HD28
.M414
no.
$34^
-116
ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
Identifying Controlling Features of
Engineering Design Iteration
Robert P. Smith
Steven D. Eppinger
Revised September 19S2
WP #3348-9 1-MS
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
M.l.T.UBtWt**
Next
Please write
to
revision:
January 1993.
address below after that date for reprints.
Identifying Controlling Features of
En^neering Design Iteration
Robert P. Smith
Steven D. Eppinger
Revised September 1992
#3348-9 1-MS
WP
Ackno^i^edginent
This research
is
funded by General Motors and by the Leaders
for
Manufacturing
Progi-am, a partnership involving eleven major U.S. manufacturing firms and
M.I.T.'s schools of engineering
and management. The authors are
also grateful
Dan Whitney, Marde Tyre, Karl Ulrich, and two anonymous reviewers from
Management Science who have provided helpful and insightful comments on
to
earlier versions of this paper.
Send correspondence
to:
Prof. Steven D. Eppinger
M.I.T. Sloan School of Management
30 Wadsworth Street, E53-347
Cambridge, Mass. 02139
'OV
1
3 1992
Ktouvcu
Abstract
Engineering design generally involves a very complex set of relationships among
a large number of coupled elements. It is this complex coupling that leads to
iteration among the various engineering tasks in a large project. The Design
Structure Matrix (DSM) is useful in identifying where iteration is necessary. The
Work Transformation Model developed in this paper is a powerful extension of the
DSM method which can predict slow and rapid iteration within a project, and
predict those features of the design problem which will require many iterations to
reach a technical solution. This model is applied to an automotive brake system
development process in order to illustrate the model's utility in describing the
main features of an actual design process.
Introduction
The goal
of this
work
is to
develop a modeling framework which
for describing engineering design iteration.
system design
to illustrate its utility in
The framework
is
is
useful
applied to brake
understanding the engineering design
process.
Engineering design
solve a given problem.
to the design process,
is
the process whereby a technical solution
There have been several attempts
to give
is
created to
formal structure
such as those of Sub [1990], Pahl and Beitz [1988] and
Alexander [1964]. This stream of research characterizes good design practice in
general terms, but does not describe what makes some design problems more
difficult
than others.
We
intend to further the development of design process
modeling by providing richness
strategies
which
to the descriptions of design
procedures and
will enable a design organization to identify the difficult portions
of their particular design problem. Strategies can then be developed to facilitate
the effective execution of these difficult aspects.
The Design Structure Matrix (DSM) serves as the
basis for our formal
analysis and will be briefly reviewed in this section. (For a more detailed overview
of the
DSM method the reader is referred to Steward [1981] and Eppinger et al.
[1991].)
The work herein extends the
utility of
analytical method, and demonstrates the
our framework for the management of engineering projects.
The philosophy
of the
DSM method
individual tasks, and the relationships
is
that the design project
among
is
divided into
these tasks can be analyzed to
identify the underlying structure of the project.
It
has been suggested that
studying the relationships between individual design tasks can improve the
overall design process,
and
is
strategies [von Hippel 1990].
shows how
a powerful
way
to analyze alternative design
Earlier work developed a modeling formalism which
different aspects of a design
problem are related [Alexander 1964].
Alexander describes a graphical technique where the functional needs of the
technology are nodes, and interactions between
tlie
segment the graph into subsections which have
cross boundaries.
needs are arcs. His idea
relatively few interactions
These graph segmentations give
rise to technical
is to
which
subsystems
which should separate the technical needs into independently solvable problems.
The
now
DSM
method
is
specific design tasks
similar to Alexander's technique, but the nodes are
and the arcs are directed and indicate information flows
between tasks. The nodes in the graph are arranged in a square matrix where
each row and
its
corresponding colunm are identified with one of the tasks.
Along each row, the marks indicate from which other tasks the given task
requires input.
its
Reading down each column indicates which other tasks receive
output. Diagonal elements do not convey any
task cannot depend upon
its
own
F,
task
B
this point, since a
completion. For example, in Figure
a simplified view of camera body design), task
and
meaning at
C
1
(based on
requires input from tasks B, D, E
requires input only fi"om task A, and task
A
needs no input
to begin.
A B
A
Set Specifications
B
Design Concept
C
Design Shutter Mechanism
D
Design Viewfinder
E
Design Camera Body
F
Design Film Mechanism
G
Design Lens Optics
H
Design Lens Housing
reason, iteration
The sub-matrix
is
a typical feature of engineering design projects [Hubka 1980].
problem defined such that the tasks
in Figiare 1 depicts a design
are sufficiently complex and interrelated so that iteration will be necessary to
complete the tasks.
