components variant 1. Level of automation 2. Axial press 3. Twist 4. CNC M/C 5. Conveyor 6. Screw 7. Feeder 8. Placer press driver Manual Automated Hybrid Bins Feeding Robotic arm Flipper mechanism Sys A Sys B Sys C Sys D Sys E Sys F Sys G
1 1 1 1 0 0 0
0 0 0 0 1 0 0
0 0 0 0 0 1 1
0 1 0 1 1 0 1
0 0 0 0 0 1 1
0 0 1 0 0 1 1
Eqs. 2′ and 3′ are the modified form of the first two constraints, and Eq. 1′ is the modified objective function. Eqs. 6 and 7 are non-negativity constraints on the auxiliary variables y and w, respectively. Min
Xv
Xu
k¼1
j¼1
xk j þ
Xn Xu i¼1
j¼1
10yi j þ
Xn Xv i¼1
k¼1
10wik
0 0 0 0 1 1 1
1 0 1 0 1 1 0
1 1 1 1 0 1 1
0 0 0 0 1 0 0
0 0 0 0 1 0 0
0 0 0 0 0 0 1
purpose of this section is not to verify the used IP model or to compare it with other association rule discovery methods as this has been already done in the corresponding publication where the model first appeared [26].
4.1 Belt tensioners/idlers assembly
ð1′Þ S.T. Xv
c x k¼1 ik k j
Xu
f x j¼1 i j k j
þ yi j ≥ f i j
i ¼ 1; …; n j ¼ 1; …; u
ð2′Þ
þ wik ≥ cik
i ¼ 1; …; n k ¼ 1; …; v
ð3′Þ
xk j þ xm j d km ≤ 1
xk j ∈ f0; 1g
yi j ≥ 0 wik ≥ 0
k ¼ 1; …; v m ¼ 1; …; u; m > k j ¼ 1; …; u
k ¼ 1; …; v j ¼ 1; …; u
i ¼ 1; …; n j ¼ 1; …; u i ¼ 1; …; n k ¼ 1; …; v
ð4Þ
The function of belt idlers and tensioners is to take up the extra slackness from the serpentine belt which drives engine accessories such as the water pump and the alternator from the crank shaft. Idlers and tensioners share a considerable similarity; the main difference is that tensioners are spring loaded to maintain a dynamic tightening force on the belt. Variety in this group of tensioners/idlers results from the diverse mechanical characteristics (e.g., torque load and damping) required by different automakers and is manifested by different Table 6 Matrix defining groups of the belt tensioners/idlers assembly system components Tensioners/idlers assembly system components
ð5Þ
ð6Þ ð7Þ
4 Automotive industry applications Two examples from the automotive industry are used to demonstrate the proposed assembly system synthesis method. The first example is a group of belt tensioners/idlers adopted from ElMaraghy and AlGeddawy [28] and the second is a new case study of a group of automobile engine short blocks. The
1 Tensioners/idlers 1 0 assembly system 0 components 0 2 0 3 0 4 0 5 0 6 0 7 0 0 8 0 0
1 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 0 0 0 0 0 0
2
3
4
5
6
7
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0
Int J Adv Manuf Technol Table 7
Association relationships between product features and assembly system components extracted by the association rule discovery IP model Tensioners/idlers features 1. Spring
1. Level of Manual Assembly automation Automated system components Hybrid
2. Damper
3. Arm
4. Fastening element
5. Alignment element
6. Bushing
Symmetric Asymmetric Ushaped
Nshaped
Bolt Pivot Fixed Self alignment alignment
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2. Axial press
0
0
0
0
0
0
1
0
1
0
3. Twist press
0
0
1
0
0
0
0
0
0
0
4. CNC M/C
0
0
0
0
0
0
0
1
0
0
5. Conveyor
1
0
0
0
0
0
0
0
0
0
0
0
6. Screw driver
0
0
0
0
1
0
0
0
7. Feeder
Bins
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
8. Placer
Feeding 0 mechanism Robotic arm 0
0
0
0
1
0
0
0
0
0
Flipper
0
1
0
0
0
0
0
0
0
0
