SOS e subjective objective system for generating optimal product concepts Amir Ziv-Av, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel and Ziv-Av Engineering Ltd, Israel Yoram Reich, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel Concept design is the most critical step in product development. To a large extent, its quality determines the fate of the product. Support for concept generation is mainly intuitive. In this paper, we review and exemplify the importance of quality product concepts and the available literature on concept generation. Subsequently, we present a method e subjective objective system (SOS) e for generating optimal concepts in diverse disciplines. The method rests on four mathematical metaphors: it is composed of objective and subjective components, it allows varying degrees of precision in modeling, it works by decomposing a complex problem into smaller sub-problems, and it uses highly simplified evaluations. SOS not only structures the decision process but also outputs the optimal concept given the customer objectives, the company context, and the available constraints. This solution is obtained by quadratic programming that allows the method to handle very large problems and solve them in negligible time. SOS has been developed over years of practical experience and research, and has been used in numerous successful real projects. We illustrate the use of the method in a real project. 2005 Elsevier Ltd. All rights reserved. Keywords: conceptual design, design practice, research methods, design tools, product configuration
M Corresponding author: Y. Reich
[email protected]
ost of the 25,000 new products introduced in the United States every year fail (Bobrow and Shafer, 1987; McMath and Forbes, 1998; Goldenberg et al., 2001). Therefore, it is critical to be able to screen out products that are likely to fail. The design stage that dominates almost any product development project as far as cost and quality, and consequently, the success or failure fate of the product is the conceptual design. The crucial role of concept generation is so profound that even in projects where decisions have been deferred
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to implementation phase, the role of concept design is still predominant (Verganti, 1999). This paper proposes a method that supports the development of quality products while considering diverse disciplines and business practices.1
1
Product concepts and configurations: state of the art
1.1
Role of concepts
We can best illustrate the essential role of design concepts by several examples. The Boeing 747 airplane is an excellent example of an exceptional design concept. It has been in service for over 35 years, serving generations of passengers with generations of outfit. Through its design, Boeing saved several billion dollars in development cost and reduced its operational risk. In 1958, BMC demonstrated through its Austin and Morris Mini Minor models how an optimal configuration of a passenger car should be. It took many years for other manufacturers to follow (in 1965 Peugeot introduced the 205, in 1973 Fiat introduced the 127, in 1976 Volkswagen introduced the Golf, in 1979 GM introduced the X Body and only in 1993 Volvo introduced the 850). Was the time lag in adopting the superior concept a lapse of understanding or was it due to corporate implementation characteristic that made this introduction suboptimal to the different carmakers at the time? Our framework offers a way to account for such context dependent situations. In contrast to these two superior example concepts, the old Volkswagen’s Transporter is an example of a bad concept. It had short wheelbase, a rear engine, and drivers were placed before the front axle. This configuration made drivers more susceptible to vibrations and more likely to injure during accidents, placed the load above the engine thus reducing car stability, and led to inferior car handling. This inferior concept lasted until 1993, when Volkswagen reversed the main configuration choices: large wheelbase, front engine, driver behind the front axle, and payload on a low floor; thus improving stability, safety, comfort, and handling. Implicitly, Volkswagen admitted its mistake. The inferior concept forced Volkswagen to spend extensive effort and cost into the detail design. For example, in order to reduce susceptibility to vibrations, the suspension system had to be designed at top quality. In addition, in order to improve safety, the front was made
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much stronger (even though without the engine and favorable car dimensioning there was nothing to absorb accident energy at the front).
