SELECTION OF DESIGN REQUIREMENTS USING QFD AND A DESIRABILITY
FUNCTION
Taeho Park1) and Arvinder Loomba2)
1)
San Jose State University (park_t@cob.sjsu.edu)
San Jose State University (loomba_a@cob.sjsu.edu)
2)
ABSTRACT
Quality Function Deployment (QFD) used to increase customer satisfaction utilizes the house of
quality (HOQ) to translate customer needs and wants into technical design requirements. HOQ is
to prioritize design requirements (DRs) to satisfy customer requirements (CRs), and then a
quality designer decides on which DRs should be embedded into the product by considering
costs, time, and customer satisfaction level. The conflicting multiple objectives, such as cost vs.
customer satisfaction level, are usually occurring in the decision process. The traditional QFD
has not addressed this multiple objective issue nor provided a methodology to treat the multiple
objectives. This research presents a desirability function approach to accommodate the multiple
objectives to achieve at the same time during the QFD decision process. A numerical example is
shown to demonstrate the suitability of the model.
1. INTRODUCTION
Quality has become one of the critical competitive strategies in today's global market. To ensure
the improvement of quality and productivity, firms have adopted Total Quality Management
(TQM) as a key element of their business goals and initiated the use of TQM methods, such as
Quality Function Deployment (QFD), design for manufacturability, and statistical process
control. Among these TQM methods, QFD has been used to translate customer needs and wants
into technical design requirements by integrating marketing, design engineering, manufacturing,
and other relevant functions of an organization. (Akao, 1990; Ansari and Modarress, 1994)
QFD originated in 1972 at Mitsubishi's Kobe shipyard site, and then Toyota and its suppliers
developed it further for a rust prevention study (Hauser and Clausing, 1988; Wasserman, 1993).
After the concept of QFD was introduced in the U.S. through auto manufacturers and part
suppliers (Sullivan, 1987), many U.S. firms, such as Procter & Gamble, Raychem, Digital
Equipment Corp., Hewlett-Packard, AT&T, ITT, GM, and Ford applied QFD to improving
communication, product development, and measurement of processes and systems (Bounds, et
al., 1994; Ansari and Modarress, 1994). Furthermore, as cited in McElroy (1989), “QFD can be
applied to whatever process you have control over: new product design, business plans,
engineering proposal systems, even reducing die transition time,” said Norman Morrell,
corporate manager of quality-product reliability at Budd Co.
The basic concept of QFD is to translate the desires of customers into product design or
engineering characteristics, and subsequently into parts characteristics, process plans, and
production requirements. Each translation uses a matrix, called the house of quality (HOQ), for
identifying Customer Requirements (CRs) and establishing priorities of Design Requirements
(DRs) to satisfy the CRs (Hauser and Clausing, 1988). Refer to Griffin and Hauser (1993) for a
discussion on the issues of identifying, structuring, and providing priorities for CRs. HOQ is
presented in a matrix form which shows (1) CRs in rows and DRs in columns, (2) their
relationships within the matrix, and (3) the correlations (i.e., dependencies) of DRs at the top of
the matrix. (See Figure 1 in the next section for details.)
1
Although the conventional approach to prioritizing DRs is easy to understand and use, there are
several methodological issues associated with it: (1) determination of the degree of importance of
CRs, (2) assignment of the relationship ratings between CRs and DRs, (3) adjustment of the
relationship ratings between CRs and DRs, called normalization, in order to insure a more
meaningful representation of the DR priorities, (4) incorporation of the correlations between DRs
to a decision process for determining appropriate DRs, and (5) consideration of cost trade-offs
among DRs. Some research has been done to resolve these methodological issues. Lu, et al.
(1994) applied the Analytical Hierarchy Process (AHP) (Saaty 1980; Saaty and Kearns 1985) to
determine the degree of importance of CRs. It should be noted that AHP is a powerful and
widely-used multicriteria decision-making technique for prioritizing decision alternatives of
interest (Saaty, 1980). Wasserman (1993) presented a linear integer programming model for
maximizing customer satisfaction subject to a cost (i.e., limited budget) constraint with a linear
function and a procedure for normalizing the relationship ratings between CRs and DRs.
However, further studies are necessary on development of a better relationship rating scheme
between CRs and DRs other than the conventional ordinal rating scale, and integration of the
correlations between DRs to a decision model for determining appropriate DRs to satisfy CRs.
Park and Kim (1998) recently presented 1) a new integrative decision model for selecting an
optimal set of DRs which incorporates all of the above issues into the conventional prioritization
processes in QFD, 2) a modified HOQ with a better approach for assigning relationship ratings
between CRs and DRs other than the current rating scheme, and 3) a quadratic integer
programming formulation for considering cost trade-offs among DRs and correlations between
DRs during the process of selecting an optimal set of DRs.
All previous research have mainly focused on selecting DRs for achieving an objective, i.e.,
customer satisfaction. The customer service level is often conflicted with some other operational
strategies (e.g., time and cost). This, this research presents a desirability function approach,
initiated by Harrington (1965), to consider the multiple objectives at the same time during the
QFD decision process. A numerical example is shown to demonstrate the suitability of the
model.
2
2. DESCRIPTION OF PRIORITIZATION PROBLEMS IN QFD
Since QFD was introduced to U.S. firms in 1983, it was applied to many industry problems (e.g.,
product design, strategic planning, renovation of a computer workroom facility, and
improvement of customer service) using the conventional QFD processes for prioritizing DRs.
Refer to Park and Kim (1998), Glushkovsky, et al. (1995), and Lockamy and Khurana (1995) for
some recent application examples.
An HOQ typically contains information on CRs, relative importance of the CRs, DRs for
satisfying the CRs, relationships between CRs and DRs, and correlations between DRs, as shown
in Figure 1.
Correlations between
Design Requirements



