A structured approach for analysis of design processes

664 E E E TRANSACTIONS ON COMPONENTS, PACKAGING, AND MANUFACTURING TECHNOLOGY-PART A, VOL. 18, NO. 3, SEPTEMBER 1995

A Structured Approach for Analysis of Design Processes

Andrew Kusiak, Member, IEEE, Juite (Ray) Wang, David W. He, and Chang-Xue Feng

Abstract-The purpose of this paper is to present a methodol- ogy for analyzing and improving design processes. The method- ology presented uses a directed graph and the corresponding incidence matrix to represent a design process or the relationship between constraints and variables in a design problem. A qualita- tive analysis approach (critical analysis and concurrency analysis) is used to analyze the process structure and improve it without considering the time aspect. The analysis explores a process structure as well as enhances concurrency of the design process. The critical analysis determines potential activities that may delay a design project and provides suggestions for improvement of the design process. A process with higher degree of concurrency is obtained and therefore the product development time should be reduced. Two examples from electronics illustrate the approach proposed.

I. INTRODUCTION

HE DESIGN process can be a source of competitive T advantage in manufacturing, in particular if the time of product development as well as manufacturing quality and productivity issues are given adequate consideration, Nevins and Whitney [l]. Due to decreasing product life cycles, it is important to reduce the time and cost of product development. In recent years, the concept of concurrent engineering has emerged. It aims at the improvement of product quality, and reducing its development time and cost. However, the complexity of the design process increases and makes it more difficult to manage.

The obstacles in managing the concurrent design process are as follows:

1) The critical path in a design process is difficult to determine, due to uncertain durations of design activities and unplanned activities involved.

2) A design project usually involves a large number of design activities and it is difficult to acquire in advance precise information about all of them.

3) Engineering changes occur as the design process pro- gresses.

4) For design activities that are performed in parallel, numerous interactions and information transfers exist. As the number and degree of interaction among ac- tivities increases, the complexity of the design process increases.

Manuscript revised August 1994. This work was partially supported by Na- tional Science Foundation Grant DDM-9215259 and contracts from Rockwell Intemational Corporation and NCS.

The authors are with the Intelligent Systems Laboratory, Department of Industrial Engineering, The University of Iowa, Iowa City, IA 52242-1527 USA.

IEEE Log Number 94097 1 1.

107&9886/95$04

5) Design process of an electronic product involves a number of iterations until design requirements are met.

A. Literature Survey

To date, no tool for management of design processes has been developed. Managers and planners of design projects are using tools that have been developed for other areas and are not particularly suitable for design applications. Some of those tools as well as their characteristics are discussed next.

The critical path method (CPM) introduces two concepts, Kelly [2]: precedence and crash. The first concept empha- sizes the interconnections between activities, namely, their predecessors and successors. The second concept allows one to minimize the duration of a project, or to minimize the crash cost. A detailed discussion of the critical path method is provided in Elmaghraby [3].

The program evaluation and review technique (PERT) is similar to the CPM approach. However, rather than a fixed start and end date of each activity, three time estimates are made:

the probable earliest completion time, the probable latest completion time, the most probable completion time.

Therefore, PERT allows one to incorporate uncertainty in a project.

The CPM and PERT tools are not suitable for managing a design process in electronics due to their weaknesses in representation and analytical capabilities. Thus the critical path of a design project cannot be appropriately identified. A comparison of CPM and PERT is provided in Hillier and Lieberman [4]. The limitations of CPM and PERT (network- based) approaches are summarized as follows:

None of the two approaches allows to represent complex relationships among design activities, e.g., cycles and various types of dependencies. Lack of an analytical tool to improve design processes, e.g., exploring parallelism among activities. Inadequate capabilities to manage the design process when it is difficult to determine or even to estimate the duration of each design activity.

A number of computer tools have been developed based on the IDEF methodology for project definition, U.S. Air Force [ 5 ] . IDEF has been designed to model decisions, actions, and activities of a system. It provides means for approaching and understanding complex systems as well as a standardized way of communicating results among users. The major advantage is

1.00 0 1995 IEEE

1

KUSIAK ef al.: A STRUCTURED APPROACH FOR ANALYSIS OF DESIGN PROCESSES 665

3 4 5

I R

that it helps to ensure quality and enforce good design practices through the use of continuous review and approval mecha- nisms. In this way, costly redesign efforts can be avoided during subsequent product development stages. IDEF tools allow to represent a process, however, they do not offer any capabilities to optimize it.