components and parts size and geometry. In this example, real historical data about seven different variants of automotive engine belt tensioners/idlers (four idlers and three belt tensioners) and the corresponding assembly system used to assemble each tensioner/idler variant (Fig. 2) are used to synthesize an assembly system for a new variant of belt tensioners. Six main product features are used to describe the seven product variants: (1) spring, (2) damper, (3) arm, (4) fastening element, (5) alignment element, and (6) bushing. Eight main system components are used to describe the corresponding seven assembly systems: (1) level of automation, (2) axial press, (3) twist press, (4) CNC three-axis milling machine (if surface finish is needed), (5) conveyor, (6) screw driver, (7) feeder, and (8) placer. Tables 4 and 5 show how the product variants and the corresponding assembly systems, respectively, are coded and formatted in binary (0–1) format acceptable by the IP association rule discovery model. Accordingly, the total number of considered product features is 10 and the total number of assembly system components is 12. The corresponding
Symmetric damper
Alignment liner Spring
N-arm
Pulley Bushing Bolt Fig. 3 New belt tensioner variant
matrix (d matrix) which defines alternatives of the same type of manufacturing capability is shown in Table 6, where a matrix cell with a value “1” means that the two system components corresponding to that cell are alternatives to each other and should not both be associated with the same feature. For example, the two alternatives of the placer, the robotic arm and the flipper, should not be both associated with the same belt tensioner/idler feature because either one would do the job of flipping the partial assembly. The association matrix obtained by the IP association rule discovery model is shown in Table 7. Seventeen association rules were discovered between the product belt tensioners/ idlers features and the corresponding assembly system components. Each cell with a value “1” in Table 7 signifies a discovered association rule between its corresponding product feature and assembly system component. Based on these results, the assembly system components are synthesized for a new belt tensioner variant that has strong commonality with the analyzed group of belt tensioners/idlers. The new belt tensioner (Fig. 3) has the following features: 1. Spring: 2. Damper: 3. Arm housing: 4. Fastening element: 5. Alignment element: 6. Bushing:
Yes Symmetric N-shaped Bolt Self alignment Yes
Int J Adv Manuf Technol Fig. 4 Real image for two different engine block models (variants)
Engine model # 1: TW3-EZX
Then, the corresponding synthesized assembly system components according to the discovered association rules feature the following system components: 1. Level of automation: 2. Axial press: 3. Twist press: 4. CNC M/C: 5. Conveyor: 6. Screw driver: 7. Feeder: 8. Placer:
Automated or manual Yes No No Yes Yes Feeding mechanism or bins Robotic arm
The new belt tensioner is very similar to one of the old belt tensioners (variant E); the main difference is the part “bushing” which exists in the new variant but does not exist in the old one. This part is associated with the alternative “bins” of the system component “feeder.” Accordingly, the assembly system for both the new product variant and the old variant E are almost the same as expected.
Table 8
Nine engine variants and their parts
Part no.