Design Requirements
Im
Degree of
DR2
DR3
DR4
rta
po
DR1
nc
Customer Requirements
e
CR1
0.3 
CR2
0.2
CR3
0.1
CR4
0.1
CR5
0.3
Absolute Importance
Relative Importance








3.8
0.35
1.6
0.15


0.9
0.08
4.5
0.42
Legends
 Strong Relationship
O Medium Relationship
 Weak Relationship
Figure 1. A Typical HOQ Matrix with a 1-3-9 Rating Scheme.
3
In conventional QFD applications, a cell (i, j) in the relationship matrix of HOQ (i.e., i-th row
and j-th column of HOQ) is assigned 1, 3, 9 (or 1, 5, 9) to represent a weak, medium, or strong
relationship between i-th CR (called CRi) and j-th DR (called DRj), respectively. The absolute
and relative importance of DRs are computed using the relative importance of CRs and the
relationship ratings (i.e., 1-3-9 or 1-5-9).
For each DR, the absolute importance rating is
computed as:
m
AIj =
W
i
(1)
Rij ,
i=1
where AIj = absolute (technical) importance rating of DRj, j = 1, ..., n,
Wi = degree of importance (i.e., importance weight) of CRi, i = 1, ..., m,
Rij = relationship rating representing the strength of the relationship between CRi
and DRj.
The absolute importance rating can then be transformed into the relative importance rating, RIj,
as
RIj =
AIj
n
 AI
.
k
k =1
The larger RIj is, the more important DRj is. Thus, without consideration of any other constraints
(e.g., cost and time), DRs should be incorporated into the product of interest in the order of their
relative importance rating to achieve more customer satisfaction.
As mentioned in the previous section, the conventional approach to prioritizing design
requirements for determining the degree of contribution to customer satisfaction has the
following methodological problems (see Park and Kim (1998) for details):
i) Determination of the degree of importance of CRs:
ii) Assignment of relationship ratings between CRs and DRs:
iii) Normalization of the strength ratings of relationships between CRs and DRs:
iv) Consideration of the correlations between DRs:
4
v) Cost-customer satisfaction trade-offs among DRs:
Some research has been done to incorporate the above methodological issues into the decision
processes of determining appropriate DRs. Analytical Hierarchy Process (AHP) has been used to
measure consistent and stable importance weights of CRs (See Aswad (1989), Akao (1990),
Armacost, et al. (1994), and Lu, et al. (1994)). Lyman (1990) recommended a normalization
norm
function of Rij
n
R
= Rij /
ij
(i = 1, ..., m) to normalize the relationship ratings in order to
j=1
have more meaningful representation of the technical importance rating of DRs. Furthermore,
Wasserman (1993) presented an extension of Lyman’s normalization procedure, which can
accommodate correlations between DRs, with the following transformation function:
n
norm
R ij
R
=
k=1
n
n
ik
R
j=1 k=1

