doi 10.1007/s00163-003-0036-2 information hiding in...

Information hiding in product development: the design churn effectAli Yassine, Nitin Joglekar, Dan Braha, Steven Eppinger, Daniel Whitney

Abstract Execution of a complex product developmentproject is facilitated through its decomposition into aninterrelated set of localized development tasks. When alocal task is completed, its output is integrated throughan iterative cycle of system-wide integration activities.Integration is often accompanied by inadvertentinformation hiding due to the asynchronousinformation exchanges. We show that informationhiding leads to persistent recurrence of problems(termed the design churn effect) such that progressoscillates between being on schedule and falling behind.The oscillatory nature of the PD process confoundsprogress measurement and makes it difficult to judgewhether the project is on schedule or slipping. We de-velop a dynamic model of work transformation to deriveconditions under which churn is observed as an unin-tended consequence of information hiding due to localand system task decomposition. We illustrate theseconditions with a case example from an automotivedevelopment project and discuss strategies to mitigatedesign churn.

Keywords Product development, Design processmodeling, Decomposition and integration, Componentand system performance generation, Information hiding,Design churn

1Introduction‘‘We just churn and chase our tails until someone saysthat they won’t be able to make the launch date.’’

(Anonymous product development manager at an auto-mobile manufacturer). The difficulty in accurately mea-suring individual activity progress within the context ofthe overall program goals is well understood by productdevelopment (PD) managers. The above quote is takenfrom a study of PD management practices at a largeautomotive company (Mar 1999). Progress oscillatesbetween being on schedule (or ahead of schedule) andfalling behind. In many instances, development tasks arerepeated and no one knows why. This is a universalphenomenon in PD settings. For instance, in the softwaredevelopment realm, Cusumano and Selby (1995) reportthat progress is measured by the number of bugs thattesters report to developers during the developmentprocess. They show a bug report oscillating from a highnumber of bugs to a low number and back to a highnumber and so on. Other histories showing oscillatorybehavior in PD processes have been observed in aero-space (Browning et al. 2002), automotive (McDaniel 1996;Mar 1999), electronics (Wheelwright and Clark 1992),and information system development (Joglekar 2001)settings.

The motivation for studying the churn phenomenonis abundant. The oscillatory nature of PD progressmakes it hard to measure actual developmentprogress and ultimately difficult to judge whether theproject is on schedule or slipping. Other unfortunateconsequences of churn may include significant increasein development times, organizational memory lapsesregarding PD problem solving know-how, and deterio-rated morale amongst developers. There are few mana-gerial guidelines available for dealing with churn.Typically, a lack of understanding for the underlyingcauses of churn leads to myopic resource allocationdecisions.

In this paper, we take an information-processing viewof PD by characterizing the development process as asequence of problem-solving activities (Clark andFujimoto 1991). Design churn is defined as a scenariowhere the total number of problems being solved (or pro-gress being made) does not reduce (increase) monoto-nically as the project evolves over time.

There are several possible explanations for churn andthis paper investigates one of them: the informationdependencies among activities; that is, the structure of thedevelopment process. The information processing viewpostulates design decomposition to be a nested series ofgeneration and testing activities (Simon 1996). If testingoccurs simultaneously with the generation activities, then

Research in Engineering Design 14 (2003) 145–161

DOI 10.1007/s00163-003-0036-2

145

Received: 6 September 2002 / Revised: 12 June 2003Accepted: 13 June 2003 / Published online: 5 September 2003� Springer-Verlag 2003

A. Yassine (&)Department of General Engineering,University of Illinois at Urbana-Champaign,313 Transportation Building, Urbana, IL 61801, USAE-mail: [email protected].: 217-333-8765Fax: 217-244-6165

N. JoglekarBoston University, Boston, MA 02215, USA

D. Braha, S. Eppinger, D. WhitneyMassachusetts Institute of Technology,Cambridge, MA 02139, USA

Original paper

the process will not churn1. In reality, generation-testingcycles have built-in delays. This paper develops a gener-ation-testing model with the capability to consider inte-gration of several generation groups in the presence ofdelays2. The structure of the development process inher-ently results in some of the information related to thedesign tasks being sometimes hidden from other devel-opers and managers3. Our premise is that in many devel-opment scenarios, design churn becomes an unintendedconsequence of information hiding. This is consistent withthe ill-structured nature of design problems (Braha andMaimon 1998)4.

Imperfect evaluation in the test activity may also causechurn. For instance, some systems exhibit nonmonotonicchange in either the variance or the expected value (andsometimes both) of design parameters due to uncertaintyin performance evaluation (Browning et al. 2002). Inorder to avoid the confounding effects of variability (as itwill only exacerbate churn), we deal only with theexpected values and exclude performance variation as aplausible source of churn. Other explanations for churnare also possible. Exogenous changes (e.g., a change incustomer requirements) to design objectives also lead tochurn (Mar 1999). Again, such changes will only con-found the analysis of our basic premise and are excludedfrom the model. Furthermore, oscillatory allocation ofresources as in ‘‘firefighting’’ models (e.g., Repenning etal. 2001) and in behavioral choice models (e.g., Ford andSterman 1999) exhibit churn-like behavior. These expla-nations are also excluded from our model based onsimilar rationales.

We explore our premise by developing a model fortracking the progress of PD processes while accountingfor information hiding. Our model divides the develop-ment process into two interdependent task sets: localand system. The structure of this problem-solving pro-cess is set up such that local tasks, by definition, cannothide information from system tasks about their indi-vidual progress and problems. On the other hand, sys-tem tasks may withhold information (gathered fromlocal tasks) for limited periods of time before releasingit to local tasks. Between these releases, the informationis hidden from local tasks, which work based on pre-viously released information. Our model focuses onchurning that is caused by these episodic releases ofinformation.

Analysis of churn due to information hiding raisesinteresting questions about the convergence of theunderlying system. We define PD convergence as a pro-

cess in which the total number of problems being solvedfalls below an acceptable threshold. That is, the problem-solving activities result in a technically feasible designwithin a specified time frame5. The main results obtainedfrom the analysis of this model are summarized asfollows:

1. The existence of design churn is a fundamental char-acteristic of the decomposition and integration of de-sign between local and system teams. More specifically,it is shown that design churn may be attributed to twomodes. The first mode reflects the ‘‘fundamental churn’’of the design process, and the second mode, termed‘‘extrinsic churn’’, may be present depending on therelative rates of work completion and the rework in-duced between system and local tasks.

2. It is possible for development processes to exhibitchurning behavior under both converging and diverg-ing scenarios. Conditions under which the total numberof design problems associated with the system and localtasks converges to zero as the development time in-creases are presented.

The rest of the paper is organized as follows. In thenext section, we discuss the literature relevant to infor-mation hiding and design churn. In Sect. 3, we propose amodel for asynchronous information exchanges in adevelopment environment. In Sect. 4.1, we introduce aPD model that involves a single local development teamand single system integration team, and that accounts forinformation hiding. The basic model is formulated andanalyzed in the rest of Sect. 4, where conditions for theconvergence of the design process as well as ‘‘pure designchurn’’ are presented. In Sect. 5, we present a generalizedmodel that involves multiple local development teamsthat exchange information, under more general infor-mation release policies, with a corresponding systemintegration team. In Sect. 6, we apply the findings of themodel to analyze the appearance design process for anautomotive product development project. In Sect. 7, wediscuss the managerial implications by identifying miti-gation strategies to counter design churn in complexdevelopment processes.

2Literature reviewInformation hiding is not a new concept in managementscience. For instance, in the supply chain managementliterature, information hiding has been justified ongrounds of either asymmetrical or distorted availability ofinformation (Lee et al. 1997). Similar ideas have beenexplored in a segment of PD literature. For instance, insoftware development projects, information hiding refersto the practice of keeping the implementation details of asoftware module hidden from other modules in the pro-gram (Sullivan et al. 2001). Typically, such practices arejustified by the desire to reduce the coordination burden.However, formal models for capturing the effects ofinformation hiding are rare in the PD literature.

1 It is customary in the PD literature to presume that a fullyconcurrent generation-testing cycle does not create more prob-lems than it solves (Smith and Eppinger 1997).2 In Sect. 3, we propose a generalized decomposition model,where the generation activities are assigned to local or specializedgroups, while testing is conducted by system-wide test and inte-gration groups.3 Wheelwright and Clark (1992) describe how PD projects fail tomeet their original potential due to intrinsic characteristics of theprocess and not due to a lack of creative people, technical skills,or management skills within the PD organization.4 We thank one of the anonymous reviewers for pointing this out.