I + * * 2 * + * *

* + * * * +

+ * 6 * +

+ * A

1 2 3 4 5 6 1 8 9

Based on the above discussion, it is clear that more detailed

(Sathi et al. [6] and Eppinger et al. [7]). A tool for man-

required. It is important to understand the qualitative properties iFi information, such as durations of activities and the resources

of activities, resources, and other project entities and the ways

structured modeling approach initiated by Steward [8]. A

9 *

project is required to manage a design process Fig, 1, Digraph of activities and the corresponding incidence matrix,

agement of design process should tolerate incomplete design 1 1 6 4 2 3 5 8 9

* * + they can be classified, aggregated, abstracted, and summarized. 5 * * +

8 * + The methodology proposed in this paper is based on a * +

directed graph and the corresponding incidence matrix are Fig. 2. Ordered incidence matrix and the corresponding digraph.

used to represent the design process. A qualitative analysis approach, including concurrency and critical analysis, that does not require durations of activities is discussed. The concurrency analysis, which is different from Steward’s [8] and Eppinger’s [7] approach, identifies and enhances the concurrency of a design process. The critical analysis evaluates the behavior of the design process, determines critical activities and provides some suggestions for improvement of the design process. Note that, in this paper, a critical activity means the activity that may block the design process. Our notion of criticality is distinct from the critical activity that is an activity in the critical path defined in the network-based approaches, Kerzner [9].

The remainder of this paper is organized as follows. Section I1 classifies dependencies among design activities and intro- duces a graph representation of the design process. Section I11 presents a structural modeling approach for improvement of the process structure and management of constraints. The concepts presented are illustrated with an example. Section IV concludes the paper.

activity incidence matrix (see Fig. 1). An entry ai j = ‘*’ in the incidence matrix means that activity (row) i is dependent on activity (column) j. An entry “+” represents a diagonal element.

No special structure is visible in the incidence matrix in Fig. 1. Using one of the triangularization algorithms (e.g., Steward [8] or Kusiak et al. [lo]), one can transform the matrix in Fig. 1 into the matrix and the corresponding digraph shown in Fig. 2. The following two facts can be easily observed in the matrix (or digraph) in Fig. 2:

the precedence relationship among activities, the coupled activities (called strongly connected compo-

Activities 6 and 7 are independent and they can be per- formed simultaneously. Activity 5 has to be performed prior to activity 8, because activity 8 depends on activity 5. Activities 1, 2, 3, and 4 are coupled and might be performed iteratively. For a better visual effect, the coupled activities 1, 2, 3 and 4 have been circled in the digraph in Fig. 2.

nents in graph theory, Bondy and Murty [ll]).

11. MODELING THE DESIGN PROCESS B. Classijcation of Dependencies in the Design Process

A. Graph Representation of the Design Process

In the paper, the design process is represented as a directed graph (named process graph) where a vertex denotes an activ- ity and a directed edge denotes a dependency. For example, “a -+ b” means that activity b is dependent on activity a.

1) Process Graph: A process graph G is an ordered triple ( V ( G ) , E ( G ) , QG) consisting of a nonempty set V ( G ) of vertices (activities), a set E ( G ) of arcs, disjoint from V ( G ) , and a mapping function QG that maps every arc onto an ordered pair of vertices (vi: vj). If there is a directed arrow from vi to vj, it is said that vj is dependent on vi.

The process graph can be also represented as an activ- ity-activity incidence matrix, Steward [8]. A non-empty ele- ment in the incidence matrix represents a dependency between the corresponding activities (row and column).

For example, consider six hypothetical design activities represented with a digraph and the corresponding activity-

To analyze and manage design process effectively, it is im- portant to understand the dependencies among design activities that are classified as follows:

1) Information Dependency: If the data required by activity B is produced by activity A, then activities A and B are information-dependent. This dependency can be modified by finding alternative data sources.

2) Technological or Causal Dependency: This dependency is due to some technical relationship between activities. For example, before initiating the finite element analysis, a design draft has to be available. Only a major change, e.g., a technological breakthrough, in the current practice may modify this dependency.

3 ) Common-Sense or Pragmatic Dependency: Common- sense dependency is due to some sensible way of or- dering activities. For example, activities in a detailed design may begin after activities in the conceptual design have been completed. This type of dependency could be

666 IEEE TRANSACTIONS ON COMPONENTS, PACKAGING, AND MANUFACTURING TECHNOLOGY-PART A, VOL. 18, NO. 3, SEPTEMBER 1995

6 7 8 9

10 11 12 13

concepts, customer requirements analysis

* * + * * + * +

+ *

* + * +

* * + * +

I Preliminary design Detail design

- Modify exisling detailed drawlngs

-Create new drawings and

- Identify options, solutions and relevant existing components and manufacturing processes

-Develop new components and integrate existing sub-system

and fabrication and assembly instructions H - Develop new manfactwing processes ins”ions

I I -Create new and update existina I I

Quality testing

coding. integration, evaluation

manufacturing sihedules -Fabrication and assembly. Y

Fig. 3. Seven phase engineering development process.

P-

Fig. 4. Process graph of Phase 3.

ignored at the cost of increased risk of success of the design.

4) Resource Dependency: This dependency is based on a conflict of resource requirements. An activity with this type of dependency can be expedited by incorporating more resources.