There
is
an established
set of
models which allow looping within a
modeling framework. This set of models
is
known
as
GERT,
for
General
Evaluation and Review Technique. Direct analysis of any but a simple
network rapidly becomes unwieldy, so simulation
project. (Taylor
is
modeling
of GERT to
effort to provide
R&D
an analytically
tractable model of the design iteration process, even for large projects.
that by preserving tractability
it
GERT
typically used to evaluate a
and Moore [1980] discuss the application
projects.) It is the intention of this
PERT
It is
will be possible to observe the relationship
hoped
between
the structiu-e of the problem and the development time of the project. Because
GERT
relies
on simulation for large projects,
it is difficult
to discern this
relationship.
For our purposes, we assume that the tasks and interrelationships of a
design problem are
known and unchangeable during
This assumption
reasonable for a firm
is
is
the course of the project.
working on a design project in an
area in which they have a significant degree of familiarity (the example of brake
system design at General Motors, which serves as the basis
described in this paper,
completely
new
There
is
fits
this category).
The assumption
for the application
is less
true for a
or rapidly evolving technology.
evidence that some companies
problem choose differing design
strategies,
who
are faced with the
same design
which implies a different underlying
design matrix. For example, to what extent they choose to work on tasks in series
or parallel affects development time significantly [Clark
and Fujimoto 1991].
Development time
We
management.
is
an important measure
believe that complex iteration
in engineering design
is
a major source of extended
development time. While the Design Structure Method
is
a useful tool to identify
the coupled blocks in which the complex iteration occurs, this work
characterize
If
how such
is
intended
to
iteration occurs.
we include task durations
in the
DSM, we can
use this description to
estimate the total duration of the project. Series tasks can be evaluated by
summing
the
their individual times,
maximum
Figure
1, if
and
parallel tasks can be evaluated
by finding
of those task times. For the project characterized by the
the task time are
a, b, c,
...
,
h,
DSM
in
the time of the camera design project
would be
a + b + max{
where
f(-)
for the
is
f(c,d.e,f)
,
g+h
}
a function, undefined as yet, corresponding
development time
to the
coupled block.
The model presented
in this paper illustrates
how
iteration time can be
evaluated for such a coupled block of tasks, and shows that the
controlling the iteration can be identified.
Each
critical features
critical feature is
a group of
parameters of the design solution which are strongly dependent on each other;
they
may
require
constraints.
The
We
many
iterations to converge, as a set, to conform to design
illustrate these concepts using a
critical features in
product qvudity, and
we
brake system design example.
brake system design are important determinants of
believe that critical features which are strongly related to
both time and quality are typical of engineering design.
Our Approach
We believe
that
it is
possible to lessen development time
restructuring the design process.
We
by analyzing and
have developed extensions
to the
DSM
framework which have allowed us
A
restructured.
probabilistic
to
suggest ways that the design process can be
previous interpretation of the quantitative
DSM
developed a
model of engineering design which predicts development time
for a
sequential design iteration process [Smith and Eppinger 1991], but that model has
proven
paper
as the
difficult to
apply to actual design projects. The model presented in this
a different interpretation of quantitative information in the
is
Work Transformation Matrix (WTM), and
Our
field
work
is
is
based on extended exposure
DSM, known
described below.
to the
brake system design
engineering organization the brake system design division of General Motors.
Our observations
include informal discussions with systems and component
engineers, internal documentation, and interviews with engineers and their
managers.
We
have found the brake system
to provide
a good subject for modeling
of the design process because of the nature of the design problem. Brake system
design
is
stable in that the technology
the base product
is
and the market are mature and the form of
not undergoing radical change. The brake system design
engineers have considerable experience with brake system design. These factors
suggest that the data contained within the brake system
rapidly,
and the knowledge which
is
DSM is
represented within the
not changing
DSM
is
well
developed.
Ours
is
a descriptive model, not an optimization model. The description
developed below can be used by the design manager to analyze the design problem,
and
to estimate
how
long the design process will take, and what aspects of the
design problem contribute to iteration time.
The novelty
in this model
is
in the application of matrix
mathematics
to
analyze development time of an iterative design process. The model relies on
standard linear algebra results. The interpretation of the relationship between
the matrix mathematics and development time
is
novel.
Design Iteration Model Development
For the purposes of our analysis, we assume that each task creates a
deterministic
amount
of rework for other tasks.
Rework
is
the
work which
is
necessary because the task originally was attempted with imperfect information
(assumptions). The rework adapts the original solution to account for the
modified information. Rework
is
measured
in percent of the time that
it
takes to
complete the task in the original iteration.