5 A formalization of convergence in terms of conditions for sta-bility is presented in Sect. 4.3.

Res Eng Design 14 (2003)

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There are several management science models thatrelate to one or more aspect of PD design churning. Wegroup these models into the following categories: set-based concurrent engineering, resource allocation, andinformation dependency. These models are describednext.

Sobek et al. (1999) describe a method to modelconvergence in Toyota’s PD process, called set-basedconcurrent engineering (SBCE). With SBCE, Toyota’sdesigners think about sets of design alternatives, ratherthan pursuing one alternative iteratively. As thedevelopment process progresses, they gradually narrowthe set until they come to a final solution. SBCEliterature does not focus on instances where designchurn is possible; however, it is possible to extend thesemodels to demonstrate and study churn (Mihm et al.2001).

Information interdependency between developmentactivities is an important feature of complex productdevelopment processes (Eppinger et al. 1994).Interdependency is manifested and measured by theamount of iteration and rework inherent in a PD pro-cess. The Design Structure Matrix (DSM) provides asimple mapping to capture interdependencies within adevelopment process (Eppinger 2001; Browning 2001;Yassine and Braha 2003). As will be shown later in thepaper, DSM models may exhibit divergent churnbehavior; however, both Smith and Eppinger (1997) andBrowning and Eppinger (2002) artificially suppress thisbehavior.

Resource allocation has been identified as a manageriallever for controlling the rate of PD process completion(Ahmadi and Wang 1999). Bohn (2000) and Repenninget al. (2001) define the ‘‘firefighting’’ syndrome as thepreemption of important, but not urgent, developmentactivities due to an imminent necessity or problem (re-ferred to as a ‘‘fire’’) in another part of the same devel-opment project (or another development project). Movingresources from one part of the project to another (or fromone project to another) may trigger a vicious cycle offirefighting. As a result, PD performance will oscillate.Conventional PD resource allocation studies (Adler et al.1995; Loch and Terwiesch 1999) model waiting effectswithout focusing on design churn.

Our treatment of design churn builds on the PD liter-ature of task concurrency, information dependency, andresource allocation constructs. In particular, we use a DSMmodel as a building block to expand upon by introducing

asynchronous information delays with these constructs6.In the next section, we establish the linkage betweenasynchronous interdependencies and the DSM.

3Asynchronous information interdependencyin design processesIn a large and complex PD project, different developmentgroups work concurrently on multiple aspects of theprocess (Joglekar et al. 2001). Work progresses within eachgroup through internal iteration. Coordination betweengroups takes place through system level testing or anintegration group. Individual (i.e., local) groups providestatus updates to the system group. This information isprocessed based on global considerations, which may re-sult in rework for some of the individual groups. Figure 1shows a schematic of the information exchanges within thePD process described above. In the left side of the figure,we describe how a set of local development teams, workingconcurrently on a common project, interact through asystem level team that coordinates and orchestrates theirindividual development efforts. The double-headed arrowsdemonstrate the two-way communication that takes place.The right side of the figure depicts the interaction processbetween a single local development team and the systemteam. The solid arrow indicates that local teams frequentlyprovide the system team with updates regarding theirprogress, while the dotted arrow indicates that the systemteam provides intermittent feedback to the local team.

The frequency of system level feedback might dependon either exogenous considerations (such as suppliers’ability to provide updates) or endogenous considerationssuch as system level test requiring a minimal turn aroundtime for a desired fidelity (Thomke and Bell 2001). If thesynchronization is effectively instantaneous, for exampleduring daily builds of Microsoft’s development cycles,then we can think about the whole process in terms of aunified (combining local and system level) structure.Smith and Eppinger (1997) have developed a method usinglinear systems theory to analyze such models and identi-fied controlling features of a unified iteration process.Unified iteration does not allow for information delays

Fig. 1a, b. Local and system bifurcationof information

6 A control theory-based matrix formulation using the DSM is aconvenient approach to build our argument. However, the coreideas can be built using alternative approaches. See, for instance,Mihm et al. (2001) for a selective evolutionary based exposition ofrelated PD decisions.

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between local and system task execution. However, manyPD processes are characterized by intermittent systemfeedback7. Hence, we explore the management of multipledevelopment teams coordinated through a system inte-gration team and subject to periodic feedback (Joglekarand Yassine 2001).

The DSM shown in Fig. 2 captures the above develop-ment setup. The DSM is composed of blocks that representseveral local development teams and a system integrationteam. The system team facilitates interactions betweenlocal teams as represented by the solid arrows in the figure.The local DSMs are internally updated at every time step(DT), and provide status information to the system DSM atti,S periodic intervals. The system DSM provides updates tothe local DSMs at periodic intervals T1,T2,…,Tm. The localand system update periods (i.e., ti,S‘s or Ti’s) may or maynot be synchronous; e.g., T1 ¼ k1DT; . . . ;Tm ¼ kmDTwhere ki are integer constants for all i’s. In addition, thedotted arrows demonstrate an instance where local teamsare allowed to interact directly (i.e., without the facilitationof the system team), in which case the local DSM Li pro-vides status information to other local DSMs at periodicintervals ti,1,ti,2, . . ., ti,m.

This type of DSM is not a pathological case. Numerousresearchers have documented the existence of this local/system bifurcation (Sosa et al. 2000). The problem cannotbe treated as a single DSM to study the churning proper-ties of the development process due to time delays andasynchrony in information transfers between the systemand different local groups.

4Asynchronous work transformation model:single local DSM case

4.1Model formulationFirst, we study a simplified version of the problem. Weassume, without loss of generality, that there exists asingle local DSM (containing the local tasks required forthe development of a component and performed by alocal development team) that exchanges informationwith a corresponding system DSM (containing the sys-tem tasks required for the development of the samecomponent and performed by a system developmentteam) at every time step. The system DSM releasesinformation every T time steps8. Consistent with Smithand Eppinger (1997), we specify that all the tasks asso-ciated with the local and system DSMs are internallyupdated at each iteration step. We label L(k) as thevector for the amount of ‘‘unfinished work’’ in the localtasks at time k. Absent of all system feedback, the pro-gress of L(k) is given by:

LðkÞ ¼WLLðk� 1Þ k ¼ 1; 2; ::: ð1Þ

The amount of unfinished work can be measured by thetime left to finalize a specific design, the number of engi-neering drawings requiring completion before the designis released, the number of engineering design studiesrequired before design release, or the number of openissues that need to be addressed/resolved before designrelease, to name a few (McDaniel, 1996). The choice isdependent on the particular design environment pertain-ing to how the status of development progress ismeasured. At this point, the choice of how to measureunfinished work is immaterial to building the theoreticalfoundations of the proposed model. However, this pointwill be revisited when we illustrate the application of themodel in a specific development environment.

WL is the work transformation matrix that captures thefraction of rework created within a local group of tasks(Smith and Eppinger 1997). Equation 1 describes the worktransformation during each iteration stage as follows.Individual local tasks finish a fraction of their work, givena constant completion rate specified in the diagonal of WL.However, this work causes some rework to be created toother dependent local tasks. The off-diagonal elements ofWL document such dependencies. The construction of WL

is detailed in Appendix 1.We augment the state space for the above model by

introducing two more vectors: S(k) and H(k). The vectorS(k) represents the amount of unfinished work in allsystem tasks at time step k, and H(k) is a vector for theamount of finished system work at time step k that is readyto be transmitted to local tasks but remains hidden until itis released. We also define a matrix WS that corresponds to

Fig. 2. DSM representation of a PD process showing local andsystem teams (Li represents a local development team, Srepresents a system team, and the captions next to the arrowsindicate the frequency of information update)

7 This is a common PD observation since system teams need timeto absorb and integrate all the local information they receivebefore sending feedback. Consequently, there is a delay from thetime system teams receive local information until the time theysend it back to local teams. Furthermore, information hiding anddelays occur due to the fact that local teams, once they receivesystem feedback, do not usually drop all things at hand andimmediately act on or respond to this new information. Usually,this new information is queued or batched with other updates.

8 The model is capable of accommodating multiple local DSMs asdiscussed in Sect. 5. Furthermore, for the sake of simplicity andease of exposition, we assume that these local DSMs and thesystem DSM have the same rank. Finally, the system can releaseinformation once or in multiple periods.


