Proceedings of
The 1996 ASME Design Engineering Technical Conference andComputers in Engineering Conference
August 18-22, 1996, Irvine, California

96-DETC:DTM-1412
FUNCTIONAL EVALUATION BASED ON FUNCTION CONTENT
Yoshiki Shimomura

Sadao Tanigawa

Hideaki Takeda

Mita Industrial Co,. Ltd.
Mita Industrial Co,. Ltd.
Graduate School of Information Science
Tamatsukuri 1-2-28, Chuo-ku, Osaka, 540Tamatsukuri 1-2-28, Chuo-ku, Osaka, 540 Nara Institute of Science and Technology
Japan
Japan
Ikoma 8916-5, Nara, 630-01
Phone: +81-6-764-3818
Phone: +81-6-764-3818
Japan
Email: simomura@mita.co.jp
Email: tanigawa@mita.co.jp
Phone: +81-7437-2-5261
Email: takeda@is.aist-nara.ac.jp
Yasushi Umeda

Tetsuo Tomiyama

Department of Precision Machinery Engineering
Department of Precision Machinery Engineering
Graduate School of Engineering, The University of Tokyo Graduate School of Engineering, The University of Tokyo
Hongo 7-3-1, Bukyo-ku, Tokyo, 113
Hongo 7-3-1, Bukyo-ku, Tokyo, 113
Japan
Japan
Phone: +81-3-3812-2111 (ext. 6481)
Phone: +81-3-3812-2111 (ext. 6481)
Email: umeda@zzz.pe.u-tokyo.ac.jp
Email: tomiyama@zzz.pe.u-tokyo.ac.jp

ABSTRACTINTRODUCTION

Function is a key concept to integrate design object modeling and design process modeling in design. We here propose
the FEP (Functional Evolution Process) model in order to integrate design object modeling and design process modeling. In
the FEP model, the model of a design object is evolved throughthree steps, i.e., function description, function actualization andfunction evaluation. Function description is the step in which adesigner modies required functions of a design object. Function
actualization depicts a process to obtain physical descriptions
from functional description. Function evaluation is a process tomeasure realizability of functions of the design object. However,among other steps, how to treat the function evaluation is oneof the most important theme, because evaluation executed bydesigners is based on subjective, ambiguous and tacit standards.
We discuss a methodology for evaluating function and propose the function content that quanties functions and enables
evaluation of functions. The function content is a similar concept of Shannon's information content and we show an example
of functional optimization based on this scheme.

Treating functions is cruicial not only for representing
design object but also for describing design process which isimportant to aid design by computers. On the other hand,
although designers somehow evaluate functions of design
objects, criteria of the evaluation dier according to each
designer and it is dicult to make them explicit 2]4]. In
order to support design and maintenance of machines by
a computer, methodology for evaluating functions should
be developed. Problems for this computerization include
the facts that function is subjective and relations between
function and physical parameter are not clear. In this paper,
we discuss relation among design and function about thisfunction evaluation and design process representation.
We rst introduce the FEP model that is a frameworkof design object and process modeling and discuss featuresof the function evaluation which is one of the basic steps of
the FEP model. Second, we propose function content as ameter for evaluating functions. Finally, we represent some1c 1996 by ASME
Copyright function modifier

Function Set: function

function body

F-B Relationship
Behavior Set: behavior: behavior sequence
B-S RelationshipPhysical Laws

ASPECT

objective objective
entityentityState Set
: state: state change

Figure 2.
Figure 1.

Structure of Function

Relationship among Function, Behavior, and State [13]part of results of functional evolution i.e., decomposed-into,
conditioned-by, enhanced-by, and described-as relations.
Decomposed-into relation This relation indicates that a function body is decomposed into sub-function bodies (seeFigure 3). This relation is an abstract-concrete on awhole-part relation.
Conditioned-by relation When a behavior A cannot actualize
a function A, a designer adds additional behavior thatrealize the function A with the behavior A. This relation denotes this operation. In Figure 4, the behavior
B is the additional behavior and this relation denotesthat a new function body B is needed to actualize afunction body A. In other words, the behavior B isnecessary condition for the behavior A. This relation
should be supported by causal relation in the behavior
level.
Enhanced-by relation This relation denotes that a new function body B is needed for satisfying a modi er A1 offunction body A (see Figure 5). In this case, though
the function body B is not a necessary condition for
the function body A, the modi er A1 is achieved betterby adding the the function body B .
Described-as relation This relation denotes that a modi er isdetailed into one or more concrete modi ers (see Figure
6).