We
which we
use a transformed version of a fully coupled Design Structure Matrix
call
the Work Transformation Matrix (WTM). There are two types of
information in a
Work Transformation
Matrix.
The
off-diagonal elements
represent strength-of-dependence measures (defined in next section). (See Figure
2a.)
The diagonal elements
in the
complete each task during the
WTM represent the time that
first iteration stage.
it
takes to
(See Figure 2b.)
It is
assumed
that there will be multiple iteration stages, and that the time for each stage
function of the
find the
sum
amount
of time spent working in the previous stage.
of the times of all stages.
We
is
wish
a
to
we
illustrate the analytical process using a simple example.
and analyze the
A:
WTM
Finally,
we present
which describes brake system design.
Work Transformation Model Assxunptions
The assumptions
•
All tasks are
•
Rework
is
model
in this
are:
done in every stage -
fully parallel iteration
created based on a linear rule - as a
%
of
work done
in
previous iteration stage
•
The parameters
in the matrix describing
work transformation behavior
do not vary with time
These assumptions allow us
use a linear algebraic analytical method on the
to
WTM.
To develop the model, we
This
is
an
n-vector,
where
first
introduce the concept of the work vector
number
n is the
of design tasks to be completed.
element of the work vector contains the amount of work
after iteration stage
indicates that
all
t.
of the
The
initial
work vector
work remains
to
u..
Each
be done on each task
Ug is a vector of ones, which
to be
completed on every task at the
work
is
beginning of the iteration process.
During each iteration stage
all
completed on
all
of the design tasks.
(For a relaxation of this assumption, where a fraction of the work
every stage see Appendix
to
be created for
We
all
4. A.)
However, work on a task
cause some rework
fi-om the design structure matrix.
iteration stage produces a change in the
Ut+1
where each of the entries
j
completed in
other tasks which are dependent on that task for information.
determine which tasks those are
task
will
is
a-,
in
A
work vector according
Every
to:
= Au,
implies that doing one unit of
creates a units of rework for design task
i.
The matrix A
work on design
is
then the
strength of dependencies portion of the
are set to zero.
The work vector
u
number
entries
= a'uq
work vectors
of each of the
The diagonal
(Figure 2a).
can be also be expressed by:
u,
The sum
WTM
of times that each of the tasks
the total work vector U, the total
is
attempted during the
is
total of
T
amount
of
iteration
stages of design process:
T
u=
X^t
t=o
or:
U=
j^A\
t=o
which can be rewritten
as:
^'(1
The model output U
done on each task in the
is
therefore in units of the original
first iteration stage.
the design organization will have done
stages.)
+
(If
element in vector U
i
60% rework on
task
i
is 1.6,
then
in subsequent
For a time-based interpretation of the matrix A see Appendix 4.B. For
now, we scale U by the task durations to obtain units of task times.
matrix which contains the task times along
is
work
its
a vector which contains the amount of time
will require
during the
first
T
If
W
is
a
diagonal (See Figure 2b), then
(in
engineer-hours) that each task
iteration stages.
B: Eligenvalue Deoompositioii
If
A has
linearly independent eigenvectors (the eigenvector matrix
invertible) then
we can decompose A
into:
10
WU
S
is
j
A=
where A
is
SAS"""
a diagonal matrix of the eigenvalues of A, and S
eigenvector matrix. (For S to be inveri;ible
it is
sufficient,
is
the corresponding
but not necessary, that
none of the eigenvalues be repeated.) The powers of A can be found by:
a'
The
total
work vector U can
=
sa's"''
therefore be expressed as:
>•
U =S
vt=o
If the
magnitude of the
design process will converge
remains bounded.)
An
maximum
(i.e.
as
S-'uo
y
eigenvalue
T increases
is less
than one, then the
to infinity the total
work vector U
eigenvalue greater than one corresponds to a design
process where doing one unit of work at some task during an iteration stage will
create
more than one imit
work
of
for itself at
some future
stage.
Such a system
is
unstable and the vector U will not converge, instead growing without bound as T
increases. (It is a sufficient, but not necessary, condition for stability that the
entries in every
A
row sum
to less
than one.)
design process which does not converge would be one where there
technically feasible solution to the given specifications, or one
environments we are modeling, that
the designers are responsible for bringing out a
technically successful product.
Transformation Matrices
and can be found in
finite
is
The remainder
new
is,
no
where the designers
are not willing to compromise to find the technical solution. This situation
likely in the design
is
is
not
routine design where
variation of a known,
of the discussion on
Work
limited to problems where a technical solution exists
time
(i.e.
eigenvalues are less than
11
1.)