5) Preferential Dependency: This type of dependency is based on the preference of an organization.

6) FunctionaWStructure Dependency: If activities belong to the same function or the same structure in a product, then they are functionally/structurally dependent.

Analysis of the dependencies among activities may lead to the weakening or even eliminating some dependencies, such as preferential dependency, common-sense dependency, and resource dependency so that the duration of design process is reduced.

C. The Phased Approach to the Design Process

Due to dynamic nature of the design process and incomplete design information, it is not possible to construct a detailed design plan prior to its execution. It is common that decisions on how to pursue the latter part of a design plan are contingent on the information not available until the early part of the plan has been executed. For example, the design project in Fig. 3 includes seven main phases. The design project starts with the development of strategic plans and marketing concept and analysis of customer requirement. Before the first phase is completed, the second phase “System definitiodrequirements analysis” is not initiated. There are several alternatives that can be generated for the phase “System definitiodrequirements

1 1 1 1 1 1 1 1 1 I 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8

II + 1 :I * + + * 4 * + *

+ * 51

: * j 16 17 18 +

Fig. 5. in Fig. 4.

Activity-activity incidence matrix corresponding to the process graph

analysis.” Depending on the status of the design project after completion of the phase “System requirements analysis,” the most suitable plan can be selected for further decomposition.

Therefore, a complete design plan is developed incremen- tally, phase by phase. Each phase ends with a review activity where the corresponding phase has to be approved before the next phase begins. The example of the design process for a fiber-optic transmission system is shown in Fig. 3.

111. STRUCTURAL MODELING APPROACH TO ANALYSIS OF A COMPLEX DESIGN PROCESS

A. Concurrency Analysis of the Design Process

As discussed in Section 11, design process can be represented as a graph or an incidence matrix. In addition to finding coupled activities, concurrency analysis explores the process structure and promotes the concurrency of activities. The triangularization algorithm presented in Kusiak et al. [12] is used for concurrency analysis of a design process.

Next, the example of a fiber-optic product is used to illustrate the concepts presented in this paper.

1 ) Example 1: Consider the design process of a fiber-optic transmission system that involves hundreds of activities. The design process is divided into seven phases (see Fig. 3). The components definitiodspecification phase (Phase 3), is the focus of this example (For the list of activities in Phase 3, see the Appendix).

The design activities involved in Phase 3 are represented as the process graph shown in Fig. 4. The matrix representation of the design process is shown in Fig. 5. Applying the triangularization algorithm (Kusiak et al. [13]) to the matrix in Fig. 5, the matrix in Fig. 6 is obtained.

Nine levels of activities are identified L(1) = {1,2}, L(2) = {C(1), C(2)}, L ( 3 ) = (91, L(4) = {10,11},L(5) = {13}, and L(6) = {C(3)},L(7) = {12,17},L(8) = {16},L(9) = {18}, where C(l) = {3,4},C(2) = {5,6,7}, and C(3) = {8,15,14} are the coupled activities that were discussed in Section 1I.A.

It is observed that the dependencies among levels of ac- tivities are indicated by elements outside the block diagonal matrices. One may attempt to remove or redefine the depen- dency among levels of activities in order to increase the degree

KUSIAK er al.: A STRUCTURED APPROACH FOR ANALYSIS OF DESIGN PROCESSES 667

performed at level 4. The concurrency of the design process increases. Another motivation for identifying the dependencies

activities 3 and 6 at level L(2). One should complete the activities 1 and 2 as soon as possible in order to begin the

3

4

5 between levels of activities is to monitor the design process. For example, activities 1 and 2 at level L(1) should precede

7

9

10

1 1 downstream activities at L(2).

I + 411 C(I)

2 + / * + <

. + .

+ * U21 * + *

4- U-’) 6 *

. + f + 4 3 J

* + + U4J

B. Discussion

The nine levels of activities in Fig. 6 are represented as a process tree (Fig. 7). A link between any two levels represents dependency between the corresponding levels. It is important to show which upstream activities impact the downstream activities. For example, there are some dependencies between level L( 1) and level L(2) activities. A manager should monitor these activities in order to avoid delay in information transfer to the lower-level activities.

A critical dependency path is defined as the maximum length chain of activities in the process tree, i.e., the path “2 - C(2) - 9 - 11 - C(3) - 17 - 16 - 18” in Fig. 7. A project manager should focus on monitoring activities on the dependency path. It should be noted that the result of concurrency analysis is a “to-be” model of the design process.

In order to measure the improvement of the design process, it is important to define some performance measures. In this paper, the following three measures are used:

1) Maximum duration of the design process

13

8

where d j is the completion time of level j activities; 2) Mean duration of the design process

I 1

f I + 4 5 ) + . I

1 - D = - C d j n

j=1

3) Interaction density among levels of activities D d = e / ( n 2 - C R 2 ) P

k=l where n is the number of rows (columns) in the activity- activity matrix, e is the total number of non-empty elements outside of the block diagonal matrices, p is the number of levels of activities, R k is the number of rows (columns) included in the block diagonal matrix.