1.2
Conceptual design and concept generation
Conceptual design could be decomposed into several activities: requirement analysis, product concept generation, and concept selection. The first and last activities enjoy the availability of tools and methods to assist practical work, for example, QFD (Akao, 1990) could be used in the requirement elicitation, understanding, and translation; and Pugh’s concept selection (Pugh, 1981) or AHP (Saaty, 1980) in the concept selection activity. In contrast, there is no widely used method in practice for concept generation (King and Sivaloganathan, 1999; Hari et al., 2001). In practice, concept generation is done by exercising knowledge, experience, and subjective judgment of those involved in the design. Issues that impact the concept generation include: value for the customer, cost, manufacturability, maintainability, reliability, etc. In fact, the vital role of the product concept in the product success mandates that every conceivable piece of useful knowledge be exercised at concept generation. It is an immense work to consider all influencing aspects on the design in an orderly fashion to drive the creation of quality concepts. While the conceptual product design carries the majority of the value of the product compared to the detailed design, its decision-making is quite ‘soft’: qualitative, and often ad hoc with few limited support tools or methods. The predominant tool for concept generation has been morphological analysis (Zwicky, 1969; Pahl and Beitz, 1996) in which each requirement is potentially addressed by several functional solutions and the designers have to figure out manually which combination constitutes the better concept. We model this manual generation by an optimization problem. The concept generation stage has also been linked to creativity, lateral thinking, brainstorming (Osborn, 1953), and other thinking qualities and creativity methods, e.g., Synectics (Gordon, 1961) or TRIZ (Altshuller, 1988). These methods mainly assist in generating the solutions for a single requirement. Product ideas or concepts also emerge from external close collaboration with customers, market surveys, lead users (Von Hippel, 1986), and suppliers. Hari et al. (2001) presented ICDM e a method that supports conceptual design by integrating different tools that address different aspects of the
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process. Nevertheless, the concept generation does not get support. Gilboa et al. (2001) devised a method for creating concepts from a morphological chart that can be used in ICDM. The method tries to fit a statistical model to several selected complete concepts by estimating the model parameters. Subsequently, the model can be used to evaluate and select other solution principle combinations. Recently, Chen and Lin (2002) presented a method for concept generation that maps functions to concepts. The method is formulated as a mathematical model that maximizes the concept functionality while minimizing its functional coupling and susceptibility to constraints. The method that we present later is more general than all these models. It addresses the mapping from customer requirements to a product concept considering as many design issues as necessary. It easily handles constraints between the different concept elements or parameters. The model is easy to use and it quickly finds the optimal solution possible in the given context. The model clearly separates between the objective concept e one that best addresses the functionality (and the one that most methods seek) and the subjective concept e the concept that is best given the context of the particular organization. Sometimes it would be fatal for an organization to attempt developing the best objective concept because it lacks the necessary knowledge, yet developing a different concept that is within its capabilities can be successful in capturing a relevant market niche.
1.3
Product concept and product configuration
Product concept and product configuration are often perceived as too very different notions but as we see shortly, they in fact lie on two extremes of a continuum as shown in Figure 1. On the one (left) extreme, when design of a new product begins, little is known about the solution, uncertainty is high. Designers try to figure out the solution principles, functions, or technologies that would govern the design in the most effective way. They have to select them so that they do not conflict. At this time, no physical components or exact dimensions are considered. We refer to this type of activity, concept generation. For example, when designing a highly accurate and fast circuit board inspecting machine, the need arises to check new technologies for supporting linear motion since the requirements push traditional technology beyond its limits. This means that even the optimal arrangement or configuration of existing components fails to satisfy the constraints. Recognizing that available technology is insufficient leads to considering new solution principles, technologies, or new materials. Each building block can emerge from exercising creativity
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Solution principles Technologies
Concept
...
Physical building blocks Dimensions
Conceptual building blocks
Concept/ Configuration
...
Configuration (as designed)
...
Configuration (as produced)
...
Figure 1 The continuum be-
Knowledge
Uncertainty tween product concept and
Time
configuration
enhancement methods but the interaction of several such ideas must be done with care. In this example, the concept being generated is that of a highly accurate and fast linear motion subsystem that needs to optimize several objectives and satisfy constraints. Shown in Table 1, the concept is described only by solution principles, technologies, and materials. The concept selected in this case was the use of air bearings with a polished granite structure. On the second (right) extreme of Figure 1 lies configuration generation as manufactured (or even as maintained). When detail design terminates, designers fix all the component definitions and dimensions of the product. Following production and inspection, almost all Table 1 Building blocks of a linear motion subsystem
Concept building blocks
Building blocks type Parameters (geometry, location, quantity)
D1 D2 D3 D4 D5 D6 D7 D8 D9 D10
Subjective objective system
Air bearings Linear ball bearings Non-circulating linear bearings Polished granite structure Cast and machined structure Welded, relaxed, and machined structure Low carbon iron Cast iron Aluminum Hard anodize coating
Parts
Principles, technology, and material 1 1 1 1 1 1 1 1 1 1
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potential uncertainties diminish and knowledge about the product is almost complete. The product is almost completely defined as built from its components and assembly operation. The remaining uncertainty and incompleteness of knowledge stem from the fact that manufactured products are partially inspected and only those inspected parts and dimensions are certain. Nevertheless, the manufactured product has a precise product configuration. In today’s practice of mass customization, each manufactured product has its own version of the product configuration. When designing products with complete knowledge, these designs turn out to be parametric or configuration design. Such designs can often be automated or receive significant computational support. An early attempt to develop a product configurator was R1: an expert system for configuring VAX computers at Digital (Bachant and McDermott, 1984). Kota and Lee (1993) described a general framework for configuration using expert system technology. Further information on the state-of-the-art in product configuration can be found in two recent reviews (Hsu and Woon, 1998; Gu¨nter and Ku¨hn, 1999). The detailed example of this paper e designing a deck lifter e is a configuration-type design where all building blocks are available and only parts and parameters are considered, see Table 2. Note that this Table 2 Building blocks of the deck lifter