C: Interpreting the E^genstructure
The eigenvalues and eigenvectors
of matrix
A determine
Much
nature of the convergence of the design process.
controls the iteration by looking at the eigenvalues
the rate and
can be learned about what
and eigenvectors as opposed
to
looking at the sequence of work vectors.
A design mode
related,
is
defined as a group of design tasks which are very closely
and working on any one
indirectly, for
of
them
creates significant work, directly or
each of the other tasks within the mode.
and eigenvectors of matrix A
The magnitude
to identify the
of each eigenvalue of
We
use the eigenvalues
design modes.
A
identifies the rate of convergence of
each design mode. The eigenvector corresponding to each eigenvalue
characterizes the relative contribution of each of the various tasks to the body of
work which converges, as a group,
By
the Perron-Frobenius Theorem (a fundamental result of matrix theory)
we know that
will
at a given rate.^
the largest magnitude eigenvalue of a coupled non-negative matrix
be real and positive [Marcus and Mine 1964]. Also, the eigenvector associated
with this eigenvalue will have positive elements.
The slowest design mode
eigenvector which
(largest eigenvalue) will therefore
is strictly positive.
This design mode gives us
have an
little
problem
with interpretation. Other design modes are, however, less obvious. Also by the
Perron-Frobenius Theorem, there
positive.
is
only one eigenvector which
We must be able to interpret negative
is strictly
and complex nimibers
in the
eigenvectors as well as negative and complex eigenvalues.
^
interpretation of the eigenvalues and eigenvectors for design problems is similar to
the eigen structure analysis used to examine the dynamic motion of a physical system. In the
discrete time description of linear dynamic systems, each eigenvalue corresponds to a rate of
convergence of one of the modes of the system (a natural frequency.) The eigenvectors identify the
The
mode shapes of natural motion, quantifying
mode [Ogata 1967].
the participation of each of the state variables in each
12
Recalling that the total work vector
U = S
U
X^'
vt=o
we
will look at
calculated by:
S'''uo
y
each of the elements in the above formula
eigenstructure of matrix
the limit as
is
A can be used
T approaches
infinity
for
U
to interpret the design
to see
how
modes.
If
the
we take
we can use the formula:
T
lim
If the
maximum
eigenvalue
is
Xa' =
(I-A)'^
not close to one, then the limit will be approached
within relatively few iterations. For the remainder of this discussion the limit
will
be used, although the analysis can also be completed for finitely
many
iterations.
This limit
is
also a diagonal matrix,
where each entry along the diagonal
corresponds to one eigenvalue and has the form:
1
1
where X
is
-X
an eigenvalue.
In the next two subsections, both real and complex eigenvalues are
discussed.
In subsection 4.2.3.3 the interpretation of eigenvectors
is
considered.
Real Eigenvalues
The
function:
1
1
is strictly
increasing over
(-1,1).
-X
The graph
13
of this function
is
shown
in Figure 3.
-0.8
-0.4
-0.6
-0.2
0.4
0.2
0.6
0.8
X
Figure 3. Graph of Magnitude vs. X for Real Eligenvalues
We
see that
all positive
sum than do
eigenvalues have the greater contribution to the series
negative eigenvalues. Therefore, as
we
consider which are the more
important design modes, we restrict our attention among real eigenvalues
to the
positive eigenvalues.
Complex Eigenvalues
For complex eigenvalues we also wish
the
sum
the limit
to find the
magnitude of the
of the infinite series. For a complex eigenvalue
a+
is:
1
1
1
- (a
-H
pi)
V(1-a)^ +
P^
Or, alternatively:
1
1
-(a-^po
'J~r^2a7oF7^
Which, using the fact that:
14
pi
limit of
the magnitude of
allows us to find an upper bound on the limit:
1
1
Also,
we can
find a lower
-(a +
pi)
bound using the
a^ + p^ <
to
-a
1
fact that:
1
show:
1
1
The graph
-1
of the upper
-0.8
-0.6
-0.4
- (a +
1
V2-2a
pi)
and lower bounds
-0.2
is
0.2
shown
0.4
in Figure 4.
0.8
0.6
a
Figure 4 Graph of Bounds on Magnitude vs. a for Complex Eigenvalues
We
see that the real part of complex eigenvalues gives bounds on the magnitude of
the siun of the infinite series corresponding to that eigenvalue.
complex eigenvalues with negative real part are not going
significantly to the
sum, and can therefore be ignored.
15
We
also see that
to contribute
By
which are
we need
the previous argviment
We
positive.
only consider those real eigenvalues
therefore need to consider only those eigenvalues which
have a positive real component, whether they are
real or complex.