The first two measures of the degree of concurrency are based on time. The shorter the duration of the design process, the higher the degree of concurrency. Usually, durations of activities are uncertain in nature. One way is to estimate the duration of an activity is to use the historical data. However, if the duration of design activities is difficult to estimate or the variation is high, the third measure based on the structure of the activity-activity matrix, might be a better choice. The lower the interaction density, the higher the degree of concurrency.

The first two definitions are explained using the data in Fig. 8, where nine levels of activities L(1), L(2), L(3) , L(4),

::I C ( 3 3 - : ;iU6J+ l I I 12

17

16 + U J

471

I R * + 4 9 1

Fig. 6. the matrix in Fig. 5.

Triangularized activity-activity incidence matrix corresponding to

L(5) , L(6)L(7) , L(8). and L(9) have been identified (see Fig. 6). Assuming the durations of each level activities are known, the maximum duration of the design process D,,, is 32. The mean duration of the design process D = (dl + d2 + d3 + d4 + d5 + d6 + d7 + ds + &)/9 = (12 + 22 + 29 + 36 + 43 + 58 + 65 + 72 + 80)/8 = 46.33. The interaction density for the matrix in Fig. 6 is Dd = 0.0438, where n = 18, e = 12, p 19, RI = 2, Rz = 5, R3 = 1, RA = 2, R5 = 1, R6 = 3, R7 = 2, Rs = 1, Rg = 1.

The benefits of concurrency analysis are as follows: 1) A design process with higher degree of concurrency may

be obtained. 2) A critical dependency path is determined without con-

sidering the time aspect. 3) The duration of product development time may be

reduced, due to the increased degree of concurrency of the design process.

C. Concurrency Analysis of Design Problems

Complex designs may involve a large number of design con- straints and variables. In most situations, a design constraint exhibits some degree of coupling, which tends to complicate constraint management. To simplify the constraint manage- ment problem and reduce the computational time of constraint evaluation, concurrency analysis is performed. To analyze a complex design, a constraint-variable incidence matrix is frequently constructed. The objective is to detect potential groups of constraints that can be evaluated concurrently, i.e., to identify overlapping variables and constraints.

To illustrate the concept of concurrency analysis of design problems, a design example of bandpass filters is used (Turner

I ) Example 2: Fig. 9 shows a series m-derived bandpass

The constraints pertaining to design of the series m-derived

~ 4 1 ) .

filter used in many electronic devices (Turner [14]).

bandpass filter are as follows (Turner [14]):

668 IEEE TRANSACTIONS ON COMPONENTS, PACKAGING. AND MANUFACTURING TECHNOLOGY-PART A, VOL. 18. NO. 3, SEPTEMBER 1995

e l e2 e3 e4 e5 e6 e7 e8 e9

e10 e l l e12 e13 e14 el5

Fig. 7. A process tree of Phase 3 of the design process.

+ * * * +

+ + * * * + *

* * * + * * * * * + * * * * +

* * * + * * * + * * * * * + * * + * * * + *

+

* * * *

* + *

*

Group of activities

t

Fig. 8. Gantt chart of the design process

LI P

Fig. 9. Series rn-derived bandpass filter.

e5: m, = 1 - f 2 f 3 I f 4 2

D. Critical Analysis of the Design Process

The analysis introduced in this section identifies critical activities without considering the time aspect. The underlying

KUSIAK et al.: A STRUCTURED APPROACH FOR ANALYSIS OF DESIGN PROCESSES 669

R f2 D f4 f l x m y z LI ~2 ~3 ci c2 c3

Fig. 1 1 . to the matrix in Fig. 10.

Triangularized constraint-variable incidence matrix corresponding

... i j ... /v& ;TI/ * +

V

(a) (b)

Fig. 12. The I-pattern. (a) Graph representation; (b) matrix representation.

concept is to identify possible patterns in the design process and to analyze this pattern accordingly. For each pattern, a critical activity is determined based on the behavior of the pattern. The patterns classified are ranked based on the process structure. For example, two activities in parallel are preferred over serial activities. The overall design process is improved by better management of critical activities in each pattern or by upgrading worse patterns to better patterns.

I) Patterns in the Design Process: A design process may include one or more patterns that reflect the dependency struc- ture among activities. The patterns in the design process are of the following types: interaction (I-pattern), cycle (C-pattern), serial (S-pattern), branch (B-pattern), merge (M-pattern), and branch-and-merge (BM-pattern). Formal properties of each pattern are defined next.

Dejinition: I-Pattern (Interaction): Let GI = (VI, E I ) be a subgraph of G (Fig. 12), where G = (V, E , Q ) is a process graph. A subgraph GI is the I-pattern if and only if it is a directed 2-cycle graph (i.e., the length of the cycle is 2).