Part name
Part code
Engine model # 2: TW5-ABA
4.2 Engine block assembly A short block is the sub-assembly of the automobile engine block found below the head gasket. Major parts of a short block sub-assembly are the cylinder block, pistons, connecting rods, crank shaft, crank shaft cap, oil pump, oil pump chain, and oil pan. It also contains many other less significant parts, mainly standard parts such as bushings, pins, bolts, nuts, and rings. Many assembly operations for a short block are either manual, semi-automated (in which powered assembly equipment or tools are used to assist the operator) or totally automated. The main assembly operations for short blocks are essentially similar for various engine models. Hence, unlike the previous example which was concerned with the system equipment level, the assembly system synthesis in this example will be mainly concerned with the level of “stations setup,” which is basically the type of assembly operation as well as the used assembly equipment, tools, fixtures, etc. Different assembly station setups are required for different engine block models depending on the cylinder block material as well as
Engine variant TW3EZX
TW3EZY
TW3EZV
TW3EZN
TW3EZM
TW5ABA
TW5ABB
TW5ABM
TW5ABE CB-V5
1
Cylinder Block
CB
CB-V1
CB-V2
CB-V3
CB-V3
CB-V3
CB-V4
CB-V5
CB-V4
2
Cylinder Liner
CL
n/a
n/a
n/a
n/a
n/a
CL-V1
CL-V2
CL-V1
CL-V2
3
Piston
PN
PN-V1
PN-V1
PN-V2
PN-V2
PN-V1
PN-V3
PN-V3
PN-V3
PN-V4
4
Connecting Rod
CR
CR-V1
CR-V1
CR-V2
CR-V2
CR-V1
CR-V3
CR-V3
CR-V3
CR-V4
5
Crank shaft
CS
CS-V1
CS-V1
CS-V2
CS-V2
CS-V2
CS-V2
CS-V4
CS-V3
CS-V4
6
Oil pump
OP
OP-V1
OP-V1
OP-V3
OP-V2
OP-V2
OP-V3
OP-V4
OP-V4
OP-V4
7
Middle case
MC
MC-V1
MC-V2
MC-V3
MC-V3
MC-V3
n/a
n/a
n/a
n/a
8
Crank shaft cap
CSC
n/a
n/a
n/a
n/a
n/a
CSC-V1
CSC-V2
CSC-V1
CSC-V2
9
Oil pump chain
OPC
OPC-V1
OPC-V2
OPC-V3
OPC-V3
OPC-V3
OPC-V4
OPC-V5
OPC-V4
OPC-V5
10
Oil pan
OPN
OP-V1
OP-V2
OP-V3
OP-V2
OP-V2
OP-V3
OP-V4
OP-V3
OP-V3
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the size and shape of the engine. For instance, aluminum cylinder blocks require piston liners while steel Table 9
Nine engine variants and their assembly station setups
Station Description no.
1 2
3 4 5 6 7
8 9 10 11
Load cylinder block to pallets Load pistons and connecting rods to pallets Assemble connecting rods to the pistons Loosen connecting rods bolts Install piston rings Insert piston-rod subassembly into liners Insert piston-rod subassembly into cylinder block Insert liners inside the cylinder block Detach middle case from the cylinder block Detach crankshaft caps
Level of automation
Station Engine variant code TW3- TW3EZX EZY
SemiST1 automated Manual ST2
Semiautomated Semiautomated Manual Semiautomated Semiautomated Manual
n/a
SemiST9 automated SemiST10 automated Manual ST11
ST20
21
Deposit silicon sealant for oil pan Install oil pan
Automated
ST21
Manual
ST22
24
ST2-S1 ST2-S1 ST2-S2 ST2-S2 ST2-S1 ST2-S3 ST2-S3 ST2-S3 ST2-S4
ST8
Automated
Install and fasten screws for oil pan Unload the short block assembly
ST1-S1 ST1-S2 ST1-S3 ST1-S3 ST1-S3 ST1-S4 ST1-S5 ST1-S4 ST1-S5
ST7-S1 ST7-S1 ST7-S1 ST7-S2 ST7-S2 n/a
Install crankshaft seals
23
TW5ABE
ST7
20
22
TW5ABM
ST5-S1 ST5-S1 ST5-S3 ST5-S3 ST5-S2 ST5-S4 ST5-S5 ST5-S5 ST5-S5 n/a n/a n/a n/a n/a ST6-S1 ST6-S1 ST6-S1 ST6-S2
ST19
17
TW5ABB
ST5 ST6
Automated
16
TW5ABA
ST4-S1 ST4-S1 ST4-S2 ST4-S2 ST4-S1 ST4-S3 ST4-S3 ST4-S3 ST4-S4
Fasten screws for oil pump
15
TW3EZM
ST4
19
14
TW3EZN
ST3-S1 ST3-S1 ST3-S2 ST3-S2 ST3-S1 ST3-S3 ST3-S3 ST3-S3 ST3-S4
18
13
TW3EZV
ST3
Detach connecting rod caps Install crankshaft in the cylinder block Install and fasten the connecting rod caps Installing chains for oil pumps Deposit silicon for assembling middle case Install and fasten screws for middle case Install and fasten screws for crankshaft caps Install oil pump
12
blocks do not. Different engine sizes also mean different sizes and perhaps geometries of the major components.