design examples and analyze the results.
MODEL OF FUNCTION

There are many approaches to represent function (e.g.,
8] 6]), however a common problem exists that function andbehavior are often confused and mixed each other 12] 3].
For instance, behavior can be de ned objectively as transitions of physical states and therefore can be derived fromphysical states of an entity and physical laws. However,function is related not only to physical behavior but also
to human perception of behavior. For example, regarding
function of a car, one may say one of its functions is \tomove" and others \to carry," even if they observe the same
behavior.
We view that function is abstracted and subjective representation of behavior and behavior is physical interpretation of changing of states which can be directly derived
from an initial state of objects and physical laws. We here
represent functions based on the FBS modeling in which afunction is represented as an association of the designer's
intention and a behavior that can actualize this function(see Figure 1)14].
In the FBS modeling, we represent a function as combination of a function body, objective entities, and functionmodiers (see Figure 2) 10]. A function body is a symbolthat carries meaning of the function in the form of verb
words like \to move" or \to carry." An objective entity isan entity that a function occurs on. A function modi er isa symbol that details the function body. A typical function
modi er is an adverb word like \precisely" or \ rmly."

FUNCTIONAL EVOLUTION PROCESS (FEP) MODEL

In a design process, functional description of a design
object is gradually re ned and detailed as the design proceeds. In order to support design by a computer, it is indispensable not only to represent functional description ofdesign objects but also to represent and to support such adesign process in which functional description is re ned anddetailed. We have model this desing process by representing evolution of the FBS model of a design object. We call

Relations among functions

Based on the structure of the function, we have de ned
four kinds of relations among functions that represent a2

c 1996 by ASME
Copyright described-as

function A
decomposed-intofunction B

function C
behavior C
state C

behavior B
state B
Figure 3.

modifier B
function B
behavior B
state B

Evolution by Decomposed-into Relation

Figure 6.

conditioned-byfunction B

modifier C
function C
behavior C
state C

Evolution by Described-as Relation

function A

behavior B
state B
Figure 4.

modifier A
function A

Object Model(FBS Model)

behavior A
state A

Process Model(FEP Model)

Function Description

Evolution by Conditioned-by Relation

Function Actualization
enhanced-byfunction B
behavior B
state B
Figure 5.

modifier A1

Function Evaluation

function A
Figure 7.

behavior A
state A

Steps of the FEP Model

function modi ers, or functional relations and removing
them.
Function actualization corresponds to the step to obtain behavioral description from the functional description
by using the knowledge about function. We have proposeda function prototype as the knowledge for function actualization 14].
Function evaluation is the step to evaluate how intended
functions are satis ed by the proposed behavioral description. A designer measures realizability of functions of thedesign object in this step.

Evolution by Enhanced-by Relation

this model functional evolution process (FEP) model 10].
A cycle of the functional evolution process consists of threesteps, namely, function description, function actualization,and function evaluation (see Figure 7), and a model of adesign object is revised by the designer after each cycle ofthe process. Namely, in the FEP model, the FBS model ofa design object is evolved through these three steps.
Function description is the step in which a designer
modi es required functions of the design object by operating function bodies, objective entities, and function modi ers. We represent this step of FEP with functional operations by a designer which include adding new functions,

Modeling an Actual Design of a Photocopier

We analyzed an actual design process of a photocopier
using the FBS and FEP schemes in the following steps:3c 1996 by ASME
Copyright sponds occurs in a design object 14]. On the other hand, adesigner judges how much a function is achieved in the design object and often compares two design candidates withrespect to the degree of satisfaction of the speci cations.
This kind of evaluation is executed with the parametric conditions described in the function modi er.
However, since this kind of evaluation is executed subjectively, it is not easy to describe the relationship between
the parametric conditions and the degree of functional satisfaction. To deal with this subjective relationship, we propose function content, which is quanti ed by using probability distribution of subjectivity of a physical parameterthat characterizes a function modi er.

1. First, we collected the documents and the technicaldrawings about a photocopier and interviewed with thedesigners to complement these documents.
2. Then we extracted FBS elements, namely, functions,function modi ers, behaviors, and states.
3. After extraction of the FBS elements, we constructed
descriptions of the FBS model at each step of the design
process (see Figure 8) and represented the FEP modelof this design process by tracing the evolution of the
FBS models (see Figure 9).
Finally, we investigated how each function or functionalmodi er was developed with functional relations in this design process and obtained following results:
Decomposed-into relation It has been claimed that decomposition of functions is the most basic procedure to deal
with functions in design 6]. In this design, we found 53
decomposed functions in this category.
Conditioned-by relation Since most of behaviors were implicit
or non-verbal in this design, it was dicult to nd suchcausal relations among functions. However by interviewing the designers, we found 10 functions in thiscategory.
Enhanced-by relation In our model, converting modi ers intofunctions is achieved by adding enhanced-by relations.
An enhanced function is found by evaluating the modi ers. The initial function model of this design had relatively a few functions and many modi ers. It implies
that interpretation of those modi ers plays importantrole in this design. In this design, we found 29 functionsin this category.
Described-as relation A typical procedure observed in this design process is adding modi ers with described-as relations. This way to add modi ers gives more detail descriptions to other modi ers. In this design, we found
30 modi ers in this category.
As we mentioned, there were relatively a few functions
and many modi ers in the initial function model of this design. It means that operating modi ers is important process
to evolve function models.