Only two vertices (activities), vi and vj, are involved in the I-pattern. Vertex vi is reachable from vj and vice versa. This pattern occurs when two concurrent design activities must collaborate with each other in order to produce the outcome required. The information flows back and forth between the two activities. Depending on the information dependency, two types of collaboration: horizontal collab- oration and vertical collaboration, are defined (Bond [ 151). In the horizontal collaboration, two collaborative activities increase the confidence level of their individual solutions and maintain the consistency of the overall solution. In the vertical collaboration, the relationship between the two activities is viewed as a client-sever relationship. The server activity requests information from a client activity to make design decisions and the client activity provides the information required to the server activity having received a request from the server activity. The server activity modifies a design

... i j k ... + * * +

* +.

Fig. 13. The C-pattern. (a) Graph representation; (b) matrix representation.

decision according to the information provided by the client activity. This process continues until a satisfactory outcome is produced. An I-pattern is easy to be identified from the matrix representation. If the entries a;j = n jz = '*' then activities i and j form a I-pattern.

The critical activity in an I-pattern, is the server activity which makes design decisions and controls the interaction process. The client activities that provide information impor- tant to the server activity are also critical, because they affect the design decision of the server activity.

Dejinition: C-Pattern (Cycle): Let Gc = (VC. E c ) be a subgraph of G (Fig. 13), where G = (V. E . Q ) is a process graph. A subgraph Gc is the C-pattern if and only if it is a directed k-cycle and k 2 2. The length of C-pattern is equal to k which is the length of the cycle.

This pattern occurs, when the level of uncertainty associated with the corresponding activities is high. The upper stream ac- tivities lead to a certain design decision, while the downstream activities provide some feedback information. This iterative process continues until the outcome produced is satisfactory. The C-pattern can be identified by Tarjan's algorithm (Tarjan 1161).

The I-pattern is a special case of C-pattern. For k = 2, it is not possible to distinguish I-pattern from C-pattern based on the matrix representation. The behavior of the two patterns is not the same. The I-pattern defined in this paper mimics a collaborative behavior of two activities, while the C-pattern corresponds to a serial design process with iterations. The length of the C-pattern measured, e.g., by the duration of serial activities, should be reduced in order to reduce the product development time. The larger the length of C-pattern, the longer the product development time. One may improve the process structure by replacing a long cycle with several short cycles (see Table I). Also, one may upgrade C-pattern to I-pattern if possible.

Dejinition: S-Pattern (Serial): Let Gs = (VS. E s ) be a subgraph of G (see Fig. 14), where G = (V, E , Q ) is a process graph. A subgraph Gs is the S-pattern if and only if Gs is a sequence of vertices VI, v2. K ; v k - 1 . Vk such that dGs (vl) = 1, d&s (vk) = 1, and the indegree dGs (vi) = 1 and outdegree d&,? (vi) = 1, where i = 2 , . . . , k - 1. The indegree d;, (vi) of a vertex vi in graph Gs is the number of arcs with tail vi. The outdegree d&, (vi) of vi is the number of arcs with head vz.

Activities in the S-pattern are serial, i.e., an activity cannot start until its predecessors have been completed. A critical activity is the activity with the maximum probability to block the downstream activities.

Definition: B-Pattern (Branch): Let Gg = (VB, E B ) be a subgraph of G (see Fig. 15), where G = (V. E . Q ) is a

670 IEEE TRANSACTIONS ON COMPONENTS, PACKAGING, AND MANUFACTURING TECHNOLOGY-PART A, VOL. 18, NO. 3, SEPTEMBER 1995

TABLE I POSSIBLE STRATEGIES TO REDUCE DURATION OF THE DESIGN PROCESS

Pattem Critical Activity Improvement Interaction .The server activity .Better control of client activities

Serial

Cycle

Branch

Merge

Branch-and-Merge

.The client activity that represents important support work

.Activity prone to reduction of its duration .Activity with the maximum impact on the design (e.g.. maximum duration) .Activity prone to reduction of its duration .Activity with the maximum impact on the design (e.g., maximum duration)

.Diverge activity

*Activities with the information produced important to the converge activity

.Diverge activity

.Activities with the information produced important to the converge activity .Activity with the maximum duration

.Better communication between the server and client activities .Set up a meeting before an activity begins .Perform some activities in parallel (or I-pattem) .Pass information to the downstream activities earlier (overlap some activities) .Pass information to the downstream activities earlier (overlap some activities) .Eliminate the cycle (set up a meeting before an activity begins .Transform a long cycle into several shorter cycles

*Complete the diverge activity as early as possible .Focus on the critical activity to reduce its duration

.Complete the diverge activity as early as possible *Focus on the critical activity to reduce its duration

i j k

* +

Fig. 14. The S-pattern. (a) Graph representation; (b) matrix representation.

e . . 1 2 . e - k ...