The Eligenvectors
This section discusses
eigenvectors
is
how
the relative importance of each task within an
interpreted, given that
that eigenvector.
We
want
to
we know the eigenvalue corresponding
to
be able to interpret the eigenvectors so that we can
distinguish which of the tasks are importsmt contributors to each design mode.
Again, consider the formula:
f T
u= s
\
I-'
Vt=0
We
S-'uo
J
see that the final two terms in this formula:
S-^Uo
give a weight for each eigenvector which
The eigenvector corresponding
a real eigenvector
negative.
is
is
both a magnitude and a direction.
to real eigenvalues is real.
Each weight
for
also real. Therefore, the direction is either positive or
The important quantities
in a real eigenvector are therefore the large
positive values if the weight is positive,
and large negative values
if
the weight
is
negative.
Complex eigenvalues have complex eigenvectors and complex weights.
Determining how the direction of the weight and the direction of the eigenvector
interact
is difficult.
contribution of the
The best way
mode
to look at the interaction is to calculate the
to the total
work vector U and see which the tasks give
large contribution to the total work.
Positive eigenvalues correspond to non-oscillatory design modes.
and complex eigenvalues describe damped
16
oscillations.
Negative
Oscillatory design
modes
indicate that the
rate,
work
but that the work
The magnitude
work vectors
is
not decreasing for
is
is
all
of the tasks in the
mode
at the
same
shifting from task to task during iteration process.
of the variability in the
amount
of
work between separate
not as important as the total magnitude of work completed. The
specifics of the variability
would be useful
work information. Instead we are looking
if
we were tracking
the individual task
at aggregate information, so the
individual variability (as indicated by the non-positivity of the eigenvector or
eigenvalue)
important. As we interpret the modes of the design process we
is less
must therefore concentrate on those modes with
large positive real eigenvalues,
or imaginary eigenvalues with a large positive real part.
An
illustration of the interpretation of the eigenvalues
given in the next section, where an example problem
is fully
and eigenvectors
is
worked.
A Simple Example
As an
illustration of the above discussion, let us consider the following 4x4
Work Transformation
(tasks C-F) in the
Matrix. This
is
a quantitative version of the coupled block
camera design matrix as shown
in Figure
1.
The tasks
in this
matrix are, in order: Design Shutter Mechanism, Design Viewfinder, Design
Camera Body, and Design Film Mechanism. The numbers can be
follows: if the shutter is completely redesigned, then
work must be redone (entry
in
row
2,
column
0.1
A=
The eigenvalue
(A)
0.3
0.1
0.3
0.1
0.1
and eigenvector
1 is 0.3),
0.2
0.3
0.4
0.2
0.5
0.2
(S) matrices are:
17
30%
interpreted as
of the viewfinder design
and
so forth.
0.674
-0.392
A=
-0.141 +0.060i
-0.
S=
L
'1
0.410
0.624
0.580
0.326
-0.067
-0.613
0.657
0.060-0.5701
0.758
-0.395 + 0.073i
-0.213
-0.065 + 0.2741
141-0.0601
0.657
0.060 + 0.570i
-0.395 - 0.073i
-0.065 - 0.274i
3.065
(I -
0.718
=
A)-^
0.874+0.0461
0. 874-0. 046iJ
The term used
vector
to see
how each
modes
of the
is
represented in the original state
is:
2.125
-0.310
S-^Uo =
0.082- 0.461
Multiplying this weighting vector by the
total
i
0.082 + 0.461
L
sum
i
of the eigenvalue matrix
we
find the
weight on the eigenvector matrix:
6.513
-0.223
(l-A)-^S-^Uo =
0.093 - 0.399i
0.093 + 0.399i
Note that the weight on the
first
eigenvector
than the other weights. Most of the work in
is
J
significantly larger in
magnitude
this iteration process is described
by
the primary design mode.
We
are
now
able to calculate the total
work
U = S(l-A)'^S-^Uo =
L
vector:
2.807
3.755
3.595
2.375
J
There has been more work completed during the process by the middle two tasks,
just as the preliminary analysis of the eigenvectors
and eigenvalues
indicated.
Brake Systran Desi^
In order to verify the utility of the
Work Transformation
technique,
we
will
demonstrate the analysis of an actual design process and show the insights
gained.
A
design structure matrix for the brake system was reported previously
[Black 1990, Black et
al.
1990.]
Transformation Matrix method
The work described here applied the Work
to the
brake system design process. In preparing
19
this analysis, the first
system design
author spent several months doing
facility of
field
work
at the brake
General Motors. That work included interviews with
brake system engineers at several
sites.