148

S(k) in a manner analogous to the relation between WL

and L(k), that is

SðkÞ ¼WSSðk� 1Þ k ¼ 1; 2; ::: ð2Þ

Combining both state equations (Eqs. 1 and 2)and incorporating both types of informationexchanges (from local to system and vice versa), weobtain the state equation (Eq. 3). This equationassumes that the system transmits all the work withheldup until the last moment before data transmittal to localtasks.

Lðkþ 1ÞSðkþ 1ÞHðkþ 1Þ

24

35 ¼

WL 0 0

WLS WS 0

0 WSH I

24

35

|fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}AHold

LðkÞSðkÞHðkÞ

24

35ð1� dTðkÞÞ

þWL WSL IWLS WS 0

0 0 0

24

35

|fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}ARelease

LðkÞSðkÞHðkÞ

24

35dTðkÞ

ð3Þ

In Eq. 3, dTðkÞ ¼P1j¼0

dðk� jTÞ is the periodic impulse train

function, where dðk� nÞ is the unit impulse (or unitsample) function defined as:

dðk� nÞ ¼ 1 k ¼ n0 k 6¼ n

�ð4Þ

As can be seen from Eq. 3, the updated amount ofdesign work for a local team depends on the team’sprevious amount of design work and the interactionwith the system team; similar conclusions can be ob-tained regarding design tasks for the system team andhidden tasks. The matrix AHold is active at each iterationstep except for every T periods when the system teamreleases its feedback to the local team and the matrixARelease becomes active. WLS is a matrix that capturesthe rework fraction created by local tasks L(k) for thecorresponding system tasks S(k). Similarly, when infor-mation is released by the system, the matrix WSL cap-tures the rework fraction created directly by the systemtasks S(k) for the local tasks L(k). WSH is a matrix thatcaptures the rework created for the local tasks by thesystem tasks, and is placed in a hidden (or holding)state until it is time to be transmitted to local tasks.When no information is being released by the system tolocal tasks, the identity submatrix in AHold guaranteesthat finished system work is carried over to the nextperiod. The identity submatrix in ARelease guarantees thatfinished system work is transmitted to local tasks,through H(k), every T time steps. Consequently, H(k)gets set to zero each T steps and is rebuilt in between.The construction of the work transformation matricesWL, WS, WLS, WSH, and WSL is dependent on thestructure of the information exchanged within thedevelopment process. In Appendix 1, we specify (con-sistent with the case study presented in Sect. 6) the worktransformation matrices based on the local and system

DSMs XL;XS; as well as the inter-component dependencymatrices XLS;XSL; which represent the interaction be-tween local and system teams9.

Individual elements within the L, S, and H vectorsrefer to the same task. To illustrate the concept, con-sider the following two tasks: door trim design andgarnish trim design related to the development of a cardoor. The state equations for this problem are shown inEqs. 5 and 6 for the case when no information is beingreleased by the system (e.g., the ‘‘body’’ integrationteam) to local tasks (e.g., the ‘‘door’’ design team), andfor the case when information is released by the system,respectively.

In this example, L1(k) and S1(k) may designate thenumber of design problems or open issues associated withthe door trim task, for the local design team and systemintegration team, respectively. H1(k) refers to the numberof door trim problems resolved by the system integrationteam awaiting to be released to the local design team. Anyproblem associated with the door trim design can reside inonly one of these three states until it is fully resolved. Notethat 1� wL

11 and 1� wL22 are the fractions of L1 and L2

respectively that can be completed in an autonomousmanner in every time step. Furthermore, wL

12L2ðkÞ andwL

21L1ðkÞ are the amounts of rework that get created fortasks L1 and L2, respectively, as a consequence of theautonomous progress. Similar interpretations can be madefor the system matrix (i.e., wS

ij).

L1ðkþ1ÞL2ðkþ1ÞS1ðkþ1ÞS2ðkþ1ÞH1ðkþ1ÞH2ðkþ1Þ

26666664

37777775¼

wL11 wL

12 0 0 0 0wL

21 wL22 0 0 0 0

wLS11 wLS

12 wS11 wS

12 0 0wLS

21 wLS22 wS

21 wS22 0 0

0 0 wSH11 wSH

12 1 00 0 wSH

21 wSH22 0 1

26666664

37777775

L1ðkÞL2ðkÞS1ðkÞS2ðkÞH1ðkÞH2ðkÞ

26666664

37777775

ð5Þ

L1ðkþ1ÞL2ðkþ1ÞS1ðkþ1ÞS2ðkþ1ÞH1ðkþ1ÞH2ðkþ1Þ

26666664

37777775¼

wL11 wL

12 wSL11 wSL

12 1 0wL

21 wL22 wSL

21 wSL22 0 1

wLS11 wLS

12 wS11 wS

12 0 0wLS

21 wLS22 wS

21 wS22 0 0

0 0 0 0 0 00 0 0 0 0 0

26666664

37777775

L1ðkÞL2ðkÞS1ðkÞS2ðkÞH1ðkÞH2ðkÞ

26666664

37777775ð6Þ

4.2Model analysisIn this section, we explore the fundamental characteristicsof the model described in Eq. 3. All proofs are presented inAppendix 2.

First, we notice that Eq. 3 can be rewritten as follows:

xðkþ 1Þ ¼ AðkÞxðkÞ

9 The local and system DSMs as well as the inter-componentdependency matrices represent the amount of rework created foreach task based on work done on the other tasks in the previousperiod.


149

where xðkÞ ¼LðkÞSðkÞHðkÞ

24

35 and

AðkÞ ¼WL dTðkÞWSL dTðkÞIWLS WS 0

0 ð1� dTðkÞÞWSH ð1� dTðkÞÞI

2664

3775 ð7Þ

Thus, the model described in Eq. 3 is a homogenouslinear difference system that is nonautonomous, or time-variant. Moreover, since the impulse train function dTðkÞis periodic with period T (recall that the system DSM re-leases information every T time steps), we conclude thatfor all k�Z (where Z is the set of all positive integers),A(k+T)=A(k). That is, the model described in Eq. 7 is alinear periodic system.

We now present some results obtained using Floquettheory (Richards 1983) for the linear periodic system givenin Eq. 710.

Definition 1Matrix C ¼ AðT � 1ÞAðT � 2Þ � � �Að0Þ is referred to as themonodromy matrix of Eq. 7.In the following we assume that the monodromy matrix is

diagonalizable11. C is diagonalizable if and only if it haslinearly independent eigenvectors. A sufficient conditionfor C to be diagonalizable is that it has distinct eigenvalues(Strang 1980). We cite the following result from Richards(1983) as Lemma 1, Theorem 1, and Corollary 1 to set upfurther analysis.

Lemma 1Let C be a diagonalizable n·n matrix, and let T be anypositive integer. Let us decompose C as C ¼ SCKCS�1

C ;where KC is a diagonal matrix of the eigenvalues of C, andSC is the corresponding eigenvector matrix. Then, thereexists some n·n matrix B such that BT=C. Moreover,B ¼ SCKBS�1

C ; where KB ¼ffiffiffiffiffiffiKC

Tp

:The following resultindicates that the analysis of the periodic system describedin Eq. 7 is reduced to the study of a correspondingautonomous linear system.

Theorem 1If y(k) is a solution of the autonomous linear system

yðkþ 1Þ ¼ ByðkÞ ð8Þ

then the general solution x(k) of the linear periodic system(Eq. 7) is given as follows:

xðkÞ ¼ PðkÞBkg ð9Þ

where P(k) is a nonsingular periodic matrix of period T,and g 2 Rn is a constant vector12.

Corollary 1The general solution x(k) of the linear periodic system(Eq. 7) is given by

xðkÞ ¼ PðkÞyðkÞ ð10Þ

where y(k) is the general solution of the autonomous linearsystem (Eq. 8).

Corollary 1 has the following interesting interpreta-tion for the information hiding problem in PD. We notethat there are two sources of oscillation that govern thedevelopment of the total number of problems beingsolved as the project evolves over time. The first sourceis associated with the periodic matrix P(k) in Eq. 10,and reflects the ‘‘fundamental churn’’ of the process.This fundamental churn may be attributed to theintrinsic characteristic of information delays betweenlocal and system task execution. The second source ofoscillation, termed ‘‘extrinsic churn’’, is associated withthe properties of the linear autonomous system (Eq. 8)as discussed in Smith and Eppinger (1997). More spe-cifically, positive real eigenvalues of B correspond tononoscillatory behavior of the solution y(k). Negativeand complex eigenvalues of B describe damped oscilla-tions. The overall property of the linear periodic system(Eq. 7) is thus the combined effect of both sources ofoscillation.