SemiST12 automated SemiST13 automated Manual ST14 Automated
ST15
Automated
ST16
Automated
ST17
Manual
ST18
SemiST23 automated Automated ST24
n/a
n/a
n/a
n/a
n/a
n/a
n/a
ST8-S1 ST8-S1 ST8-S1 ST8-S1
ST9-S1 ST9-S1 ST9-S2 ST9-S2 ST9-S1 n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
ST12S1 ST14S1 ST18S1 ST19S1 ST20S1 ST23S1 n/a
ST12S1 ST14S1 ST18S2 ST19S1 ST20S2 ST23S2 n/a
ST12S1 ST14S1 ST18S1 ST19S1 ST20S3 ST23S3 n/a
ST12S1 ST14S1 ST18S2 ST19S1 ST20S3 ST23S3 n/a
ST12S1 ST14S1 ST18S2 ST19S1 ST20S3 ST23S3 n/a
ST10S1 ST12S1 ST14S1 ST18S1 ST19S1 n/a
ST10S2 ST12S1 ST14S1 ST18S3 ST19S1 n/a
ST10S1 ST12S1 ST14S1 ST18S2 ST19S1 n/a
ST10S2 ST12S1 ST14S1 ST18S3 ST19S1 n/a
n/a
n/a
n/a
n/a
ST25S1 ST26S1 ST27S1 ST28S1 ST29S1 ST30S1 ST31S1
ST25S1 ST26S1 ST27S1 ST28S2 ST29S2 ST30S2 ST31S1
ST25S3 ST26S3 ST27S2 ST28S3 ST29S3 ST30S3 ST31S1
ST25S2 ST26S2 ST27S2 ST28S2 ST29S2 ST30S2 ST31S1
ST25S2 ST26S2 ST27S2 ST28S2 ST29S2 ST30S2 ST31S1
ST24S1 ST25S3 ST26S3 ST27S2 ST28S3 ST29S3 ST30S3 ST31S2
ST24S2 ST25S4 ST26S4 ST27S4 ST28S4 ST29S3 ST30S3 ST31S2
ST24S2 ST25S4 ST26S4 ST27S3 ST28S3 ST29S4 ST30S3 ST31S2
ST24S1 ST25S4 ST26S4 ST27S4 ST28S3 ST29S3 ST30S4 ST31S2
Int J Adv Manuf Technol
ST 15
ST 18
ST 19
ST 11
ST 9
ST 7
ST 20
ST 21
ST 22
ST 23
ST 24
ST 14
ST 16
ST 13
Operator
ST 12
Automated assembly equipment (e.g. robot)
ST 5
Manually-operated equipment (e.g. manual press)
ST 3
ST 4
Tool Box
ST 2
ST 1
Bins of parts and/or supplies
Fig. 5 Schematic layout for the TW3-EZX engine model
Hence, different tools, fixtures, and assembly equipment settings would be needed for different engine models. Accordingly, it would be beneficial to extract association relationships between engine short block components and the assembly station setups to expedite the process of assembly planning and system setup when a new engine model is introduced for assembly on the same assembly facility. The actual data available for this example is for two 4-cylinder inline engine models that an OEM automotive company used to produce before at different periods (Fig. 4). Data representing additional seven variants (instances) are generated based on the original two engine block variants. For confidentiality reasons, company information will not be revealed and altered engine model acronyms are used. The same steps followed in the belt tensioners/idlers example are applied in this example. The difference is products and systems encoding method. The short block parts (10 parts) are used as product features to describe and encode different short block variants. For the corresponding assembly systems, there are 24 assembly stations; each assembly system is represented by the various stations and their setup. Table 8 shows the product data representation and Table 9 shows the corresponding assembly system data representation. The term “n/a” used in the two tables stands for “not applicable” (i.e., does not exist). The setup of a given station is represented by the symbol “S” followed by the setup number; for instance, “ST4-S3” stands for station 4 with setup number 3. It should be mentioned that the level of details considered in this example for both the products and the systems are simplified compared to reality for demonstration