" k 1-q *

(a) (b)

Fig. 15. The B-pattern. (a) Graph representation; (b) matrix representation.

process graph. A subgraph GB is the B-pattern if and only if the pattern GB is a one-level rooted tree with root v1 and vertices 24.213 , . . . , Vk in the first level, such that the indegree dGs(v,) = 1. for i = 2 to I C .

This pattern exists when the downstream activities await some design information produced by an upstream activity. The critical activity in B-pattern is the diverge activity. After the diverge activity is completed, the activities in the first level are performed in parallel.

Dejinition: M-pattern (Merge): Let GhI = (V&. E,\!) be a subgraph of G (see Fig. 16), where G = (V, E , rII) is the process graph. A subgraph G11.r is a M-pattern if and only if V(Gbf ) = { v ~ , u ~ : ~ ~ , u k - 1 . ~ k } and vertex u k has the arcs

-. 1 k- l k

(a) (b)

Fig. 16. The M-pattern. (a) Graph representation; (b) matrix representation.

from vertices u1. u2. . . . . U - 1 incident to it, such that

there is no arcs between VI. u2. . . . . p - 1. The M-pattern occurs when an activity has more than

one predecessor directly connected to it. A converge activity (vertex uk in Fig. 16), can begin only after all preceding activities have been completed. The activities that produce the output (e.g., information or components) important to the converge activity are critical activities. More than one critical activity may exist in this pattern. After receiving the information required, a converge activity may begin without all predecessors completed. The activity with the maximum probability to take the longest time becomes a critical activity.

If all successors of an activity have only one predecessor in the B-pattern (i.e., the diverge activity, vertex v, in Fig. 15), then the pattern identified is called a "perfect" B-pattern. In practice, however, some successors may have more than one predecessor. This type of B-pattern with the successors having more than one predecessor is called a BM-pattern, because it combines the properties of the B-pattern and M-pattern.

Definition: BM-Pattern (Branch-And-Merge): Let G B A ~ = ( V B A I . EBnf) be a subgraph of G (see Fig. 17), where G =

KUSIAK et al.: A STRUCTURED APPROACH FOR ANALYSIS OF DESIGN PROCESSES 67 1

(V, E , @) is a process graph. A subgraph GBMis the BM- pattern if and only if the pattern GBM is a one-level rooted tree with root v1 and vertices vp, v3, . . . , vk in the first level, such that at least one vertex vi has the indegree dc,, (vi), where i E [2,lc].

The critical activities in the BM-pattern are also critical for the B-pattern and M-pattern.

In general, an I-pattern tends to be shorter than a C-pattern. However, poor communications among activities in the I- pattern may deteriorate its performance (Kim er al. [17]). Also, a B-pattern, M-pattern, and BM-pattern are preferable over a S-pattern, because some of the activities in the B- pattern, M-pattern, and BM-pattern are performed in parallel. The design process may be improved by replacing one pattern by a preferable one. The possible strategies to improve the design process for each pattern are summarized in Table I.

The overlapping approach mentioned in Table I suggests overlapping some serial activities (see Fig. 18). In other words, each activity begins while the prior activity has not been completed, and thus each activity has to allow for contingencies due to uncertain inputs from the prior activities. Similarly, a prior activity must release its current solution to the later activities to check whether conflicts may arise. If a conflict arises, members of a design team should resolve it. The time when an activity may begin is subject to control. Overlapping should reduce the number of cycles, but each individual activity may take longer time to be completed. However, duration of the entire design process should be reduced.

A procedure for classifying the patterns existing in the design process is presented next.

Pattern Classification Procedure (PCP) Step 1: Identify I-patterns existing in the process

graph. Merge the activities involved in the I-patterns.

Step 2: Identify C-patterns existing in the process graph.

Merge the activities involved in the C-patterns. Step 3: Continue the following steps, until no pattern

can be identified.

graph. (1) Identify S-patterns existing in the process

Merge the activities involved in the S-patterns. (2) Identify B-patterns existing in the process

Merge the activities involved in the B-patterns. ( 3 ) Identify M-patterns existing in the process

Merge the activities involved in the M-patterns. Go to (1).

graph.

graph.

Step 4: Identify BM-patterns existing in the process graph.

Each pattern can be identified based on its properties. Steps 1 and 2 identify all the cycles existing in the process graph and merge each pattern into a vertex. Step 3 determines the remaining patterns in the process graph. The order of the patterns affects the result of condensation. To preserve

p 1 2 ... k ...

(a) (b)

Fig. 17. The BM-pattern. (a) Graph representation; (b) matrix representation.

the dependency structure of the process graph, S-patterns are determined first, then B-patterns, and M-patterns. If no further patterns can be recognized, then stop at Step 3. The last step is to determine the remaining BM-patterns in the design process. Note that an activity may be included in more than one BM- pattern. Since the purpose of critical analysis is to identify potential critical activities, overlapping does not affect the result produced.