Corollary 1 allows the development of conditions underwhich the linear periodic system (Eq. 7) converges (i.e., asthe time increases to infinity the total number of designproblems associated with the system and local tasks con-verges to zero). We show in Sect. 4.3 that the eigenvaluesand the eigenvectors of the matrix B determine conditionsof convergence.

4.3Conditions for stabilityIn this section, we present conditions under which thetotal number of design problems associated with the sys-tem and local tasks converges to zero as the time increasesto infinity.

First, we note that the zero solution is an equilibriumpoint13 of Eq. 7. Next we introduce the definitions of sta-bility of the equilibrium point.

Definition 2The equilibrium point x� is

10 Floquet theory has been mainly applied in the mathematicaland the physical sciences (Kuchment 1993). However, to the bestof our knowledge, Floquet theory has not been applied in thesocial and management sciences.11 This assumption is reasonable as discussed in Smith andEppinger (1997). Even if this assumption is violated, our quali-tative results will remain unchanged; however, the computationof the underlying matrices becomes more complicated.

12 Any solution of Eq. 8 may be obtained from the generalsolution by a choice of vector g based on initial conditions.13A point x* is called an equilibrium point of Eq. 7 if x� ¼ AðkÞx�for all k‡0.


150

1. Stable if given egt; 0 there exists d ¼ dðeÞ such thatx0 � x�k k < d implies xðkÞ � x�k klt; e for all k‡0. x� is

unstable if it is not stable.2. Globally attracting if limk!1 xðkÞ ¼ x� for any initial

work vector x0.3. Asymptotically stable if it is stable and globally

attracting.

Intuitively, the zero solution is stable if the totalnumber of design problems associated with thesystem and local tasks remains bounded as the projectevolves over time. Asymptotic stability requires theadditional condition that the total number ofdesign problems associated with the system and localtasks converges to the origin for any initial workvector.

When the PD process involves time delays andasynchrony in information transfer between thesystem and local group, conditions for the convergenceof the development process are of vital importance forPD management. Before we present stability conditionsfor the asynchronous work transformation model, weintroduce the so-called Floquet exponents and Floquetmultipliers of the linear periodic system (Eq. 7). Floquetexponents are the eigenvalues k of B, while thecorresponding eigenvalues kT of the monodromy matrix(C) are the Floquet multipliers. We have the followingresult:

Theorem 2The zero solution of Eq. 7 is stable if and only if theFloquet exponents have magnitude less than or equal to 1,and asymptotically stable if and only if all the Floquetexponents have magnitude less than 1.

The following provides an additional result that ex-plains the behavior of solutions of the asynchronous worktransformation model:

Corollary 2The zero solution of Eq. 7 is stable if the Floquet multi-pliers have magnitude less than or equal to 1 andasymptotically stable if all the Floquet multipliers havemagnitude less than 1.

A direct consequence of Theorem 2 is that the Flo-quet exponents and their corresponding eigenvectors(i.e., eigenvectors of B) determine the rate and nature ofconvergence of the design process. Consistent withSmith and Eppinger (1997), we use the term designmode to refer to an eigenvalue of B along with itscorresponding eigenvector14. The magnitude of eacheigenvalue of B determines the geometric rate of con-vergence of one of the design modes, while the corre-sponding eigenvector identifies the relative contribution

of each of the various constituent tasks to the amount ofwork that jointly converges at the given geometric rate(Smith and Eppinger 1997). The eigenvector corre-sponding to the largest magnitude eigenvalue of B (mostslowly converging design mode) provides useful infor-mation regarding design tasks that require a significantamount of work. More specifically, the larger the mag-nitude of an element in that eigenvector, the strongerthe element contributes to the slowly converging designmode.

4.4Conditions for ‘‘pure churn’’‘‘Pure design churn’’ is defined as a scenario wheredevelopment progress oscillates freely as the projectevolves over time and neither convergence nor diver-gence occurs. Pure design churn means that the amountof unfinished work does not decrease simultaneously forall of the tasks. Instead, the amount of unfinished workshifts from task to task as the project unfolds. The abovescenario is represented by particular solutions that areperiodic, i.e., solutions x(k) where for all k�Z,xðkþ NÞ ¼ xðkÞ for some positive integer N. The fol-lowing results hold:

Theorem 3

1. The linear system (Eq. 7) has a periodic solution ofperiod T if the monodromy matrix C has an eigenvalueequal to 1.

2. The linear system (Eq. 7) has a periodic solution ofperiod 2T if the monodromy matrix C has an eigenvalueequal to )1.

3. If the largest magnitude eigenvalue of the monodromymatrix C equals 1 and is strictly greater (in absolutevalue) than any other eigenvalue, then the limitingbehavior of the general solution of the linear system(Eq. 7) is periodic with period T.

5Asynchronous work transformation model:multiple local DSM caseIn this section, we consider the general case where mul-tiple local teams are coordinated through a system inte-gration team and subject to periodic feedback. Morespecifically, the m local DSMs are internally updated andprovide status information to others (local and systemDSMs) at every time step. The system DSM provides up-dates to the m local DSMs at periodic intervals T1;T2;:::;Tm

as shown in Fig. 2.We label Li as the vector that designates the amount of

unfinished work of the tasks of local team i (i=1,...,m) attime k. Let ni denote the number of local tasks in local teami, and let n ¼

Pni denote the total number of tasks in all of

the local teams. Individual elements within the Li

(i=1,...,m), Si, and Hi vectors refer, correspondingly, to thesame task. In general, the system of equations is written asfollows:

14 For autonomous linear systems (i.e., A(k)=A), the period of thematrix A(k) is T=1, the monodromy matrix C=A, and theFloquet multipliers are simply the eigenvalues of A. Thus, theSmith and Eppinger (1997) model is a special case of Eq. 7.


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In the above expression, WLi is a work transformationmatrix that captures the fraction of rework created withinthe group of tasks of local team i. WS is the work trans-formation matrix that captures the fraction of reworkcreated within the system tasks. WSi,Hj is a nj·ni matrixthat captures the fraction of finished system work createdby system tasks Si(k) for the local tasks Lj(k) , and is heldin Hj(k) until the next scheduled information release.

WLi,Lj is a nj·ni matrix that captures the fraction of reworkcreated by local tasks Li(k) for the local tasks Lj(k). WLi,Sj isa nj·ni matrix that captures the fraction of rework createdby local tasks Li(k) for the system tasks Sj(k). Sinceinformation is released by the system to local team i onlyat periodic intervals of Ti, the ni·ni diagonal submatrixð1� dTi

ðkÞÞI guarantees that finished system work is car-ried over to the next period. When information is releasedby the system to local team j, the nj·ni matrix dTj

ðkÞWSiLj

captures the fraction of rework created directly by thesystem tasks Si(k) for the local tasks Lj(k). The ni·ni

diagonal sub-matrix dTiðkÞI indicates that information is

transmitted to the local tasks Li(k) indirectly through theholding state Hi(k).

The next result shows that the model described inEq. 11 is a special case of a linear periodic system. Once theperiod of the matrix A(k) is identified, the monodromymatrix C can be determined, and the results presented inSect. 4 can be readily employed.

Theorem 4If the system team provides updates to m local teams atperiodic intervals T1,T2,...,Tm, then the fundamental periodT of the linear matrix A(k) is the least common multiple ofT1,T2,...,Tm; i.e., T ¼ lcmðT1;T2;:::;TmÞ:

Following a similar reasoning as in Theorem 4, it can beshown that any periodic information release policy willlead to a linear periodic system, and thus can be analyzedusing the tools presented in Sect. 4. For example, the localteams may provide status information to others (local andsystem teams) at periodic intervals t1;t2;:::;tm; tsystem;rather than at every time step; or any team (local orsystem) may provide information status to others (local orsystem teams) at nonuniform (but periodic) intervals.Indeed, any such periodic information release policy canbe transformed to a model where all elements aij(k) of thelinear matrix A(k) are periodic functions (with possibly

nonidentical periods). In this case, Theorem 4 can beadapted by letting the fundamental period T of the linearmatrix A(k) be the least common multiple of the periods ofthe elements aij(k).

6Case study: the automotive appearance design processIn this section, an illustration of the asynchronous worktransformation model in a real product development pro-cess, previously reported by McDaniel (1996), is presented.We intend to demonstrate internal process dynamics, showthat oscillatory patterns arise in an asynchronous PD pro-ject, and assess several mitigation strategies by exploitingthe results developed in the paper. In Sect. 6.1, we provide ageneral overview of the nominal automotive appearancedesign process. Section 6.2 demonstrates how to constructthe underlying work transformation matrices. Then, inSect. 6.3 we analyze the base case model. Section 6.4assesses the efficacy of churn mitigation strategies based onthree operational scenarios. Finally, results of sensitivityanalysis are presented in Sect. 6.5.