Concept building blocks
Building blocks type Parameters Parts Principles, (geometry, technology, location, and material quantity)
D1 D2 D3 D4
Upon a light standard truck Upon a heavy standard truck Addition of a cutout driver cabin Addition of a special lowered, in front of the front wheels driver cabin D5 Based on an automotive system C ‘Manitu’ hydraulic system D6 A standard ‘scissors’ stage without a power unit and valves D7 Four telescopic pistons C upper and lower structure D8 A P.T.O hydraulic power unit D9 Standard parallel lifting control unit D10 Hydraulic stabilizers
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example could easily turn into a (partial) concept generation if we modified one requirement that the deck lifter needs to fulfill: for example, the ship decks might have obstacles preventing the use of a truck or even a forklift. In between the two extremes lie designs that are not solely new nor perfectly understood. They involve a combination of known parts and new technologies or design principles. In many cases the new technologies are introduced to address more demanding requirements. For example, when designing a laser plotter the need to design a high throughput accurate plotter demanded introducing new technologies into the building blocks pool and selecting between the admissible concepts that they can permit; all the building blocks of the laser plotter are given in Table 3. The complete concept or configuration is created for satisfying the constraints and maximizing the product quality. The concept selected for this case was: Vacuum Rotating Drum, Constant Focus scanner, Hundreds of Beams Scanner, Linear Scanner Movement, and Vacuum System. Finally, it should be noted that between the two extremes, we could locate the trajectory that a new design follows starting when its concept is generated, until its detailed design and production. Following the creation of the concept from solution principles, they are gradually Table 3 Building blocks of a laser plotter
Concept building blocks
Building blocks type Parameters (geometry, location, quantity)
D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14
Subjective objective system
Vacuum rotating drum Static inner drum Flat vacuum table Constant focus scanner Rotating mirror scanner Polygon F-theta scanner Single beam scanner Dozens of beams scanner Hundreds of beams scanner Automatic focus Pressing substrate system Linear scanner movement Linear drum/table movement Vacuum system
Parts
Principles, technology, and material
1 1 1 1 1 1 1 1 1 1 1 1 1 1
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replaced through embodiment by physical building blocks and dimensions. Such a process could iterate since new requirements or constraints may emerge during design, rendering previous solutions defunct (Braha and Reich, 2003). The iterations occur until the product becomes well defined.
In summary, product concept or configuration varies along some dimensions but they all involve combining elementary building blocks into a complete system such that they work best together without violating mutual constraints.
1.4
Definitions
We use the following definitions throughout the paper: Customer characteristics are product properties that are specified by the customer or the product users. Implementation characteristics are product properties derived from the context of the organization and its capabilities, for example, a capability to mass-produce a product, which determines the product production cost. Engineering environment are product descriptors such as components, parameters, or technologies, used by designers to describe the design solution. An optimal objective product concept is the best product concept that can be found without taking into account any resource, organization, or issues such as investment, risk, knowledge, etc. The only governing aspect is functionality along the product life cycle. An optimal subjective product concept is the best product concept that is independent of functionality, but addresses all implementation characteristics such as manufacturability, simplicity, cost, risk, investment, know-how, etc. A decision layer is a part of the objective or subjective concept formulation that organizes the relevant information in relation to the layer topic (e.g., product simplicity) and contributes a term to the objective or subjective product concept formulation. A decision layer weight is the relative importance placed by the customer and/or designer on each of the decision layers. Constraints are dependencies and limitations placed on the use of various combinations of building blocks when creating the product concept (see Section 2.3). An optimal concept is formed by combining the formulations of the objective and subjective product concepts and solving it.
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SOS is formulated as a maximization problem, where a function that includes all contributions, objective and subjective is formulated and maximized subject to constraints. Both solutions can be formulated using several decision layers, each addressing a single customer or an implementation characteristic. SOS allows constructing the optimal concept for each layer and contrasting it with the overall optimal concept.
1.5
Preview of paper
The goal of this research has been the development of a comprehensive method that is domain independent and flexible in its ability to incorporate new business decisions such as outsourcing product design or intellectual property policy (Reich and Ziv-Av, 2003). The method should be quite simple, in the spirit of QFD (Akao, 1990), enabling its use by diverse engineering teams. We call the method SOS: Subjective Objective System. In this research, we have followed mainly a case study methodology (Yin, 1984; Reich, 1994). We have put the method to work on a variety of real design problems ranging from miniature, high accuracy optomechanical systems, up to very large transportation equipment. We have also conceptually checked its applicability in diverse areas such as service (e.g., configuring patent agreement) and press (e.g., designing a new journal) industries. In addition to leading to optimal concepts, SOS use in various design review meetings (preliminary design review, etc.) as a means of presentation and explanation was followed by focused discussion, easy concept approval, and overall customer satisfaction. We are in the process of checking the method with highly skilled experienced designers in about ten different industries. This paper describes SOS e a subjective objective system for generating optimal product concepts. The method integrates information about the market, organization, and technology, and outputs the best concept configuration addressing the market opportunity. The method is demonstrated on a real case study.