There are four questions which must be answered in constructing the
Design Structure Matrix.
We must
first
tasks in the design process. Second,
determine
of the various steps or
all
we must determine
flows between the various tasks. Third,
all
we must determine
of the information
the relative
importance of each of the information flows (quantifying the off-diagonal elements
in the matrix). Fourth,
we must estimate
The brake system data presented
the time
it
takes to complete each task.
in this paper includes data of the first
three types, but does not include any explicit time data.
Many
of the observations
about the controlling features of the design process can be made without having
the time data available. In particular,
we
are able to identify the total
number
of
iterations taken on each task.
The brake system
DSM from Black et al.
[1990]
is
shown
in Figure 5a.
The
matrix demonstrates a problem which can be divided into a block of complex,
coupled design parameters at the center of the matrix, preceded by and followed
by a group of sequential and parallel parameters. The coupled block
in Figure 5b.
matrix;
it is
(We
realize that Figure
5a
is
20
expanded
too small to see the details of the
included to demonstrate the overall structure of the
includes over 100 design parameters.)
is
DSM, which
'"-.
i
leads to pulsation, and elevated lining temperature leads to rapid wear of the
brake linings. More
specific causes
remain unknown. Detailed analysis of these
problems continues, and some progress
engineers
is
Specifically,
The sentiment among
being made.
is
that none of these problems will be solved' in the near future.
brake systems cannot be designed so that
nfl
customers ever
complain about these three problems. These problems are believed
consequences of using dry friction
These three problems
to stop
to
be inherent
a vehicle.
(noise, pulsation
and wear) have been
identified
by
designers and their managers as the controlling features' of the
design/test/redesign iteration problem they experience.
WTM
As shown below, the
analysis confirms that these are indeed controlling issues in design
iteration,
and
details the specific contributing
parameters
The match
for each.
between designer perception and analytical identification lends credence
to
both
approaches.
Using the Work Transformation Method to Identify Iteration Drivers
Using the
analjrtical tools described previously,
we can more
rigorously
identify the parameters within the large coupled block which compose the most
interrelated sets of parameters.
The
original
DSM
analysis of the brake system
identified parameters within the large block [Black 1990]. This
analysis by recognizing that
some
work furthers the
of the parameters exhibit stronger
interdependence than others, and that tightly coupled parameters consequently
require
more
iteration during the design process.
would be interpreted as controlling
require
on the
The dominant design modes
features' or design drivers', in that they
more engineering time during the design process
critical
sind they are likely to be
path of the design project.
To perform
this analysis,
Work Transformation
Matrix.
we
translate the binary
DSM (Figure
5b) into a
In lieu of precise numerical values in the
22
Work
Transformation Matrix
to
for the
brake system, the individual
cells
be of either weak, medium, or strong dependence. (See Figure
diagonal values
of time that
it
is
an estimate of the amoimt of work
6.)
Each
(as a percent of the
for the
downstream
organization were asked to describe
amount
task.
why each
The engineers
in the design
piece of information
was necessary
relative importance of each of the pieces of input information.
Each
these information flows were classified by the authors as either a strong,
or
weak dependency.
We
of
medium
then assigned numerical values to the dependencies
We
which were described by the engineers.
strong,
ofF-
took to complete the task during the original iteration) that the
upstream task creates
and the
were estimated
medium, and weak dependence,
the identification of the design drivers
have used the values
respectively.
is
0.5, 0.25, 0.05 for
Our experience shows
that
robust against minor changes in the
values entered in the matrix.^
This robustness can be demonstrated in two ways: (1) If we scale all of the values in A by a
constant factor, the eigenvectors will be unchanged. The eigenvalues will simply scale, and our
interpretation of the analysis will not change. (2) If we scale only one set of values (say strong
dependence becomes 0.6 instead of 0.5), then there would be no significant changes to the resulting
eigenstructure. More details on sensitivity of the eigenvectors to the weights are given in [Smith
2
1992].
23
3 5
2
Iteration
Repetitions
-r
until
Completion
1
.5
-^.
+
+
+
10
15
20
Design
Mode
Figure?. Brake System Eigenvalues
25
25
30
Task#
The
first
design
mode
is
primarily composed of (52) Vehicle Deceleration
Rate and (59) Pedal Force Required, with lesser input from (34) Pressure at Rear
Wheel Lockup,
Brake Torque
(35)
vs. Skidpoint, (58)
Dash
Deflection, (61) Pedal
Mechanical Advantage, (63) Front Lining Material and (64) Booster Reaction
Ratio.