6.1Appearance design process overviewAppearance design refers to the process of designing allinterior and exterior automobile surfaces for whichappearance, surface quality, and operational interface isimportant to the customer. Such design items include, forexample, exterior sheet metal design and visible interiorpanels. Appearance design is the earliest of all physicaldesign processes, and changes in this stage easily cascadeinto later development activities causing costly rework.This is avoided by allowing ‘‘stylists’’ (from the industrialdesign group) to work closely with ‘‘engineers’’ (from theengineering design group). While stylists are responsiblefor the appearance of the vehicle, engineers are responsiblefor the feasibility of the design by ensuring that it meetssome functional, manufacturing, and reliability require-ments. Figure 3 shows the industrial design process withinthe context of the overall automotive product developmentprocess. The industrial design portion is allotted approx-imately 52 weeks for completion in a typical vehicle pro-gram.

Records from the study company, shown in Fig. 4,indicate churning behavior for a specific vehicle program.While the curves presented in the figure show churn in

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both interior and exterior subsystem development, ouranalysis of the churn phenomenon will be limited to theinterior design process involving the styling and engi-neering development organizations.

Information exchanges from styling to engineering takethe form of wireframe CAD data generated from claymodel scans, referred to as scan transmittals of surfacedata. Scan transmittals are scheduled at roughly six-weekintervals (i.e., T=6). Information exchanges betweenengineering and styling occur on a weekly basis through ascheduled feasibility meeting. During these meetings var-ious engineering groups provide feedback to styling oninfeasible design conditions. Therefore, with this infor-mation transfer setup engineering will be the local team, asdefined in our model, and styling will be the system team.

In addition to the cross-functional information ex-changes between styling and engineering, informationflows also occur within functional groups. For example,within engineering, a hand clearance study would compileinformation about the front door trim panel and the frontseat to determine whether the two components physicallyinterfere, and whether the space between them meetsminimum acceptable requirements.

Finally, an appropriate metric by which to measuredevelopment progress needs to be defined. We choose touse the number of open design issues (or open problems)although it may be convenient, in other developmentenvironments, to use different measures of progress suchas the time to finish a design task. Our choice is justifiedby the fact that the company we are investigating tracksopen issues on an ongoing basis through minutes from theabove mentioned feasibility meetings. Time to completionestimates are normally forecasted based on the open issuesstatus.

6.2Construction of work transformation matricesFrom the program management perspective, the vehicleinterior is segmented into subsystems, or components.These components represent major subassemblies ofthe interior, and include typical components such as theinstrument panel, the front door trim panels, and thecenter console. This level of component aggregation isused primarily because these components have been theunit of management and budgetary control forengineering design work, and because the companydefined a number of standard engineering designstudies to be performed on each component at this level.

The DSMs XL;XS for the engineering and industrialdesign processes are shown in Figs. 5a and 5b,respectively. The transformation of component-leveldesign information to system-level design information,as used within the industrial design group, is capturedby the ‘‘dependency’’ matrix XLS in Fig. 5c. Thistransformation is typically performed on a weeklybasis, when the engineering group provides feedback tothe industrial design group on infeasible conditions.Similarly, the dependency matrix XSL in Fig. 5dcaptures the impact of industrial design on the engi-neering process at each scan transmittal (on a six-weekinterval).

The average autonomous completion rates per com-ponent are shown along the diagonal of the local andsystem DSMs (i.e., XL and XS; respectively)15. To set abase level of normalized resource usage for each com-ponent, engineers defined the resource usage intensityrequired to accomplish the autonomous completionrates presented in Fig. 5 as one resource-week. TheDSMs for styling and engineering were obtained bycirculating a survey instrument to both groups.Respondents were asked to populate the DSM by esti-mating the pairwise coupling (i.e., dependency strength)between components using S, M, W, or N ratings (i.e.,strong, medium, weak, or none, respectively). Theseestimates were converted into numerical values (byassigning a probability of 0.3, 0.2, 0.1, and 0 for theS, M, W, and N, respectively). Local and system DSMs,as determined by the average of responses of the sur-veys, are shown in Figs. 5a and b. A complete expla-nation of the DSM and dependency matrices in Fig. 5 isgiven by McDaniel (1996).

Fig. 3. Appearance design in relation to total devel-opment process

Fig. 4. Churning behavior observed in a family of vehicleprograms (McDaniel 1996)

15 These rates are obtained by estimating the autonomous com-pletion time for each component and using an exponential decayfunction.


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6.3Base case analysesFor the base case, the largest magnitude eigenvalue of B is0.9943. Because this eigenvalue is so close to 1, this meansthat the system is stable under the above operating condi-tions, and converges very slowly (see Theorem 2). Byinspecting the eigenvector corresponding to the largestmagnitude eigenvalue of B, we observe that the magnitudes(in descending order) of the elements are as shown in Fig. 6.

The interpretation of the ranking, in Fig. 6, is that thelarger the magnitude of an element in this eigenvector, themore strongly the element contributes to the slow con-vergence of this mode of the design process. Thus, theranking of the eigenvectors gives useful information foridentifying the structure of the total work vector. Thisinterpretation is supported by examining the cumulativework, which is obtained by simulating the design process

for 52 weeks, as shown in Fig. 616. We see that the cumu-lative work associated with the local ‘‘instrument panel’’(i.e., L6) is more than the work done on other local tasks.This is primarily due to the large work associated with thesystem instrument panel (see the cumulative work of S6)and the long information delay (T=6) between local andsystem task execution. This phenomenon can be seen byexamining the specific traces for individual local compo-nents as shown in Fig. 7a. As can be seen, the instrumentpanel has the largest number of open design issues at everypoint of time. Also, the oscillatory changes in design statusinduced by new information contained in scan transmittals

Fig. 5a–d. Local, system DSMs, and system/local conversionmatrices

Fig. 6. Eigenvector and corresponding total work

16 For instance, by comparing the local tasks we see that, in allcases, the largest terms in the total work vector are also the largestterms in the largest eigenvector. In our case, the second largesteigenvalue is much smaller than the largest eigenvalue; thus, thesecond mode does not contribute significantly to the total work.


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are apparent. Finally, we observe that even in the completeabsence of external changes, the appearance design processis not completed on time. Design rework and oscillatorybehavior in the process result from the decomposed pro-cess structure and product architecture, and can never beeliminated from the appearance design process. We con-clude that the appearance process must be redesigned tospeed up convergence and mitigate churn.

6.4Mitigation scenariosRecall that the development process is stable, under thebase operating conditions, but converges slowly. McDaniel(1996) reported that several mitigation strategies wereimplemented by the engineering and styling teams inorder to speed up the rate of design progression needed tomeet the required completion date. The analysis developedin this paper provides insight regarding means forachieving stability for a diverging process or speeding upconvergence for a slowly converging process. Note that

some of the mitigation strategies might eliminate thechurn completely while others might mitigate churn bydamping it at a quicker rate. In particular, three types ofmitigation strategies can be applied:

1. Increasing the autonomous design completion rate foreach component (i.e., increasing the fraction of workthat can be completed in an autonomous manner inevery time step).

2. Lessening the pairwise coupling (i.e., dependencystrengths) between components.

3. Increasing the frequency with which design informationis transmitted from the industrial design to the engi-neering process (i.e., reducing the information delay T).

The first strategy can be implemented, for instance, byapplying resources (work efforts) above the normalizedbase-case level, which will result in increased progressbeing made on the independent, autonomous components.The extra resources may be obtained through design

Fig. 7a–d. The effect of mitigation strategies on the behavior ofthe system


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technology, personnel training, overtime, skill level, andother determinants of design productivity. The second andthird strategies can be accomplished, for instance, by usingthe knowledge of the intercomponent coupling as an aid tomaking colocation on teaming arrangements (McCord andEppinger 1993), or by using a variety of formal andinformal mechanisms to facilitate the management of de-sign information flows (Braha 2001).

Figures 7b and 7c present the effect of the first twomitigation strategies on the behavior of the base-casemodel. Scenario 1 represents expending 2.5 normalizedresource-weeks and scenario 2 represents modifying theengineering coupling structure by eliminating the weakdependencies. In all cases, the increase in total resourceexpenditure and reduction in the magnitude of the engi-neering intercomponent dependencies are applied to themore complex local components (i.e., center console (L2),door trim panel (L3), and instrument panel (L6), seeFig. 7). Figure 7d shows the combined effect of thesestrategies on the total number of open issues.