2 Example: designing a deck lifter 2.1 Problem description In some cargo ships, the distance between decks can be modified to accommodate different goods. Each deck is built of square parts that are supported in its corners by vertical pillars that go through all the decks. A vehicle can drive on the deck and move from one deck to another
Subjective objective system
517
using a ramp. The height modification is carried out by a vehicle that moves on one deck and supports, using a vertical lifting device, each deck part above it, while the part’s location is being changed. Once the part is placed, the vehicle moves to the next deck part. A priori constraints included the following. The height adjustment would be in the range between 2 and 5 m. The vehicle would be a diesel engine and would be based on an existing vehicle platform. The lifting device would be hydraulic, and while in lifting position, the vehicle should be supported through its frame and not on its suspension and tiers.
2.2
Customer requirements
The customer requirements include: 1. Good maneuverability to minimize moving time from one deck part to another. 2. Good operator view. 3. Easy entrance into driver compartment. 4. Comfortable driver compartment. 5. Operator’s safety in malfunction. 6. Durability for ship roll loadings. 7. Low weight. 8. Maintainability.
2.3
Implementation characteristics
The implementation characteristics set by the manufacturer include: 1. 2. 3. 4. 5.
Minimal cost of mass production. Minimal cost of development investment. Minimal cost of mass production preparation. Maximum design simplicity. Minimal project risk.
2.4
Implementation building blocks
The following concept building blocks have been identified: 1. 2. 3. 4. 5. 6.
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Light truck automotive system. Heavy truck automotive system. Cut driver compartment. Special driver compartment placed low, before the front axle. Off-road forklift automotive system. Standard scissors lifting platform.
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7. Four telescopic hydraulic pistons. 8. Hydraulic power system operated from the truck power take off (PTO). 9. Control system for pistons’ parallel movement. 10. Hydraulic stabilizers. The following is a subset of the constraints that act on the implementation characteristics: 1. Select only one type of platform: light or heavy truck or forklift automotive system. 2. Select only one type of lifting device. 3. If we use four telescopic pistons, they should also be made parallel. 4. A hydraulic scissors stage can only be placed on a heavy truck due to its weight. 5. The use of a truck mandates modifying the driver compartment to satisfy the minimal height constraint.
The use of SOS for designing the solution accompanies the description of the method in the next section.
3
Optimal concept generation
We start by describing the overall organization of the method, and continue with presenting the method’s details.
3.1
The layers’ organization
Figure 2 shows the general arrangement of m layers. There is a layer for each customer requirement (e.g., see Section 2.2) or implementation characteristics (e.g., see Section 2.3). The vector D of length n, denotes the engineering environment components and is the same for all layers. We assume the availability of a database of existing components or parameters (e.g., Tables 1e3) or that the design team that uses the method can provide building blocks for potential inclusion into the product concept. In many areas, these building blocks are well identified (e.g., aircraft design); nonetheless, conceiving a product concept is a challenging task (e.g., defining the concept of a new aircraft). In situations where building blocks are missing or additional need to be identified, designers can be assisted by various creativity methods (e.g., TRIZ). The elements of D take 1 or 0 values depending on whether they are incorporated or not in the design concept (e.g., the vector of the deck lifter configuration shown in Figures 6 and 8 with the building blocks of Table 2 is D ¼ ð0; 0; 0; 0; 1; 0; 1; 0; 1; 0ÞT ).