 kj
for i = 1, ..., m; j = 1, ..., n,
ij

(2)
 jk
where  kj denotes an element of the correlation matrix representing the correlation
between DRk and DRj.
He also presented a QFD planning process model considering linear cost-benefit trade-offs
among DRs. His linear integer programming formulation for selecting appropriate DRs included
1) an objective function of maximizing technical importance ratings of DRs to be selected, and 2)
a linear cost constraint subject to a targeted total cost. The linear programming formulation,
however, did not take into account correlation between DRs.
Park and Kim (1998) employed a new rating scheme for the relationship between CRs and DRs,
using a most commonly-used multiattribute decision method (i.e., Swing Method) and
considered the correlation between DRs in the mathematical programming for selecting an
optimal set of DRs. Their integer mathematical programming is to maximize a single objective of
customer satisfaction.
3. A MULTIPLE OBJECTIVE MODEL FOR THE QFD SELECTION PROCESS
5
Using a desirability function approach, a mathematical programming model for selecting
appropriate DRs in consideration of multiple objectives is described in this section. Suppose that
an objective function, ŷ j , is to be transformed to dj. Suppose that yjmin and yjmax denote the
smallest value and maximum acceptable value of ŷ j , respectively, and r is a constant (r>0).
Then, dj is defined as follows:
i) For the smaller-the-better (STB) type objective functions, such as cost and time,
1, ŷ j  y j min ,

r
max

yj
 ŷ j 

 , y j min  ŷ j  y j max ,
d j   max
min


 yj
 y j


max
0, ŷ j  y j
,


(3)
ii) For a larger-the-better (LTB) type response, such as a customer satisfaction level,
0, ŷ j  y j min ,

 ŷ  y min  r

j
j
 , y min  ŷ  y max ,
d j   max
j
j
j
min 
y
 j  y j 

max
1, ŷ j  y j ,
(4)
The value of r, subjectively specified by the user, determines the shape of the desirability
function. Examples of the desirability function with several different r values are shown in Figure
2. As illustrated in the figure, the desirability function dj is concave, linear, and convex when
0<r<1, r=1, and r>1, respectively. If a convex shaped function is used, the desirability value
diminishes more rapidly when ŷ j moves away from yjmin toward yjmax (but more slowly when ŷ j
gets close to yjmax) than when using a linear or concave shaped function.
6
The overall desirability, D (0  D  1), is defined by combining the individual dj's using a
geometric mean (Harrington (1965)), i.e.,
D = (d1d2...dm)1/m.
1.20
1.00
Desirability
0.80
r=0.3
0.60
r=0.6
r=1
0.40
r=2
r=3
0.20
0.00
x
Figure 2. Examples of the desirability function with several different r values.
In the QFD design problem, the objective function could be to find a solution which maximizes
the value of D, i.e., selection of DRs that achieves the optimal compromise among objective
functions, such as maximization of a total absolute technical importance rating, minimization of
total costs, minimization of total time required for the new design changes. Therefore, it can be
formulated using nonlinear programming as follows:
Maximize D = (d1d2...dm)1/m
7
subject to
Xi = 0 or 1,  i = 1, …, n.
where Xi = i-th DR,
Xi = 1 (0) means the corresponding DR will (not) be included in the new design,
respectively,