purposes. A schematic layout of the assembly system for one of the engine variants is shown in Fig. 5. The layout would not be significantly different for other short block variants. The next example illustrates the differences between different setups for the same station. Station 3 assembles connecting rods to the pistons where a manual press is used to insert the pin that connects the rod to the piston. Engine sizes vary, and accordingly, the size of the piston-rod sub-assembly is different. Hence, a different insertion head for the manual press as well as different fixtures for the piston and the connecting rod would be needed (see Fig. 6). Other stations such as station 6 (Fig. 7) where the piston-rod sub-assembly is inserted into the cylinder liner also require different setups for similar reasons. Another example for differences between setups of the same stations is the fastening of the crankshaft caps done at station 17. Pneumatic equipment is used to tighten all the
Inseron head
Fixtures
Fig. 6 Assembling piston to the connecting rod at station 3
Int J Adv Manuf Technol
Silicon nozzle
Fixtures
Fig. 7 Insertion of the piston-rod sub-assembly into the cylinder liners at station 6
crankshaft cap nuts simultaneously as shown in Fig. 8. Setups for the used assembly equipment vary for different engine models in which the distances between the screwing nuts as well as the nuts sizes are different. Accordingly, different tightening heads and machine setups are needed. The same reasoning applies to similar stations where screws are tightened using pneumatically powered equipment such as station 23 used for tightening the oil pan screws. One more example is the need to change the setup for the automated assembly equipment used in station 21 to place silicon sealant for sealing the oil pan (Fig. 9). A different path for the nozzle is required depending on the geometry and size of the oil pan. Different specification for the used silicon sealant may also be needed depending on the cylinder block and oil pan materials. The binary-coded format for Tables 8 and 9 needed as input for the IP association rules discovery model is given in Tables 10 and 11, respectively, in Appendix A. The obtained association matrix with 83 discovered rules between product features (engine block part variants) and assembly system components (station setups) is shown in Table 12 in Appendix A. Hence, for a given new engine model with a new short block design that shares a considerable number of part variants with the existing engine block models, the obtained association rules indicate the required assembly stations and their setup. For instance, consider a new short block with
Fig. 9 Deposit of silicon for oil pan seal at station 21
following combination of part variants which does not have a middle case part: 1. Cylinder block: 2. Cylinder liner: 3. Piston: 4. Connecting rod:
CB-V2 CL-V2 PN-V3 CR-V3
5. Crank shaft: 6. Oil pump: 7. Middle case: 8. Crank shaft cap: 9. Oil pump chain: 10. Oil pan:
CS-V4 OP-V4 n/a CSC-V2 OPC-V1 OPN-V2
The corresponding preliminary assembly system according to the obtained association results in Table 12 is as follow: ST1-S2 ST2-S3/S4 ST3-S3 ST4-S3 ST5-S5 ST6-S1 ST7-n/a ST8-S1
ST9-n/a ST10-S2 ST11-S1 ST12-S1 ST13-S2 ST14-S1 ST15-n/a ST16-n/a
ST17-S2 ST18-S4 ST19-S4 ST20-S4 ST21-S2 ST22-S1/S2 ST23-S2/S3/S4 ST24-S2
The synthesized system uses 20 stations out of the 24 available stations, since the association matrix does not recommend having stations 7, 9, 15, and 16 which are not needed for a variant that does not have the part “middle case.”