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Figure 2 The organization of layers
There are constraints between the candidate design building blocks. They are modeled by: % gk ðD1 ; .; Dn Þ ¼ bk ; k ¼ 1; .; R R
ð1Þ
In SOS, the constraints gk are linear functions of the independent variables D. This modeling is one of the sources of strength of the method since it allows solving the problem as a regular optimization without resorting to combinatorial enumeration (see later). This modeling can account for diverse constrains such as: -
-
520
Mutual exclusiveness: If three components D1, D2, D3 compete to be incorporated in the product and only one could be selected then the constraint D1 CD2 CD3 ¼ 1; Dj ¼ 0; 1; j ¼ 1; 2; 3, makes sure that only one would be selected for the design concept. Functional necessity: When component D1 must be selected if component D2 is selected we get D1 D2 R0. This works since if D2 is set to 1, D1 must be set to 1 also in order to satisfy the equation. If D2 is set to 0 (not selected), D1 can assume any value to satisfy
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the equation. If the necessity works in both ways, the constraint becomes D1 D2 ¼ 0. In the deck lifter problem the constraints are: 1Þ D1 CD2 CD5 ¼ 1 10Þ D2 CD5 %1 2Þ D3 CD4 CD5 ¼ 1 11Þ D3 CD4 %1 3Þ D6 CD7 ¼ 1 12Þ D3 CD5 %1 4Þ D6 CD9 ¼ 1 13Þ D4 CD5 %1 5Þ D7 CD10 ¼ 1 14Þ D5 CD6 %1 6Þ D1 CD2 %1 15Þ D5 CD8 %1 7Þ D1 CD5 %1 16Þ D5 CD10 %1 8Þ D1 CD6 %1 17Þ D9 CD10 %1 9Þ D1 CD10 %1 18Þ D7 D1 R0
19Þ 20Þ 21Þ 22Þ 23Þ 24Þ 25Þ 26Þ 27Þ
D8 D1 R0 D9 D1 R0 D2 D6 R0 D8 D2 R0 D7 D5 R0 D9 D5 R0 D8 D6 R0 D6 D10 ¼ 0 D7 D9 ¼ 0
ð2Þ
Figure 3 shows the arrangement of information in the lth layer and Figure 4 depicts the ‘maximizing product simplicity’ layer of the deck
Figure 3 The layout of a single layer
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521
(a)
Upon A Heavy Standard Truck
Addition For A Cutout Driver Cabin Addition For A Special Lowered, In Front of The Front Wheels Driver Cabin Based On An Automotive System+"Manitu" Hydraulic System A Standard "Scissors" Stage With Out A Power Unit And Valves
8E-11 1 1
1
Parallel Lifting Control Unit
Hydraulic Stabilizers
Based On An Automotive System+"Manitu" Hydraulic System
1
(b)
1
0
1
0
1
-1
-1
-1
0
Hydraulic Stabilizers
1
A P.T.O Hydraulic Power Unit
Addition For A Special Lowered, In Front Of The Front Wheels Driver Cabin
0 -1 -1
4 Telescopic Pistons+Upper & Lower Structure
Cutout Driver Cabin
0
1 1 -1 1
A Standard "Scissors" Stage With Out A Power Unit And Valves
Upon A Heavy Standard Truck
1
LIljk
Parallel Lifting Control Unit
A P.T.O Hydraulic Power Unit
1
0
0 1 0
4 Telescopic Pistons+Upper & Lower Structure
0
-1
-1 1
-1 1
-1
-1 -1 -1
Present configuration overall design simplicity Value of the simplest possible design Value of least simple design Normalized design simplicity
1
Value of Design Simplicity
Upon A Light Standard Truck
(c)
Upon A Light Standard Truck
Configuration Vector (Exists/Not Exists)
Dj The subjective solution for Max.Design Simplicity
(a)
3 3 -6 1
LVl
(d)
Figure 4 Deck lifter e information for deriving the optimal subjective configuration for maximizing product simplicity: (a) concept elements, (b) interactions between elements LIljk, (c) the concept elements values Dj that appear on the first row and column, and (d) the quality LVl (Equation 3)
lifter example. The matrix LIl denotes the influence of the engineering environment components D on attaining the customer or implementation characteristic Ll. Each entry LIljk in the matrix specifies how much the incorporation of the two design building blocks Dj and Dk is assisting in attaining the overall value of the layer. LVl ¼
n X j¼1
Dj
n X
ð3Þ
LIljk Dk
k¼1
The diagonal elements LIljj simply specify the contribution of Dj towards LVl.