Delays in information flows (introduced by scantransmittal intervals) from the industrial design to theengineering process have a destabilizing effect on systembehavior. For example, Fig. 8 presents the behavior ofthe system for various information delays. As can beseen, increasing the information delay results in moreextreme churning behavior. Moreover, even though allscenarios are converging, the increased churningbehavior leads to slower convergence rates. Indeed, byinspecting the convergence rate (i.e., largest magnitudeeigenvalue17 of the matrix B) of the appearance designprocess, for various delays between consecutive infor-mation releases, we observe that convergence slows

monotonically for longer delays. To illustrate the eco-nomic cost of churn, we inspect the amount of totalwork in the system over the ‘‘convergence’’ period (i.e.,the time required to complete 99% of the initial totalwork). We see that the work associated with the infor-mation delay T=6 is about 10% more than the totalwork associated with the delay T=1.

We also notice in Fig. 6 that the accumulation of ongoingchanges in the industrial design group related to the localinstrument panel (see the cumulative work of H6) is largerthan the magnitudes of other elements. Thus, it may bepossible to reduce the impact of the accumulated designinformation by using differential delays among compo-nents; that is, by increasing the frequency with which designinformation is transmitted from the industrial design to thelocal components that have the most destabilizing effect ontotal system performance. For instance, consider thescenario where the industrial design team provides updatesto the local engineering tasks L2, L3, and L6 at shorter peri-odic intervals of T1<6 weeks (while maintaining the delayfor the others at T2<6 weeks). According to the multiplelocal DSM model of Sect. 5, the local DSM is now partitionedinto two local teams, DSM1={L2, L3, L6} and DSM2={L1, L4,L5, L7, L8, L9, L10}. By applying the results18 of Sect. 5, Fig. 9plots the convergence rate (i.e., largest magnitude eigen-value of the matrix B) for the base scenario under (1) fivedifferential information release policies, T1=j and T2=6 forj=1, 2, ..., 5, and (2) overall information release policy T=j forj=1, 2, ..., 5. As can be seen, the differential delay policyconsistently achieves better ‘‘performance’’ (larger conver-gence rate) than the corresponding uniform policy; that is,the differential delay policy with T1=j and T2=6 achievesbetter performance than the uniform information release

Fig. 8. The effect of delay on the churning behavior

17 Recall that the larger the eigenvalue the slower the system’sconvergence rate.

18 According to Theorem 4, the fundamental period of the mo-nodromy matrix is 30=lcm(5, 6).


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policy with delay T= for every j=1, 2, ..., 519. Note that eventhough the relative changes in the maximum eigenvalues aresmall, the corresponding changes in the completion timesfor the project were significant.

6.5Sensitivity analysisThe model developed in this paper enables us to performsensitivity analysis. For example, let aL

2 be the autono-mous local center console completion rate (correspond-ing to the element in row two, column two in the localDSM). Assume that the other elements in the local DSMare set to their values as specified in Fig. 5. Figure 10aplots the largest magnitude eigenvalue of B against aL

2 : Ascan be seen, any value of aL

2gt; 0 will have a stabilizingeffect on the system behavior (see Theorem 2). A similarplot for the local overhead system (Fig. 10b) suggests thatthe convergence rate is completely insensitive to itsautonomous completion rate as long as it is greater than

0.05. Consequently, any increase in total resourceexpenditure for a bottleneck component (such as thecenter console) will be effective in improving the systemperformance.

7Discussion and conclusion

7.1Case study limitationsThe model and scenario analysis presented in this paper aimat illustrating the fundamental process characteristics andproviding managerial insights on the effects of differentmitigation strategies. The following observations will assistin assessing the limitations of our case study in context:

(A) The interior design is completely separable from theexterior design. The overall appearance design pro-cess is subject to a number of influences as it operateswithin the total automotive product developmentcycle. These influences are considered inputs to theappearance design process. Here, the scenarios areconstructed to represent as closely as possible anisolated interior design process that is independent of

Fig. 9. The effect of delay policyon the largest eigenvalue

Fig. 10a, b. The effect of autonomous completion rate onconvergence

19 The advantage of reducing the information delay should beweighed against the possibe additional resources and undesirableside effects. Exploration of these tradeoffs is beyond the scope ofthis paper.


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exterior design actions (e.g., full exterior carryover inwhich all relevant exterior design information isknown to component engineering groups).

(B) In order to facilitate downstream tooling design,prototype development, and testing, and ultimatelyto meet the desired product introduction date, theappearance design phase of the process must becompleted within a specified amount of time. Thus,an important input to the appearance design processis the program work schedule, indicating plannedprogress in design feasibility and expected status atvarious program milestones. This input is used bythe appearance design process (primarily by theengineering process) participants to assess the cur-rent state of the design versus the scheduled state,and to make corresponding adjustments in effortlevels via resource allocation and workload policies.For instance, if a component design is behind sche-dule, that group will usually work overtime in aneffort to catch up. In our model, we assume that theresource usage intensity required to accomplish theautonomous completion rate of the various tasks isuniform throughout the project.

(C) The interior design is not free of midstream programdirection changes. The term program direction referscollectively to the current set of assumptionsregarding product content, performance, variablecost, investment, quality, and other program attri-butes. Changes in the program direction are con-sidered by process participants to be a critical sourceof the difficulties encountered during appearancedesign. The detailed data on program directionchanges are not available. In our model, we proceedby assuming that the program has perfect initialknowledge of the ultimate desired product contentand component cost, investment, and quality level;however, we do not incorporate program directionchanges over the duration of the project.

Owing to the above mentioned limitations, duplicationof the historical behavior of the specific vehicle program(as shown in Fig. 4) remains beyond the scope of thisstudy. A lack of replication of the progress history bringsup the issues of validity for the model and the case study.

7.2Model validityIt is best to validate the process structure to illustrateconsistencies between constructs that are included withinthe model, and the resulting process dynamics againstex-post records to establish face validity toour model. Illustration of external validity, i.e.,applicability of the model in generic settings, is alsodesirable. The complexity of the design process andthe scarcity of hard data and good records on theappearance design process mean that a quantitativevalidation of the model is questionable (Huber-Carolet al. 2002). We restrict our discussion to a qualitativecomparison of our results and the observed processdata. In particular, we draw the reader’s attention to thefollowing:

(A) The constructs of managerial relevance are consideredby the model and their interdependencies are based oninterviews conducted in the field study (McDaniel1996). We have neither added any additional con-structs nor have we deleted any details from these fieldobservations.

(B) Support for the model validity has also beenobtained by asking engineers and engineeringsupervisors to rank the ‘‘complexity level’’ associ-ated with the ten particular interior componentsthat are captured in the full model (McDaniel1996). The complexity levels are expressed by thenumber of standard engineering design studiesassociated with each component (which is indi-rectly affected by the ‘‘churn’’ and convergence ofeach component). The ranking of the top threecomponents (i.e., instrument panel, door trim pa-nel, and center console) is aligned with the threecomponents that were identified to have the mostdestabilizing effect on total system performance asdepicted in Figs. 6 and 7. In particular, it has beenobserved by engineers that the instrument panel isconsistently behind schedule, and that it has thelargest number of open design issues for the lon-gest period of time as predicted by our model. Ithas also been observed that the appearance designprocess is not completed on time at the nominaldate of week 52, as demonstrated by our model. Inaddition, the local components (e.g., the overheadsystem) that have been found to be completelyinsensitive to its autonomous completion rate (seeSect. 6.5) are aligned with the engineers complexitylevel rankings.

(C) The periodic jumps in the number of openssues, which occur in response to the updatedstyling design information. In the periods betweenscan transmittals, the engineering group workswith the information it has regarding the vehicledesign, without disturbance by styling updates, sowork progresses relatively smoothly. Styling reactsto the ongoing engineering design changes, how-ever, and because information about this reactionis available to engineering only following scantransmittals, the release of updated styling infor-mation into the system results in some designissues being opened or reopened. This releasedrives the sharp changes in status, which representsetbacks in progress due to the structure ofproduct development.

(D) It has been observed by the process participants thatlengthy delays in information exchanges betweenstyling and engineering is a major source in pushingeach component’s status further away from itsscheduled status, in alignment with our previousdiscussion (see Sect. 6.4).