What
this design
requires the greatest
acceptable design
column in Table
is
1.
mode shows
number
is
that the group of design parameters which
of design iterations before convergence on the final
the stopping distance problem, represented by the
Solving this problem assures that the brake system
stop the car without creating uncontrollable skidding.
for this
first
problem has been developed, and
it is
A
is
going to
performance simulation
a good predictor of actual
performance. These iterations can therefore occur quickly. Because of this
analytical tool, the large
number
of iterations on the first design
mode no longer
strongly affects the total time of the development process. This model
nevertheless confirms that the stopping performance problem
controlling feature
which
is
the fundamental
affects design iteration.
The second design mode
is
composed of primarily
(40) Splash Shield
Geometry, (48) Airflow under Wheel Space, (54) Rotor Cooling Coefficient and (56)
Rotor Width, with lesser input from (53) Temperature at Components and (104)
Rotor Material. All of these factors are technical parameters corresponding
overheating and cooling. This second design mode, which
cooling coefficient/rotor material problem,
noise generation,
is
is
composed
to
of the
related to the problems of lining
life,
and pulsation problems. For these thermal' problems, there
are few analytical or simulation tools available to the designer.
are required to converge upon a design solution, but there
is
Many
iterations
no guarantee that
those iterations can be rapid. Field or laboratory testing must be used to
27
eventually converge on a solution which meets the criteria at a relatively high cost
in time.
The design modes analysis has been able
controlling features correctly.
This success
We
dominant
made evident by
and wear would be found
priori prediction that noise, pulsation
fundamental design issues.
is
to identify the
the engineers' a
to
be the
not only confirmed this, but also described these
problems more precisely and showed how coupled these issues
are.
Discussion and Conclusion
The
goal of developing this type of model of engineering design
to provide engineering
managers information which
design cycle. Knowledge of the
iteration enables a
manger
will
be able
help to shorten the
critical sets of interrelated
to concentrate resources
is to
tasks which lead to
on these tasks so that the
iterations can occur as rapidly as possible.
The example of brake system design given above showed that the Work
Transformation Model
is
able to
match the observed behavior concerning which
design tasks are responsible for the bulk of the iteration. The model
is
able to
identify the features in the brake system design problem which control the total
amount of time taken
whether
it is
in the iteration process.
The question remains open
possible to identify the matrix data for a problem with which the
design organization has less familiarity.
Applying the model
organization.
to a
new problem would
The organization would be
beginning the design process. There
is
provide
new knowledge
able to identify the critical issues prior to
the problem of whether or not the
information required to construct the
Work Transformation Model can
generated reliably on a new problem.
We
class of problems
which are
to the
hypothesize that there
sufficiently well understood
28
is
be
an important
such that the engineers
involved can identify the tasks and the information dependencies (the information
necessary to construct the matrix), without being able
features of the overall problem. This
analysis
is
is
to identify
the controlling
the class of problems for which this type of
relevant and useful.
This paper has developed the
Work Transformation Model, which
analytical extension to the Design Structure Matrix,
and applied
it to
is
an
an actual
design process. The analysis demonstrates the utility of eigenvalues and
eigenvectors of the
Work Transformation Matrix
in interpreting the
work which must be completed during the design
iteration process.
amount
of
The
eigenvectors can be used to identify the 'controlling features', those elements of a
coupled design problem which require the greatest number of iterations to reach a
technical solution.
The Work Transformation Matrix can serve as a
analyzing coupled design problems.
We
useful diagnostic tool in
believe that this analytical
method can
lead to improvements in design processes by focusing attention on the slowly
converging design iteration modes. For the brake system design process we
suggest that improved simulation of the thermal and vibrational aspects of the
design problem
may
accelerate solution development.
In general, the
identification of the controlling features provides a crucial piece of information
which enables a manager
to allocate resources in order to lessen
development
time.
References
Alexander, Christopher, Notes on the Synthesis of Form, Harvard University
Press, Cambridge, 1964.
Systems Design Methodology Applied to Automotive Brake
System Design, Master's Thesis, M.I.T. Departments of Management and
Mechanical Engineering, May 1990.
Black,
Thomas
A., "A
"
29
Thomas A., Charles H. Fine and Emanuel Sachs, "A Method for Systems
Design Using Precedence Relationships: An Application to Automotive Brake
Systems," Working Paper, Leaders for Manufacturing Program, Massachusetts
Black,
Institute of Technology,
May
1990.
Clark, Kim B., and Takahiro Fujimoto, Product Development Performance:
Strategy, Organization, and Management in the World Auto Industry, Harvard
Business School Press, Boston, 1991.