If we solve the following optimization problem:
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max LVl subject to: % gk ðD1 ; .; Dn Þ ¼ bk ; k ¼ 1; .; R R Dj ¼ 0; 1; j ¼ 1; .; n
ð4Þ
We would get the best combination of D that maximizes the value of the . layer and satisfies the constraints. We denote this value by LVmax l Similarly, we denote by LVmin the minimal value of the layer obtained l by the worst combination of D. The best combination for layer ‘maximizing product simplicity’ is D ¼ ð0; 1; 1; 0; 0; 1; 0; 1; 0; 1ÞT and LVmax ¼ 3 and the worst combination l is D ¼ ð0; 0; 0; 0; 1; 0; 1; 0; 1; 0ÞT and LVmin ¼ 6. l
The normalized layer value is given by: NLVl ¼
3.2
LVl LVmin l min LVmax LV l l
ð5Þ
The optimal solution
The optimal solution takes into account the contribution of all layers. We use a weighted additive function to obtain the overall contribution. Elsewhere, we provide a general rationale for using such formalism in support systems that assist designers in exploring the solution space (Dobrescu and Reich, 2003). In the formulation, each characteristic l (whether customer or implementation) is assigned a weight wl. To reduce subjectivity, these weights could be obtained by methods such as AHP (Saaty, 1980, 1997). Consequently, the problem becomes: m X max Q ¼ wl NLVl l¼1
subject to: % gk ðD1 ; .; Dn Þ ¼ bk ; k ¼ 1; .; R R m X wl ¼ 1
ð6Þ
l¼1
Dj ¼ 0; 1; j ¼ 1; .; n
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523
This formulation is an integer quadratic programming with linear constraints, which is easily solved by a variety of numerical techniques (Grossmann, 2002). Our experience in solving numerous such problems suggests that optimal solutions are obtained by relaxation of the variables to continuous (i.e., 0%Dj %1; j ¼ 1; .; n), employing simple optimization algorithms, and rounding continuous values to nearest integer if they turn to be different. This simple approach bypasses the costly enumeration often used in configuration problems. This approach has been implemented in Excel spreadsheet and has been used in all the practical cases. Solving Equation (6) by optimization amounts to a search in the space of concepts. In this search, only a small fraction of the possible concepts is generated and evaluated. This is the generation process that is hidden from the designer since it is performed behind the scenes by the solution algorithm. Only the result e the optimal solution e is displayed. The mathematical formulation does not differentiate between different layers. Nevertheless, conceptually, we subdivide them into the aforementioned objective and subjective types. The objective layers represent the contribution of the customer characteristics or requirements (Section 2.2) and the subjective represent the implementation characteristics (Section 2.3). Therefore, the optimal objective solution is derived by only considering the objective layers and the subjective by taking into account the subjective layers. The objective solution becomes the target for attainment since it best addresses the customer requirements without constraining the solution by any context related aspect.
3.3
Practical simplification
When some of the layers have diagonal LI matrices, LIljj j ¼ k ; LIljk ¼ 0 jsk
ð7Þ
they could be combined into a single matrix. Assume without loss of generality that the first d layers are such. Therefore, the contribution of one of these layers l could be calculated as: LVl ¼
n X j¼1
Dj
n X k¼1
LIljk Dk ¼
n X j¼1
Dj LIljj Dj ¼
n X
LIljj D2j
ð8Þ
j¼1
but since Dj ˛ 0; 1 , the equation becomes
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LVl ¼
n X
ð9Þ
GIlj Dj
j¼1
where GIlj ¼ LIljj :
ð10Þ
The contribution of the d layers would be GV ¼
d X
wl
n X
ð11Þ
GIlj Dj :
j¼1
l¼1
Parallel Lifting Control Unit Hydraulic Stabilizers
0 0
0 0
Complying Value Of Each Functional Characteristic
0 1
Hydraulic Stabilizers
A P.T.O Hydraulic Power Unit
Parallel Lifting Control Unit
1 0 1 -1
Based On An Automotive System+"Manitu" Hydraulic System
Addition For A Special Lowered, In Front Of The Front Wheels Driver Cabin
1 -1 0 -1
0 0
1 2
(c)
(e)
wi
LVl .
(a)
(f)
Good maneuverability
0
1 -1
1 -1
0
0
0
0
0
-1
0
0
0 -1
1
1
0
0
0
0
0
1
1 *
1
1
0
1 -1
0
1
0
0
0 = -3E-09
Good operator eyesight Easy entrance into driver compartment Comfortable driver compartment Operators Safety In Malfunction
-1
1
0
0
1 -1
0
0
1
Durability for ship roll loadings
-0 1 0 1 0
0
0
-1
Quality Score
Addition For A Special Lowered, In Front Of The Front Wheels Driver Cabin Based On An Automotive System+"Manitu" Hydraulic System A Standard "Scissors" Stage With Out A Power Unit And Valves 4 Telescopic Pistons+Upper & Lower Structure A P.T.O Hydraulic Power Unit
-1 -1 0 -1
GIlj
Weight Related To Characteristic :1,2,3
Addition For A Cutout Driver Cabin
0 -0
A Standard "Scissors" Stage With Out A Power Unit And Valves
Upon A Heavy Standard Truck
4 Telescopic Pistons+Upper & Lower Structure
Upon A Light Standard Truck
Cutout Driver Cabin
Dj
Upon A Heavy Standard Truck
(b)
Upon A Light Standard Truck
(d)
Configuration Vector (Exists/Not Exists)
Our practical experience in numerous applications is that in many cases, the objective layers are diagonal or they could be modeled as such in the conceptual design stage. Consequently, the objective layers could be simplified into a single matrix. In the deck lifter example, this is precisely the situation as shown in Figure 5. In contrast, for implementation
3 3
3 6
1
-1
3
3
1
0
1
-1
Low weight 0 -1 1 -1 1 -1 1 -1 0 -1 2 2 1 1 1 0 -1 1 -1 -1 -1 -1 -3 Maintainability 1 Contributes=1 Neutral = 0 Disturbs= -1 Overall Functional Quality
4 -3 11 GV Max Functional Quality: The Quality Of The Best Functionally Qualified Possible Configuration 11 Min Functional Quality: The Quality Of The least Functionally Qualified Possible Configuration -17 Normalized Functional Quality 1
(g)
Figure 5 Deck lifter e information for deriving the optimal objective concept: (a) customer characteristics, (b) engineering environment elements, (c) the relation GIlj, (d) the concept elements values Dj, (e) the complying value LVl, calculated by Equation (9), (f) the weight wi and (g) the quality GV, calculated by Equation (11)
Subjective objective system
525
characteristic such as cost or simplicity, the interactions modeled by the layers are highly important. In the example of this paper, we simplify the objective layers into a matrix described next.