Modeling Method

We use SD method (Semantic Dierential method) 5]
for making correspondence between function modi ers andphysical parameters. The SD method is a method for representing human subjectivity quantitatively by making correspondence between evaluation and physical values that canbe evaluate objectively. The SD method employs a psychological test and principal component analysis1]. Here,
we de ne the probability of subjectivity of a modi er for acertain parametric value as the rate of persons who recognize that the modi er is achieved mostly at this parametricvalue in a certain group of testees.
As a result of the psychological test developed by the SD
method, we can obtain the probability distribution of subjectivity about evaluation against physical parameters (seeFigure 11). By quantifying function modi ers in this way,
we can represent the balancings or negotiations betweendierent modi ers. In the following sections, we de ne thefunction content that represents degree of satisfaction of afunction by using the probability of subjectivity.
Function Content

As we discussed, function evaluation is to measure functional satisfaction. However, each process of function evaluation can yield dierent result and the distribution of results of function evaluation processes indicates the degree
how the function has acceptable de nition. We introduce
concept function content as the degree of tness of de nitionof function.
From our experience to observe functionality in design, we assume these three criteria which function content
should satisfy.

MODEL OF FUNCTION EVALUATION

Here, we assume that functions are classi ed into two
types, namely, verbal type that is embodied as physicalbehavior and adverbial type that is embodied as physicalparameter. First type of function corresponds to function
body and second type of function corresponds to function
modi er 10].
A function body is evaluated in a binary manner, thatis, whether or not the behavior to which the function corre-

1. Because higher probability of subjectivity means thatthe function is supported by more persons, high probability should provide high value of function content(assumption 1).
4

c 1996 by ASME
Copyright M1: beautifuly
M2: effectively
M3: speedy
M4: exactly

Ds

Ds

Ds

to copy information on originals to plain papers

D

D

D

M6: uniformly
M5: effectivelyD

to translate light and shade on
original to distribution of optical intensity
M11:live longD

to transmit distribution ofDs
optical intensity
to generateD
E (M6)
light
M10:clearly
to raise luminance inE (M5)
to receive distribution D
specific direction
to balance amount of lightof optical intensity
to light up withD
distribution ofDDM9:exactly
optical intensity
to
light
up
lineally
lamp
light adjusting reflector
to relay distribution of
mirror # 1
plate
optical intensity
to move lightEsourceholizentallyslit
DD
to light up thesurface of original

M7: effectively

D

E

D

D

(M9)

(M10)

to hold optical diffusion

to transmit driving power
M8: smoothly

to generate driving powerE

to keep distribution of lightintensity away unwanted lightto maintain optical path

M12:strongly

(M7)

E

to restrict direction of(M8)
movement to horizon
to stabilize light source unit 1

wire
pulleyto bring exposed
face close to plane

motor
dual drive

to stabilize
rotation

Figure 8.

mirror # 2,3

mirror # 4

slit

Mn: modifier namefunction namelens coverCrod- bar

field lensDs: described-as

relation typeto move light source toinitial point

D: decomposed-into
C: conditioned-by
E(Mn): enhanced-by(related modifier)state(structure)

An FBS Model of the Photocopier2. If the distribution of the probability of subjectivity hasa peak, it means that there is a common sense about
the function and importance of the function is high.
We model this as the mean function content. In otherwords, if the shape of the distribution is more sharp, themean function content should be higher (assumption 2).
3. We should be able to explain the dierence of results offunction evaluation by dierence of groups (assumption
3).

predictability has more value to use. Here we de ne function content similar to de nition of information content butchange the de nition of probability to complement the difference among these two concepts.
Shannon de ned the information content as the changeof entropy by receiving the information . Entropy H (S ) of
an information source S is given as the following equation.