Eppinger, Steven D., Daniel E. Whitney, Robert P. Smith and David A. Gebala,
"Organizing the Tasks in Complex Design Projects," Sloan School of
Management Working Paper 3083-89-MS, 1991.
Gebala, David A., and Steven D. Eppinger, "Methods for Analyzing Design
Procedures," ASME Design Theory and Methodology Conference, Miami, 1991.
Hubka, Vladimir, Principles of Engineering Design, Butterworth
Scientific,
London, 1980.
Marcus, Marvin, and Henryk Mine, A Survey of Matrix Theory and Matrix
Inequalities, Allyn and Bacon, Boston, 1964.
Ogata, Katsuhiko, State Space Analysis of Control Systems, Prentice Hall,
Englewood
Cliffs, N.J.,
1967.
Pahl, Gerhard, and Wolfgang Beitz, Engineering Design:
Approach, Springer, New York, 1988.
A
Systematic
Smith, Robert P., and Steven D. Eppinger, "A Model for Estimating Development
Time of a Sequential Engineering Design Process," Sloan School of Management
Working Paper 3160-90-MS, 1991.
Smith, Robert P., "Development and Verification of Engineering Design Iteration
Models," Ph.D. Thesis, M.I.T. Sloan School of Management, August 1992.
Steward, Donald V., "The Design Structure System: A Method for Managing the
Design of Complex Systems," IEEE Transactions on Engineering Management,
Vol. EM-28, No. 3, pp. 71-74, 1981.
Suh,
Nam P.,
The Principles of Design, Oxford University Press,
New
York, 1990.
Taylor, Bernard W., and Laurence J. Moore, "R&D Project Planning v^dth
Q-GERT Network Modeling," Management Science, Vol. 26, No. 1, pp. 44-59, 1980.
von Hippel,
Eric,
"Task Partitioning:
An
Innovation Process Variable," Research
Policy, Vol. 19, pp. 407-418, 1990.
30
Appendix A
In these appendices are two extensions to the
It is
Work Transformation Model.
shown here that the two extensions add generahty
to the original
model, but
are only slight modifications. The primary insight obtained from the analysis
that the eigenvalues and eigenvectors of A are
features, even with a
We
term
all
of the
work
is
all
work on every task
The new
is
attempted creates work
control rule
define a modified
of the
to
work
policy.
We
can
in every stage,
The work which
is
we do a
not
be completed in future stages.
for other tasks as in the original model.
becomes
u,+i
We
all
work load
in each stage.
attempted during the current stage remains
Work which
executed during every iteration
this a control rule, since this is a
generalize the control rule. Instead of doing
proportion p of
the most important analytical
more general model.
In the original model
stage.
still
is
=[(1-p)l + pA]Ut
0<P^1
work transformation matrix A* such that
A* = [(l-p)| + pA]
We
can find the eigenvectors and eigenvalues of the matrix A*:
A*=[(1-p)l + pSAS"^]
A*=S[(1-p)l + pA]S-''
The matrix
is
[(1-p)l
+ pA] must be the eigenvalue matrix of A* since
seen that the eigenvector matrix S of A*
is
the
same
eigenvalues of A* are a convex combination of A and
I.
as that of A.
diagonal.
It
The
Since the eigenvalues have
been increased, the convergence has been slowed (which
31
it is
is to
be expected since we
are only doing a proportion of the work in each stage.) The shape of the
convergence remains unchanged.
Appendix B
The second extension
below that this
is,
The
considered.
treats time in a
more
in fact, identical to the original
basis for the
new formulation
explicit
way
in
manner.
shown
It is
which time was
uses the vector u
as a work time
vector.
=
u?.i
The
initial
work time vector
is
A\^
the initial work vector weighted by the time for each
task:
uJ
where
= Wuo
W is a diagonal matrix of the task times
Each element
in the
Wj.
work time transformation matrix A
time that one hour of task
j
creates for task
The new work time transformation matrix
Repeating the analysis done
the
amount
of
work
or
i,
Wi
t_
A^ =
is
is
written compactly as
WAW~^
for the original system, the total
be found by
it_
S"^W-''uJ
t=o
Substituting for the initial work time vector
32
work time vector can
u^ =
ws
S-iyV^Wuo
t=o
U^ =
WS I-'
S"'Ur
t=o
which reduces
which
is
to
the expression originally given for weighting the total work vector by the
task times.
I
92b
\
13
33
Date Due
APR.2 0n9i'
DECta
pp'-
OCTO Igii
OCT
?
^^
-:^
Lib-26-67
MIT LIBRARIES DUPL
3
TOfiD
ODVim??
MIT Libraries
lilllll
3
fllfli
9080 007 194 779
T