E. Illustrative Example

1) Example 3: Using the pattern classification procedure, the patterns shown in Figs. 19-21 are determined from the design process in Example 1. Based on the patterns identified, one can abstract the design process as a hierarchical structure shown in Fig. 22. This hierarchical view provides a focus for improvement of the design process. According to the rules listed in Table I, one may refine critical activities in each pattern or upgrade the nonpreferable patterns.

F. Discussion

Fig. 19 shows the C-patterns identified in the process graph. The activities belonging to a C-pattern should be of interest to a project engineer, due to the information flowing back and forth between activities. The analysis of the C-pattern is discussed next.

A design activity may interact with several other activities. For example, as a design engineer performs the activity “Desigdselect components (activity 6),” s h e requires support from other areas; such as a reliability engineer for updating MTBF estimate and PFR prediction (activity 5), a manu- facturing engineer for providing components manufacturing technology guidance (activity 7), and a purchasing engineer for providing components selection list (activity 2).

The server activity is identified by the row and column of the incidence matrix with the maximum number of entries. It is observed from the matrix in Fig. 23 that activity 6 has two client activities. The server activity (activity 6) initiates this relationship and client activities (activities 5 and 7) support information to the server activity. The client activities have to be active until the server activity is completed.

Activity 6 is a critical activity in pattern C2. because it controls other client activities. Monitoring the progress of activity 6 significantly reduces duration of pattern C2. Another option is that persons participating in the activities included in pattern C2 may have to meet to reduce the number of iterations.

For the S-pattern shown in Fig. 20, some activities may be performed in parallel. For the BM-patterns identified in Fig.

612 IEEE TRANSACTIONS ON COMPONENTS, PACKAGING, AND MANUFACTURING TECHNOLOGY-PART A, VOL. 18. NO. 3. SEPTEMBER 1995

Activitv A Activitv A

(a) (b)

Fig. 18. The serial activities: Non-overlapping versus overlapping. (a) Serial activities without overlapping; (b) serial activities with overlapping.

B1 B2 B3 B4

Fig. 21. The B-patterns.

Process graph c 1 c 2 c 3

Fig. 19. The C-patterns.

s 4 w 3 4 5 6 7

Fig. 22. Hierarchical structure of the process graph in Fig. 4 Fig. 20. The S-patterns.

5 6 7 Server activity 21, four diverge activities, S3 in B1, activity 9 in B2, activity

11 in B3, and C3 in B4 are the potential critical activities. If they are completed, then the downstream activities may begin.

IV. CONCLUSION

The goal of this research was to present an approach to model the design process and to analyze it without detailed design information. The directed graph and the corresponding incidence matrix were used to represent the design process. To simplify and increase the efficiency of the design process, one needs to analyze the relationship among design activities and organize them, accordingly. A qualitative analysis approach, critical analysis and concurrency analysis, that do not require durations of activities were developed to analyze the process structure and to improve the design process.

The purpose of concurrency analysis was to identify and enhance the concurrency of the design process. One may attempt to remove or redefine the dependency between levels of activities to increase the degree of concurrency that reduces the product development time. A better design plan with higher degree of concurrency is obtained and therefore the product development time is reduced.

The critical analysis determines critical activities and pro- vides some suggestions for improvement of the design process. Six basic patterns were defined so that any design process can be classified and transformed into a hierarchical structure. For each pattern, the critical activity is determined without considering the time aspect. The overall design process can be improved by better management of critical activities in each pattern or by upgrading a poor quality pattern into a better one.

The concurrency analysis improves the design process based on the process flow; while, the critical analysis is based on the process structure. The purpose of the two approaches is

Fig. 23. The server activity in pattern C2

the same; i.e., improvement of the design process without the availability of detailed information. One approach com- plements the other.

The benefits of the approach proposed are as follows: A structured view of the design process is provided. Critical activities are determined that should be of focus during the design process. The critical activities should be completed early in order to reduce the product devel- opment time. The degree of concurrency of the design process is enhanced which reduces the product development time. The information flow or dependency structure between activities can be refined so that the product development time is reduced.

The future research is to develop a knowledge-based system employing domain-specific knowledge to analyze the design process based on the types of dependencies between design activities. Some dependencies may be removed by redefining design activities or adding more resources. Another extension is to adapt the concurrency and critical analysis approaches to monitor the design process.

APPENDIX

PROCESS OF A FIBER-OPTIC TRANSMISSION SYSTEM ACTIVITIES INCLUDED IN PHASE 3 OF THE DESIGN

1) Update requirements assessment. 2) Develop components list.

1

KUSIAK et al.: A STRUCTURED APPROACH FOR ANALYSIS OF DESIGN PROCESSES 613

3) Perform logistic analysis of transmission systems. 4) Update logistic analysis report.