H (S ) = ;Shannon models a information source as probabilistic
in nature. He de nes a quantity called entropy, which isa measure of the unpredictability of information from theinformation source 9] 7]. Function evaluation can also beviewed probabilistic. Since function evaluation is a measureof satisfaction of function which depends humans judgementof value, it is intrinsically unpredictable. The dierenceis that function that evaluated with less unpredictability
has more value to use, while information with more un-

XM pi log2 pi
i=1

(1)

where

pi : occurring probability of ai
a1  : : :  aM : output unit of information source Entropy H (S ) is also called the mean information content I ,which means the average of information content when one
5c 1996 by ASME
Copyright Figure 9.

Functional Evolution in Design of a Photocopier Design

knows an output from the information source S . On theother hand, the information content of an output I (p) is
given by the following equation.

I (p) = ; log2 p

F =;

i=1

(4)

Where
i : probability of subjectivity of i1
M : value of physical parameters
p

(2)

v

v :::v

Firstly, while the information content I (p) means thescale of unknownness, the function content (we call thisF (p)) means the scale of satisfaction of the function according to the assumption 1. Secondly, while the mean information content I is minimum when one of p1  : : :  pM is 1 andothers are 0 and it is maximum when p1  : : :  pM = 1=M

Here, we de ne F (p) and F by using the idea of theinformation content as follows.

F (p) = ; log2 (1 ; p)

XM pi log2(1 ; pi)(3)6c 1996 by ASME
Copyright Function Layer

ThinlyBeautifully

Fast

To Copy

Thickly

To Create Backgroud

To Create Image

Behavior Layer

Function Content Layer

State Layer

Parameter Layer
15<v<30p1<3.5Function Body
Function Modifier
Behavior
State
Function Content

Figure 10.

Parameter
Function Hierarchy
Modification
Human Recognition
Physical Laws

M / FC Relation
FC / P Relation
P / S Relation

Relation among Function, Behavior, State and Parameter(occurring probabilities of all output units are equal), themean function content F takes opposit value of I basedon the assumption 2, namely, F is maximum when one ofp1  : : :  pM is 1 and others are 0, and it is minimum when
p1  : : :  pM = 1=M . Furthermore, the assumption 3 is explained by the fact that change of probability distribution
is caused by change of the groups of testees (see Figure 11).

contrary, the mean function content should be low fora function modi er that has low importance.

 Point 2: Dierence of groups

The probability distribution should reect dierencesof groups of testees.

 Possibility of functional optimization

If we succeed in quantifying function modi ers by using the function content, we can optimize the evaluation of the function modi er by nding out the valueof physical parameter that makes the function content
maximum.

EXPERIMENTS OF FUNCTION EVALUATION

In order to verify usefulness of our method for the function evaluation, we executed an experiment of the function
evaluation. We take image quality of photocopiers as an
example.
We verify the following points with this experiment.

Method of the Experiment

We here explain the SD method which we used for obtaining the function content.
The probability of subjectivity is needed for obtaining
the function content. We extract the probability of subjectivity by using SD method 5]. The SD method is a psycho- Point 1: Characteristics of the function content

The mean function content should be high for a function
modi er which the testees consider important. On the7c 1996 by ASME
Copyright Probability Distribution of Subjectivity

logical evaluation method which is eective for quantifying
human ambiguous impression.
This method is executed in the following steps:
1. Present some dierent samples to testees (see Figure
12).
2. Extract the impression about each sample from the testees.
The testees represent their impression by using the formshown in Figure 13, which consists of some sets of adjectives(here, they are the function modi ers).
The conditions of the experiment are as follows.
1. We set two groups according to occupations of testees
namely, one group consists of engineers and the otherconsists of desk workers. We present two same sets ofsamples to two groups.
2. In order to evaluate the letter image, we chose a function modi er \beautifully." However, since this vocabulary was too abstract, we could not determine thequantity of impression directly. Therefore, we decomposed the function modi er \beautifully" into lower
three function modi ers \clearly," \thickly" and \withbright background," which contribute to \beautifully"
higher, by using principal component analysis 1] (seeFigure 14).
3. We obtained physical parameters, which control thesethree function modi ers eectively and can be controlled directly by actuators in the machine, by using
principal component analysis again.
4. In order to obtain the mathematical function of probability distribution of subjectivity, we converted discrete
probability of subjectivity derived by the SD method
into continuous function.

1.0

Function Modifier: clearlyGroup AGroup B

0.0

Physical Parameter's Value

Figure 11.

Probability Distribution of Subjectivity

Figure 12.