3.4
Objective concept generation
Let us consider the requirement maneuverability as an example of translating the information into the mathematical model. In the case of a vehicle with two axles, maneuverability is dependent on the general dimensions of the system. In particular, the length and rotating radius between walls that is determined by the wheelbase, maximal wheel steering angle, and number of steered axles (one in a truck and two in a forklift). The size of both trucks is similar and larger than the forklift. Therefore, the trucks get 1 for negative impact on attaining the maneuverability requirement. The cutout driver cabin gets C1 since it does not increase the length of the truck. A special driver compartment in front of the bumper gets 1. The forklift gets C1 due to its short wheelbase, short length, and double-axle steering. Other items are irrelevant to this requirement therefore get 0 value. In this way, the matrix GIlj is constructed. The remaining choice is the relative importance of the requirements. The information for the optimal objective concept formulation is given in Figure 5. The figure includes the equation notations. The result (item (h) in the figure) also specifies how far is the generated concept from the best functional concept. The concept that satisfies this formulation, i.e., the best concept as far as functionality, is shown in Figure 6.
3.5
Subjective concept generation
The subjective layers were mentioned in Section 2.3. We will show how the subjective optimal solution for maximizing simplicity engineering characteristic (EC) is generated. The heavy truck makes it simple to assemble all the system parts and therefore, EC22 ¼ C1. The light truck is average ( EC11 ¼ 0) and the forklift is most complex ( EC55 ¼ 1).
Figure 6 Deck lifter e optimal objective concept
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A sliced driver compartment is simple ( EC33 ¼ C1) and one put in front of the bumper is complex (EC44 ¼ 1). The off diagonal terms indicate the coupling between the building blocks. For example, a sliced driver compartment is more complex in a heavy truck than in a light truck due to difference in the height of the truck frame; therefore, EC23 ¼ 1 and EC13 ¼ 1. Maximizing EC will lead to the simplest product concept. The information for deriving the optimal subjective concept reflecting the desire to maximize design simplicity is given in Figure 4, the subjective concept is shown in Figure 7. This concept differs markedly from the objective concept, which is much more complex design. In the same way, we can generate the optimal solution for each subjective layer and expect to get a variety of concepts, each geared toward its layer’s goal. The overall best concept is one that maximizes the objective and subjective layers simultaneously while satisfying the constraints. It will change depending on the preferences regarding the importance of the different layers. In the particular example, the focus was functionality for the customer and the final result was the optimal objective concept whose final design is also depicted in Figure 8. Since SOS not only assists in concept selection but also generates the concept, we can run sensitivity analyses on different evaluations and obtain the sensitivity of the concept. Moreover, since the concept is an integration of various building blocks, we can assess the sensitivity of each with respect to different evaluations. Such study is left for future work.
4 Discussion 4.1 Summary of SOS and its relation to other methods SOS allows modeling design information in several orders of resolutions. In the first order, layers are condensed into a matrix
Figure 7 Deck lifter e optimal subjective concept
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Figure 8 Deck lifter e the product
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assuming that the different concept building blocks do not interact to satisfy the requirements. The layers that are condensed into a matrix are comparable to the main room of the House of Quality (Akao, 1990). It records the contribution of product concept elements to attaining customer characteristics. In the second order, the layers are maintained, assuming that there are binary interactions between concept building blocks. If needed, the method can easily accommodate more detailed information on the relations between three or more concept components but their practical use would be negligible. In addition, such incorporation would complicate the mathematical model. The structure of layers is reminiscent of the House of Quality roof that represents interactions between engineering characteristics; however, in SOS, they are square, potentially asymmetric, matrices, and each layer handles a single customer or implementation characteristic. Reich and Levy (2004) introduced such matrices for the roof of the House of Quality in order to provide a more accurate model of reality. SOS organizes these interactions differently, making explicit the connection between the information resolution and the structure of the layers. More importantly, QFD deals with prioritizing engineering characteristics (on a quantitative scale), whereas SOS deals with discrete choices that build up a product concept and their mutual constraints. SOS is modular and standardized: -
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Layers can be deleted and introduced. The method of calculating layer priority is open and flexible, e.g., AHP could be used as well as other methods with their benefits and limitations. Layers can be replaced by more complex assessment methods (e.g., simplicity using information content, assemblibility using Dewhurst et al. (2001) method) as long as they could be incorporated in the optimization formulation, Equation (6), in the calculation of Q.