More complete modeling and validation would berequired to make more detailed observations. Thisrequirement suggests possible record-keeping actions thatcould assist management at the subject company indeepening its understanding of the appearance design


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process. Detailed vehicle program records should be keptand analyzed, including such data as weekly component-level design status, weekly component resource usages,and number of times design files or drawings are ex-changed or accessed, as well as a record of all productchanges that were made. These types of records wouldhave the additional benefit of enabling input–output cor-relation analysis to be used to quantitatively estimate theintercomponent coupling parameters, rather than relyingon survey techniques. They would also improve the esti-mation procedure of the average autonomous completionrate per component (by which engineering personnel wereasked to artificially decouple the interior components andmake a professional judgment about how quickly eachcomponent could be designed on its own).

7.3ConclusionThe model described in this paper provides managerswith operational insights that explicitly capture the fun-damental characteristics of a development process. Itallows managers to experiment with several ‘‘what-if’’scenarios in order to explore and compare the effects ofsubsequent managerial actions of improvement. However,a basic revelation of the model is that design churn is anunavoidable phenomenon and a fundamental property ofa decomposed development process where the product orprocess architecture dictates delays in feedback infor-mation amongst the development groups. Consequently,the most significant insight this model brings to man-agers is to avoid making myopic resource allocationdecisions based on the observance of churn (Joglekar andFord 2003). The fluctuation in development progresscannot be avoided, but can be managed once managersunderstand its sources. Our model reveals several mainsources of churn:

(a) Interdependency of process or product structure isapparent when the development occurs within amonolithic group; however, it is usually hidden,ignored, or forgotten once the process is decom-posed into multiple groups. Fully anticipating,understanding, and accommodating this structurecan explain why the tasks seem difficult, frustrating,and prone to change.

(b) Concurrency of local and system execution may helpin expediting the development process; however,careful timing and magnitude of feedback are nec-essary to provide development groups with enoughtime, between feedbacks, to understand and react tothese feedback flows. If these flows are not carefullyplanned, they might drive the process unstable bygenerating more rework than the development teamscan handle.

(c) Feedback delays are an important factor in developinga clear understanding of the development process andplay a major role in determining the system stability.In combination with the interdependency structure,delays are the main reason why development prob-lems (issues) believed to be solved (closed) tend toreappear (reopen) at later stages of development.

While exposing churn as a fundamental property of adecomposed development process, our model also pro-vides managers with three mitigation strategies to combatdesign process churn, divergence, or slow convergence.These strategies are:

1. Timing-based strategies: these strategies advocate theminimization of delays for specific tasks that contributethe most to the slow convergence of the developmentprocess. Our model provides a quantitative approach toidentify these bottleneck tasks. Once identified, strate-gies for reducing the time delays for these tasks shouldbe implemented. These include the early release ofpreliminary information and divisive overlapping(Krishnan et al. 1997). Our illustration shows thatacceleration of the synchronization frequency for alltasks may not be as effective as accelerating, by thesame amount, the synchronization frequency for thebottleneck tasks.

2. Resource-based strategies: these strategies allow localand system teams to work faster (as captured by thediagonal elements of both WL and WS) by incorporatingmore resources. Our illustration shows that workingfaster on all the tasks simultaneously may not be aseffective as allocating the same amount of resourcesonly to the bottleneck tasks.

3. Rework-based strategies: these strategies suggest thatlocal groups ignore low priority local or system feed-back (as captured by the low rework fractions in WLiLj

or WSiLjÞ: A similar strategy is to reduce the values ofWLiLj or WSiLj by requiring that local or system teamsnot produce much feedback to local groups. Both thesestrategies benefit from a modular architecture.

All the above strategies are effective in mitigating thethree sources of churn (i.e., interdependency, concurrency,and feedback delays) either individually or collectively. Wehave demonstrated the impact of these strategies using theautomotive appearance design process.

We have developed a model for a development processbased on decomposing it into two groups: local and sys-tem. The model incorporates two types of informationflows: (1) information flows that reflect internal reworkwithin local and system groups, possibly generatinginternal rework; and (2) information flows that reflectstatus updates from local to system tasks and feedbackfrom system to local tasks. These information flowsinfluence both ‘‘fundamental’’ and ‘‘extrinsic’’ churn anddetermine the shape and rate of convergence of thedevelopment process.

Several extensions to our model are possible. First, costelements associated with the information release andinformation processing activities may be incorporatedwithin our model. This may result in a convex formulationthat allows for the optimal determination of the informationdelay T (e.g., Thomke and Bell 2001). Second, except for thelocal and system autonomous rates of completion, ourmodel does not explicitly account for resource allocationpolicies. Thus, explicitly incorporating resource allocationas a decision variable may lead to the discovery of betterresource allocation policies in the context of decomposeddevelopment processes. Finally, the linearity assumption in


159

our model can be relaxed, and nonlinear formulationsmay be developed. For example, our model can bemodified by incorporating time-varying rework fractions,which are reduced with time as the development processunfolds.

Appendix 1

Specifications of work transformation matrices (WL, WS,WLS, WSH, WSL)The specification of the work transformation matrices isbased on the assumption that only work that is done in theprevious period is considered to create rework as a normalcourse of operation. Let XL ¼ aL

ij

� �be the local DSM. The

work completion coefficient aLii � aL

i is the local autono-mous completion rate for task i at each iteration step. Thecoupling coefficient aL

ij (for i 6¼ j) is the amount of rework

created for local task i per unit of work done on local task j.Consequently, the elements of the work transformationmatrix WL become wL

ii ¼ 1� aLi and wL

ij ¼ aLija

Ljj (for i 6¼ j).

The system DSM XS and work transformation matrix WS

are defined similarly.The interaction between the local and system teams iscaptured by the intercomponent dependency matrices

XLS ¼ aLSij

� �and XSL ¼ aSL

ij

� �: The coupling coefficient

aLSij is the amount of rework created for system task i per

unit of work done on local task j. Similarly, the couplingcoefficient aSL

ij is the amount of rework created for localtask i per unit of work done on system task j. Consequently,the elements of the work transformation matrix WLS

are wLSij ¼ aLS

ij aLjj: The matrix WSL is defined as wSL

ij ¼ aSLij aL

jj:

Finally, the ‘‘holding’’ matrix WSH is defined as

WSH=WSL.

Appendix 2

Proof of Lemma 1, Theorem 1, and Corollary 1See Richards (1983).

Proof of Theorem 2From Theorem 1, x(k) is a solution of the linear periodicsystem described by Eq. 7 if and only if yðkÞ ¼ P�1ðkÞxðkÞis a solution of the linear autonomous system described byEq. 8. The matrix P(k) is nonsingular and periodic. Thus,the stability of the linear periodic system (Eq.7) is equiv-alent to the stability of the associated linear autonomoussystem (Eq. 8). Consequently:

1. If the largest magnitude eigenvalue of B (i.e., the largestmagnitude Floquet exponent) is less than 1, then everysolution x(k) of Eq. 7 satisfies limk!1 xðkÞ ¼ 0:

2. If the largest magnitude eigenvalue of B is less than orequal to 1, then every solution y(k) of Eq.8 remainsbounded for k‡0.

3. (Only if part). Assume that the largest magnitudeeigenvalue of B is greater than 1. Then there is a

solution y(k) of Eq. 8 such that limk!1 xðkÞ ¼ 1; andthe zero solution is unstable.

Corollary 2Since the eigenvalues of B are the Tth roots of the eigen-values of the monodromy matrix C, corollary 2 immedi-ately follows.

Proof of Theorem 3From Theorem 1, the general solution x(k) of Eq. 7 may bewritten as xðkÞ ¼ PðkÞyðkÞ where y(k) is the general solu-tion of the linear autonomous system (Eq. 8). For thelinear autonomous system, it can be verified that thegeneral solution can be written as yðkÞ ¼ BkSBg; where SB

is the eigenvector matrix of B and g ¼ ðg1; g2; :::; gnÞ02 Rn:

The powers of B can be found by Bk ¼ SBKkBS�1

B ; where KB

is a diagonal matrix of the eigenvalues of B. Consequently,

yðkÞ ¼ BkSBc ¼ SBKkBg

¼ ½n1; n2; :::; nn�

kk1 0

kk2

. ..

0 kkn

266664

377775

g1

g2

..

.

gn

266664

377775

¼ ½kk1n1; k

k2n2; � � � ; kk

nnn�

g1

g2

..

.

gn

266664

377775

where ½n1; n2; :::; nn� is the eigenvector matrix for B.Hence the general solution x(k) of Eq. 7 may be given by

xðkÞ ¼ PðkÞyðkÞ ¼ ½kk1PðkÞn1; k

k2PðkÞn2; � � � ; kk

nPðkÞnn�

g1

g2

..