Example of Samples

RESULTS OF THE EXPERIMENT

the function modi er \with bright background," which isdominated by kinds of paper material. This result satis ed
the Point 1.
Figure 15 also indicates that the mean function content about the function modi er \clearly" in engineers ishigher than in desk workers. This result denotes that theengineers have stronger common criteria for the machine's
performance than the desk workers. This result satis es the
Point 2.

Quantifying Function Modifier

Functional Optimization

We can obtain the values of physical parameters which
maximize the function content of the function modi er\beautifully" if we can decide weights of sub-modi ers depicted in Figure 14.
Here, we decided weights of the sub-modi ers as shownin Figure 16 by using the rates of the mean function contents
that represent their importance. By using these weights, we
obtained the value that maximizes the function content of
the modi er \beautifully" (see Figure 17). Table 1 depicts
the results of comparison between the image created by using this value and the image created by using original design
value (see Figure 18). In Table 1, the output image createdFigure 15 depicts function contents of two function
modi ers \clearly" and \with bright background" achieved
from two types of occupations, namely, engineers and desk
workers. Here, the parameter \surface potential" makes
both of the mean function content of three function modiers maximum. Figure 15 signi es that the mean function
content of the function modi er \clearly" is higher thanthe mean function content of the function modi er \withbright background," and this trend is notable in the engineers. This dierence tells that the testees considered thefunction modi er \clearly" more important, which is considered as one of the machine's basic performances, than8c 1996 by ASME
Copyright Function Content

SD Scale and Semantic Profile
Sample No.

very

considerably Fair considerably very

bright

dark

clear

uncleareven

unevendistinct

indistinct

thick

thin

smoothroughbackgraund dirtiness

deep

light

detailed

coarse5

Figure 13.

4

3

2

F:0.458
F:0.233

Surface Potential on the Photo Conductor

backgraund darkness

backgraund cleanness

Engineers
Desk Workers(V)

Function Content

backgraund brightness

Function modifier:clearly

1

Example of the Test Chart

Function modifier:with bright backgroundEngineers
Desk Workers
F:0.092
F:0.056(V)

Surface Potential on the Photo Conductor

beautifully

Figure 14.

clearly
thickly
with brightbackgroundFigure 15. Comparison between the Results of Function Evaluation

Decomposition of Function Modifier

beautifully(F)by the function content was supported by larger number oftestees than the original one. This result veri es the Point
3.
Furthermore, this dierence can be explained as follows:

Figure 16.

0.639
0.236
0.125

clearly(F1)
thickly(F2)with bright (F3)background

Functional Decomposition with Weights

 The value of the original design is determined as a resultof negotiation among many other function modi ers,
such as, \evenly," \smoothly," and so on. Therefore
we cannot say that this derived value is optimal for
actual commercial machine. Nevertheless, this result of
optimization ts subjective evaluation of functions oftestees.
 It is dicult for a designer to examine all combinationsof parameter values with considering many function
modi ers because of hugeness of search space and ambiguity of function evaluation. Therefore, the designer
could not nd out the optimum value. The functional

optimization based on the function content proposed
here will be a strong method for solving this problem.
In short, the experiment clari ed that the function
content satis ed points 1-3. Therefore, we conclude that
we succeed in quantifying function modi ers for evaluatingthem by using the function content. Moreover, usefulnessof our approach is clari ed by the experiment of the optimization.
9c 1996 by ASME
Copyright tifying functions, which are subjective concepts, by relatingthem to physical parameters. For this purpose, we introduced a value called function content. We evaluated an
actual design based on the function content and veri ed
correctness and usefulness of the function content as themethod for function evaluation. As an application of thismethodology, we show an example of functional optimization based on the function content.
Future works includes:

Engineers

clearly
F1

thickly
F2- Making the dierences between the function evaluationsof the actual design and the function evaluation basedon this framework more clear by analyzing the results ofdecision making in actual design based on this method.
- Developing a self-maintenance machine 11] which canmake repair planning more exible by using this method
for its fault diagnosis and repair planning.

Function Content

with bright background
F3

Design Value
C1

Surface Potential on the Photo Conductor

F =(0.639F1+0.236F2+0.125F3) takes maximum value at C1.
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Figure 17. Decision of Values of Physical Parameters by Using the
Function Content

Output Image by the Optimized Value

Output Image by the Design Value

Figure 18.

Comparison between Output Images

Table 1.

Evaluation about the Output Images

Support the result by the function content 17/25
Support the result by the original value
8/25

CONCLUSION

In this paper, we proposed the FEP (FunctionalEvolution-Process) model in which a design object is gradually evolved according to results of functional evaluation.
Furthermore we discussed human function evaluation as animportant step of design and proposed a method for quan10c 1996 by ASME
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c 1996 by ASME
Copyright