Tightening heads
Fig. 8 Fastening of the crankshaft caps at station 17
5 Discussion The association rule discovery model employed in this research is a general model that can extract association relationships between any two corresponding/paired groups of data (e.g., input and output parameters of a given manufacturing process) and is not only limited to
Int J Adv Manuf Technol
the presented case studies. It is an Integer Programming model, and most modern solvers are now able to reach the global optimal solution for Integer Programming models. Furthermore, the model has been already tested using several randomly generated examples, and the global optimal solution was obtained in all of them including the two automotive examples presented in this manuscript. In both case studies, the model was programmed and solved using LINGO solver. The solution time in each case was less than 1 s on a PC of 2.8 GHz quad core processor and 4 GB RAM. This demonstrates the potential ability of the model for handling considerably larger problem sizes than those considered. The used examples from automotive industry illustrate how the proposed assembly system synthesis is systematically applied. The IP model is simple to program and solve using a commercial solver, and the association rule results are explicitly provided in a clear matrix format with no further interpretation or filtering steps required. In order to be able to use the proposed assembly systems synthesis method, practitioners need to be familiar only with IP programming. The proposed method is strongly recommended as a great means for saving in product development time and effort for assembly applications where frequent product design changes and updates take place, as seen in the automotive and other consumer goods industries. Using two examples instead of just one example was to show the potential industrial significance of applying the proposed assembly system synthesis method to a variety of assembly products. However, this also highlights the fact that each assembly system synthesis problem would have its own characteristics; and hence, there is still a considerable input expected from the prospective practitioners of the proposed method with regard to the scope and the level of details by which the synthesis problem should be concerned and correspondingly the way by which the products and systems are to be described and encoded. It is possible to obtain multiple alternatives for the same assembly system component by the IP model as it was shown in the used examples. This is mainly because the model seeks the association rules that completely satisfy the input data instances. In many cases, some of these alternatives are more advanced means of achieving the same result than the alternatives. A simple way to resolve this issue is for the designer to choose the more advanced alternative as it most likely encompasses the capabilities of the less advanced alternative, albeit often more expensive. More consistent input data (i.e., the consistent utilization of the same assembly system components for the same product variants), as well as having larger number of data instances should increase the discrimination
ability of the model and hence minimize the likelihood of having multiple solutions.
6 Conclusions A new systematic method for assembly system synthesis using an Integer Programming association rule discovery model was presented. It extracts association relationships between assembly system components and product features based on data for existing and legacy assembly products and their assembly systems. Such association relationships are used to synthesize assembly systems / select their components for new product variants that fall within the scope of the existing/old ones. The synthesized systems would be used as a basis for finalization and fine tuning by the system designers and integrators. The application of proposed assembly systems synthesis method was demonstrated through two case studies of automotive products; an engine belt tensioner/ idler and engine block. Results that are consistent with the used assembly data instances were obtained in both examples. The computational times used by the IP model for the two examples reveal its potential to deal with much larger sizes of data than what already considered in this paper. From an implementation point of view, the proposed assembly system synthesis method is systematic and the utilized model is simple to program and solved with a commercial solver. The method greatly supports the rapid development of assembly systems for new product variants and generations particularly for applications that involve frequent design changes, such as in the automotive industry. Size and quality (e.g., consistency) of the used data are the main factors affecting the quality of the synthesis solutions obtained by the proposed approach. Future work would investigate minimizing or eliminating producing multiple alternatives of assembly system components.
Acknowledgments Research support and funding from the Natural Science and Engineering Research Council of Canada and Canada Research Chairs (CRC) are acknowledged. Funding This study was funded by the Natural Science and Engineering Research Council of Canada and Canada Research Chairs (CRC). Conflict of interest The authors declare that they have no competing interests.