.

gn

26664

37775

ðB:1Þ

From Eq. B.1 we see that the general solution x(k) of Eq. 7may be given by xðkÞ ¼ UðkÞg; i.e., each of the columnvectors of UðkÞ is a nontrivial solution of Eq. 7. Letx̂ðkÞ ¼ kk

i PðkÞni be such a nontrivial solution. We have

x̂ðkþ TÞ ¼ kkþTi Pðkþ TÞni ¼ kT

i kki PðkÞn ¼ kT

i x̂ðkÞðB:2Þ

Notice that kki is an eigenvalue of the monodromy matrix

C, i.e., kTi is a Floquet multiplier of the linear periodic

system (Eq. B.1). Thus, there exists a solution x̂ðkÞ of thelinear periodic system (Eq. B.1) such thatx̂ðkþ TÞ ¼ kT

i x̂ðkÞ; and this is the reason we call kTi a

multiplier. Now,

(i) If the matrix C has an eigenvalue equal to 1, thenkT

i ¼ 1 and from Eq. B.2 there exists a periodicsolution of period T.


160

(ii) If the matrix C has an eigenvalue equal to )1, thenkT

i ¼ �1 and from Eq. B.2 there exists a periodicsolution of period 2T.

(iii) Let the local and system work transformationmatrices be coupled and non-negative. Conse-quently, the monodromy matrix C will be coupledand non-negative. Thus, in many applications,CL>0 for some power L (i.e., C is primitive) forL>0. By the Perron-Frobenius theorems for primi-tive matrices one of its eigenvalues k�C is positivereal and strictly greater (in absolute value) than allother eigenvalues, and there is a positive eigen-vector corresponding to that eigenvalue. Sincek�B ¼

ffiffiffiffiffik�C

Tp

; according to Eq. B.1, the largest mag-nitude eigenvalue of B is also positive real, andthere is a positive eigenvector corresponding to thateigenvalue. Therefore, the long-term behavior of thesystem has the form

xðkÞ � c1ðk�BÞkPðkÞn ðB:3Þ

If the largest eigenvalue of C is equal to 1, then it followsfrom Eq. B.3 that the long-term behavior of the system isperiodic of period T.

Proof of Theorem 4Since T is the least common multiple of T1,T2,...,Tm, itfollows that there are integers a1,a2,...,am such that T=aiTi

for 1 £ i £ m. Let k‡0 be any time point. Assume that attime point k the system team provides updates only to thelocal teams i1,i2,...,ij. From the information release policy itfollows that there are integers b1,b2,...,bn such thatk ¼ bi‘Ti‘ for i‘ 2 fi1; i2; � � � ; ijg and k ¼ bi‘Ti‘ þ ei‘ fori‘ 62 fi1; i2; � � � ; ijg where 0lt; ei‘ lt; Ti‘ : Consider time pointk+T.For i‘ 2 fi1; i2; � � � ; ijg; kþ T ¼ bi‘Ti‘ þ ai‘Ti‘ ¼ðbi‘ þ ai‘ÞTi‘For i‘ 62 fi1; i2; � � � ; ijg; kþ T ¼ bi‘Ti‘ þ ei‘ þai‘Ti‘ ¼ ðbi‘ þ ai‘ÞTi‘ þ ei‘Thus, we conclude that at timepoint k+T the system team will provide updates only to thelocal teams i1,i2,...,ij. Consequently, the fundamental peri-od of the linear system (Eq. 11) is T.

ReferencesAdler P, Mandelbaum A, Nguyen V, Schwerer E (1995) Project to

process management: empirically-based framework for analyzingproduct development time. Manage Sci 41(3):458–483

Ahmadi R, Wang RH (1999) Managing development risk in productdesign processes. Oper Res 47(2):235–246

Bohn R (2000) Stop fighting fires Harv Bus Rev, July–August 83–91Braha D (2001) Data mining for design and manufacturing. Kluwer,

BostonBraha D, Maimon O (1998) A mathematical theory of design: foun-

dations, algorithms and applications. Kluwer, BostonBrowning T (2001) Applying the design structure matrix to system

decomposition and integration problems: a review and newdirections. IEEE Trans Eng Manage 48(3):292–306

Browning T, Deyst J, Eppinger SD, Whitney D (2002) Adding value inproduct development by creating information and reducing risk.IEEE Trans Eng Manage 49(4):443–458

Browning T, Eppinger SD (2002) Modeling impacts of processarchitecture on cost and schedule risk in product development.IEEE Trans Eng Manage 49(4):428–442

Clark K, Fujimoto T (1991) Product development performance:strategy, organization, and management in the world autoindustry. Harvard Business School Press, Boston

Cusumano M, Selby R (1995) Microsoft secrets. Free Press, New York

Eppinger SD (2001) Innovation at the speed of information. Harv BusRev 79(1):149–158

Eppinger SD, Whitney DE, Smith R, Gebala D (1994) A model-basedmethod for organizing tasks in product development. Res Eng Des6(1):1–13

Ford D, Sterman J (1999) Overcoming the 90% syndrome: iterationmanagement in concurrent development projects. Working paper,Texas A&M University

Huber-Carol C, Balakrishnan N, Nikulin M, Mesbah M (2002)Goodness-of-fit tests and model validity: statistics for industryand technology. Birkhauser, Boston

Joglekar NR (2001) Data collected at Factory Mutual InsuranceCompany, Norwood, MA

Joglekar NR, Yassine A, Eppinger SD, Whitney DE (2001) Perfor-mance of coupled product development activities with a deadline.Manage Sci 47(12):1605–1620

Joglekar NR, Yassine A (2001) Management of informationtechnology-driven product development processes. In:Ganeshan R, Boone T (eds) New directions in supply-chainmanagement: technology, strategy, and implementation.AMACOM, New York

Joglekar NR, Ford D (2003) Product development resource allocationwith foresight. Eur J Oper Res (in press)

Krishnan V, Eppinger SD, Whitney DE (1997) A model-basedframework to overlap product development activities. Manage Sci43(4):437–451

Kuchment P (1993) Floquet theory for partial differential equations.Operator theory, advances and applications. Springer, BerlinHeidelberg New York

Lee H, Padmanabhan V, Whang S (1997) Information distortion in asupply chain: the bullwhip effect. Manage Sci 43(4):546–558

Loch C, Terwiesch C (1999) Accelerating the process of engineeringchange orders: capacity and congestion effects. J Prod InnovatManage 16(2):145–159

Mar C (1999) Process improvement applied to product development.MS thesis, MIT

Marcus M, Minc H (1964) A survey of matrix theory and matrixinequalities. Allyn and Bacon, Boston

McCord KR, Eppinger SD (1993) Managing the integration problemin concurrent engineering. Sloan School of Management, WorkingPaper #3594–93–MSA

McDaniel CD (1996) A linear systems framework for analyzing theautomotive appearance design process. Master’s thesis (Mgmt./EE), MIT

Mihm J, Loch C, Huchzermeier A (2001) Modeling the problemsolving dynamics in complex engineering projects. Working pa-per, INSEAD

Repenning N, Gocalves P, Black L (2001) Past the tipping point: thepersistence of firefighting in product development. Calif ManageRev 43(4):44–63

Richards J (1983) Analysis of periodically time varying systems.Springer, Berlin Heidelberg New York

Simon H (1996) The sciences of the artificial. MIT Press, CambridgeSmith RP, Eppinger SD (1997) Identifying controlling features of

engineering design iteration. Manage Sci 43(3):276–293Sobek D, Ward A, Liker J (1999) Toyota’s principles of set-based

concurrent engineering. Sloan Manage Rev 40(2):67–83Sosa ME, Eppinger SD, Rowles CM (2000) Designing modular and

integrative systems. ASME conference on design theory andmethodology, Baltimore

Strang G (1980) Linear algebra and its applications. Harcourt BraceJovanovich, New York

Sullivan KJ, Griswold WG, Cai Y, Hallen B (2001) The structure andvalue of modularity in software design. In: Proceedings of the jointinternational conference on software engineering and ACM SIG-SOFT symposium on the foundations of software engineering,Vienna

Thomke S, Bell D (2001) Sequential testing in product development.Manage Sci 47(2):308–323

Wheelwright S, Clark K (1992) Revolutionizing product development.Free Press, New York

Yassine A, Braha D (2003) Four complex problems in concurrentengineering and the design structure matrix method. ConcurrentEng Res Appl (in press)


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