SOS scope is very different from Pugh concept selection; it generates concepts whereas Pugh concept selection selects between available candidates. Nevertheless, there could be a synergy between the two methods. On the one hand, if Pugh concept selection is used, one could model the candidates with their components and interactions between them with respect to each decision criterion. Instead of evaluating a candidate with respect to a datum, the candidate will receive the
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evaluation of each criterion as if it were a layer. This would lead to a more accurate evaluation between the alternatives. On the other hand, SOS produces one optimal concept. However, we could instruct it to generate the 2nd best concept and so forth. In this way, we could generate a list of several best candidates. Subsequently, these candidates could be judged along new criteria externally to SOS by a team of experts using Pugh concept selection. This exercise could be executed with variation on evaluations and layers’ priorities (weights). This makes SOS an easy exploration tool.
4.2
Experience with SOS
SOS has been developed over years of practice and research and evolved into a method for generating optimal product concepts. The method in its present form has already been used in six design projects and it was used to verify the results of eight other design projects. The complete list include: Mini-Van Vehicle, PCB Verification Station, Garden Chair, Inner-Drum Plotter, Turbine Blades Laser Inspection System, Combat Tank, Trailer, Mini A.G.V Robot, deck lifter, Screw Based Sorter Elevation System, Plotter Plates Loading/unloading System, High Speed/High Accuracy Linear Bearing System, Heavy Mobile Launcher, and Upgrade-Accessories for Preprint Plotter. Over the years, SOS use improved tremendously as well as its formulation. For example, starting with the product requirements, collecting or generating the building blocks, and generating the matrices for problems similar to the deck lifter example went down roughly from 25 to 8 h. SOS has been particularly useful in the following design stages: 1. Conceptual design e This is the main reason for developing SOS. 2. Design reviews e Using SOS to present the results in preliminary design reviews (PDRs) has been very productive in focusing the teams on the important issues and addressing them successfully. When used in conceptual design, SOS has provided the following benefits: 1. Reduction of errors e The systematic consideration of all issues leads to generating successful concepts early on in the development process. Without it, errors are easier to surface leading to wasting time and money in unnecessary design iterations.
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2. Improved confidence in the design e Using SOS improves the confidence that the solution indeed solve the problem successfully since all the relevant issues have been considered in a systematic manner. This confidence has led to the saving of development time. 3. Improved designs e Independent of the mathematical model that produces an ‘optimal’ solution, the results produced by SOS has been judged by designers independently to be excellent solutions.
5
Conclusions
SOS builds concepts or configurations out of available building blocks and has the following properties:
1. The method is applicable to many domains (including nonengineering, such as: design a new journal or a banking service). 2. Considering the method utility, it is reasonably easy to understand and execute. 3. The method is flexible and can accommodate new business issues such as outsourcing. Layers could be added to it to enrich any problem representation. Each layer could use the scale that best fits its semantics (e.g., $ for cost, time for life cycle, etc.). 4. The method works well in industrial settings as practiced by the authors. We plan to continue evolving SOS and expand its capabilities. We also intend to approach its evaluation using different research methods in the near future. These include conducting workshops and surveys in industry and use the method in design project courses.
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Saaty, T L (1997) That is not the analytic hierarchy process: what the AHP is and what it is not Journal of Multi-criteria Decision Analysis Vol 6 pp 320e339 Verganti, R (1999) Planned flexibility: linking anticipation and reaction in product development projects Journal of Product Innovation Management Vol 16 pp 363e376 Von Hippel, E (1986) Lead users: a source of novel product concepts Management Science Vol 32 pp 791e805 Yin, R (1984) Case study research and design Sage Publications, Beverly Hills, CA Ziv-Av, A and Reich, Y (2003) SOS e subjective objective system for generating optimal product concepts, in CD-ROM Proceedings of the 14th International Conference on Engineering Design (ICED), The Design Society Zwicky, F (1969) Discovery, invention, research through the morphological approach Macmillan, New York 1. This paper combines parts from, and extends two recent conference papers (Reich and Ziv-Av, 2003; Ziv-Av and Reich, 2003).
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