Int J Adv Manuf Technol
Appendix A
Table 10
Encoded product variants for the engine block assembly Engine variants
Products features
1
2 3
4
5
6
7
8 9
10
TW3EZX
TW3EZY
TW3EZV
TW3EZN
TW3EZM
TW5ABA
TW5ABB
TW5ABM
TW5ABE
TW3EZX
1 2 3 4 5 1 2
1 0 0 0 0 0 0
0 1 0 0 0 0 0
0 0 1 0 0 0 0
0 0 1 0 0 0 0
0 0 1 0 0 0 0
0 0 0 1 0 1 0
0 0 0 0 1 0 1
0 0 0 1 0 1 0
0 0 0 0 1 0 1
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0
1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1
0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0
0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0
1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0
0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0
0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0
0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0
3 1 2 1 2 3 4 5 1 2 3 4
0 0 0 1 0 0 0 0 1 0 0 0
0 0 0 0 1 0 0 0 0 1 0 0
1 0 0 0 0 1 0 0 0 0 1 0
1 0 0 0 0 1 0 0 0 1 0 0
1 0 0 0 1 0 0 0 0 1 0 0
0 1 0 0 0 0 1 0 0 0 1 0
0 0 1 0 0 0 0 1 0 0 0 1
0 1 0 0 0 0 1 0 0 0 1 0
0 0 1 0 0 0 0 1 0 0 1 0
Int J Adv Manuf Technol Table 11
Encoded assembly systems for the engine block assembly Engine variants TW3-EZX TW3-EZY TW3-EZV TW3-EZN TW3-EZM TW5-ABA TW5-ABB TW5-ABM TW5-ABE
Assembly system stations 1
1 2 3 4 5 1 2 3 4 1 2 3 4 1
1 0 0 0 0 1 0 0 0 1 0 0 0 1
0 1 0 0 0 1 0 0 0 1 0 0 0 1
0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 0 1 0 0 1 0 0 0 1 0 0 0 1
0 0 0 1 0 0 0 1 0 0 0 1 0 0
0 0 0 0 1 0 0 1 0 0 0 1 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0
0 0 0 0 1 0 0 0 1 0 0 0 1 0
2 3 4 5 1 2 3 4 5 6 1 2 7 1 2 8 1 9 1 2 10 1 2 11 1
0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1
0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1
1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1
1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1
0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1
0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 1
0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1
0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1
0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1
12 1 1 13 1 1 2 0 3 0 14 1 1 15 1 1 2 0 3 0 16 1 1 2 0 3 0 17 1 0 2 0 18 1 1 2 0
1 0 1 0 1 0 1 0 0 1 0 0 0 1 0
1 1 0 0 1 0 0 1 0 0 1 0 0 0 0
1 0 1 0 1 0 0 1 0 0 1 0 0 0 1
1 0 1 0 1 0 0 1 0 0 1 0 0 0 1
1 1 0 0 1 0 0 0 0 0 0 1 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 1 0 0
1 0 1 0 1 0 0 0 0 0 0 0 1 0 0
1 0 0 1 1 0 0 0 0 0 0 1 0 0 0
2
3
4
Int J Adv Manuf Technol Table 11 (continued) Engine variants TW3-EZX TW3-EZY TW3-EZV TW3-EZN TW3-EZM TW5-ABA TW5-ABB TW5-ABM TW5-ABE 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0
1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0
1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0
0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1
0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0
0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0
23 1 2 3 4 24 1 2
1 0 0 0 1 0
0 1 0 0 1 0
0 0 1 0 1 0
0 1 0 0 1 0
0 1 0 0 1 0
0 0 1 0 0 1
0 0 1 0 0 1
0 0 1 0 0 1
0 0 0 1 0 1
19
20
21
22
Table 12
Obtained association matrix for the engine block assembly Product features 1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 1 2 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 1 2 1 2 3 4 5 1 2 3 4 Assembly system stations
1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 5 2 1 2 3 4 3 1 2 3 4 4 1 2
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 1 0 0 0 1 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 1 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
Int J Adv Manuf Technol Table 12 (continued) Product features 1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 1 2 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 1 2 1 2 3 4 5 1 2 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 11 1 0 0 12 1 0 0 13 1 0 0 2 0 0 3 0 0 14 1 0 0 15 1 0 0 2 0 0 3 0 0 16 1 1 0 2 0 0 3 0 0 17 1 0 0 2 0 0 18 1 0 0 2 0 0 3 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 19 1 2 3 4 20 1 2 3 4 21 1 2 3
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0
5
6 7 8 9 10
3 4 1 2 3 4 5 1 2 1 2 1 1 2 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
Int J Adv Manuf Technol Table 12 (continued) Product features 1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 1 2 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 1 2 1 2 3 4 5 1 2 3 4 4 22 1 2 3 4 23 1 2 3 4 24 1 2
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
References 1. 2.
3.
4.
5.
6.
7.
8.
9.
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