[17] J. S. Kim, L. P. Ritzman, W. C. Benton, and D. L. Snyder, “Linking product planning and process design decisions,” Decision Sciences, vol. 23, no. 1, pp. 44450, 1992. 5 ) Update Mean-Time-Before-Failure estimates and Peak-

Failure rate prediction. 6) Desigdselect components. 7) Provide components manufacturing technology guid-

8) Create testing specification. 9) Establish regeneration spacing model. 10) Performance testlequipment design. 11) Develop component module specification. 12) Create interface requirement specifications. 13) Order testlequipment parts. 14) Review system specifications. 15) Release product specifications. 16) Approve product specifications. 17) Review product specifications. 18) Receive product specifications approval.

ance. Andrew Kusiak (M’90) received the Ph.D. degree in operations research from the Polish Academy of Sciences, in 1979.

He is Professor and Chairman of the Depart- ment of Industrial Engineering at the University of Iowa, Iowa City, Iowa. He is interested in engi- neering design and manufacturing. He has authored and edited numerous books, including Intelligent Manufacturing Systems (Prentice Hall 1990), and published research papers in journals sponsored by various societies, including AAAI, ASME, IEEE,

IIE, ORSA, and SME. He serves on the editorial boards of numerous journals, edits book series, and is the Editor-in-Chief of The Journal of Intelligent Manufacturing.

REFERENCES

[ I ] J. L. Nevins and D. E. Whitney, Concurrent Design of Products and Processes: A Strategies for the Next Generation in Manufacturing. New York: McGraw-Hill, 1989.

[2) J. Kelly, Jr., “Critical path planning and scheduling: Mathematical basis,” Operations Res., vol. 9, no. 3, pp. 296320, 1961.

[3] S. Elmaghraby, Activity Networks: Project Planning and Control by Network Models.

[4] F. Hillier and G. Lieberman, Introduction to Operations Research. 5th ed. New York: McGraw-Hill, 1990.

[5] U.S. Air Force, “Integrated computer aided manufacturing (ICAM) architecture, Part 11: Vol. IV-Functional Modeling Manual (IDEFO),” Air Force Materials Lab, Wright-Patterson AFB, Ohio, AFWAL-tr-81- 4023. 1981.

New York: John Wiley, 1977.

A. Sathi, T. E. Morton, and S. F. Roth, “Callisto: An intelligent project management system,” AI Mag., vol. 7, no. 5, pp. 34-52, 1986. S. D. Eppinger, D. E. Whitney, R. P. Smith, and D. A. Gebala, “Organizing the tasks in complex design projects,’’ in 2nd Int. Con$ Design Theory and Methodology, ASME, 1990, pp. 3 9 4 6 . D. V. Steward, Systems Analysis and Management; Structure, Strategy, and Design. H. Kerzner, Project Management. New York: Van Nostrand Reinhold, 1989. A. Kusiak, J. Zhu, and J. Wang, “Algorithms for simplification of the

New York: Petrocelli Books, 1981.

design process,” in Proc. NSF Design and Manufact. Sys. Con$, 1993, pp. 1107-1111.

[ l 11 J. A. Bondy and U. S. R. Murty, Graph Theory with Applications. New York: North-Holland, 1976.

[12] A. Kusiak and J. Wang, “Decomposition of the design process,” J . Mechan. Des., vol. 115, no. 4, pp. 687495, 1993.

[13] A. Kusiak, N. T. Larson, and J. Wang, “Reengineering of design and manufacturing processes,” Comput. Industrial Eng., vol. 26, no. 3, pp.

[14] R. P. Turner, Electronic Conversions, Symbols, and Formulas. Blue Ridge Summit, PA: TAB Books Inc., 1975.

[I51 A. H. Bond and R. Ricci, “Cooperation in aircraft design,” Res. Eng. Design, vol. 4, no. 2, pp. 115-130, 1992.

[I61 R. Tarjan, “Depth-first search and linear graph algorithms,” SIAM J. Comput., vol. 1, no. 2, pp. 146160, 1972.

521-536, 1994.

Juite (Ray) Wang received the B.S. degree in industrial engineering from The National Tsing Hua University, Taiwan, ROC, in 1985, and the M.S. and Ph.D. degrees in industrial engineering from The University of Iowa, Iowa City, in 1990 and 1994, respectively.

He is an Associate Professor of Industrial En- gineering at The Feng Chia University, Taiwan. He is interested in applied artificial intelligence, engineering design, and concurrent engineering.

David W. He received the B.S. degree in metallur- gical engineering and the MBA degree.

He is currently a Ph.D. candidate in the De- partment of Industrial Engineering at The Univer- sity of Iowa. He has published papers in IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION and European Journal of Operational Research.

Chang-Xue Feng received the B S and M.S de- grees in mechanical engineering from Wuhan Uni- versity of Transportation Science and Technology, and the M S degree in industnal engineenng from the University of Iowa, Iowa City, where he IS

pursuing the Ph D degree in industnal engineenng His research interests are in concurrent engineer-

ing and manufactunng Mr Feng is a student member of ASME, ASQC,

IIE, ORSA, SME, and TIMS.