 = a set of selected DRs (i.e., Xi’s in  = 1),

ŷ j = a value of j-th objective with a set of selected DRs,  ,
dj = a desirability function for the j-th objective,
defined by Equation (3) for a STB type objective function, or
defined by Equation (4) for a LTB type objective function,
4. APPLICATION TO BUILDING INDOOR AIR QUALITY IMPROVEMENT
4.1 Description of the Building Indoor Air Quality Problem
During the last decade, concerns have been expressed regarding indoor air quality for nonindustrial buildings. (Refer to Eaton (1995), Banham (1994), and Buckler (1994)) Such indoor
air quality problems, classified as Sick Building Syndrome (SBS) or Building Related Illness
(BRI), have occurred in all types and ages of structures, namely from newly constructed
buildings to renovated facilities or old buildings.
Today, most commercial buildings are
mechanically ventilated with virtually no natural ventilation from the outside.
Moreover,
designers, owners, and operators have tried to minimize unwanted air infiltration because rising
energy costs are the primary cause of the "tight building syndrome," along with various
chemicals present in building materials and furniture. In addition to other physical factors in the
workplace (e.g., lack of windows, temperature variations, and poor ergonomic design), poor
8
indoor air quality is viewed as a major building occupant complaint. (Banham, 1994; Lunau,
1993; Moseley, 1990)
Recently, employees working in the Business Tower (BT) building at San Jose State University
(SJSU) suffered from poor indoor air quality and expressed complaints of being sleepy and tired
at work. Stuffiness was a common complaint, along with the presence of flies within the
stairwell entrance vestibules; a large accumulation of dust particles in the building was also
found. (I&A Engineering, 1994) The following is a list of problems identified: (1) stuffiness, (2)
temperature, (3) dust particles, (4) ventilation, (5) odors, (6) housekeeping, and (7) flies. Thus, a
study was conducted in 1994 to test indoor air quality for gases, volatile organic components, and
contents of particulate matters, such as dust.
The BT building with a closed environment (that is, all windows are sealed) was designed in
1968 and completed by 1970-1971. The ten-story building’s Heating, Ventilation, and Air
Conditioning (HVAC) system consists of a double duct constant volume air distribution system.
The air supply system has a floor-mounted double inlet centrifugal fan with a cooling coil and
heating coil arranged side by side on the ground floor. The separate heating and cooling ducts
are then routed into the shaft to the 10th floor. The ground floor air intake system is composed
of a grade level outside air intake louver and pneumatically-controlled motorized intake dampers.
The air is then drawn through a prefilter and final bag filters before entering the supply fan room.
The return air system employs a non-ducted return air plenum pregnable, which is also typical of
HVAC system designs today. Return air from each thermal zone enters the ceiling cavity and is
drawn back to the central shaft return air opening. The exhaust air is delivered to a plenum
9
where it is then relieved out of the building through the exhaust louver/damper combination, or
recirculated into the mixed air plenum where it is mixed with outside air before entering the fan
system.
The indoor air quality study for the BT building recommended the following actions to improve
the mechanical BT HVAC operating systems, resulting in a better working and health
environment for occupants in the building (I&A Engineering, 1994):
(1)
Air Plenum: All linear boards should be removed from supply plenum walls and replaced
with new 2” of 3 lb density matt faced acoustic lining.
(2)
Door Seals: All fan plenum door seals shall be removed and replaced with new tight fitting
weatherstripping to reduce air leakage and uncontrolled infiltration.
(3)
An eighteen-gage galvanized sheet metal condensation drain should be installed under the
chilled water cooling coils.
(4)
Dampers: The air damper motors should be tested and/or replaced as necessary.
(5)
Plumbing Risers: The shaft should be provided with two-hour fire rated access panels at the
toilet room wall adjacent to the shaft at each door.
(6)
Air Delivery Systems: Air delivery systems, including air supply fan and air return fan,
should be upgraded with more HP motors.
(7)
Janitor Closet Ventilation: A dedicated roof mounted exhaust fan should be installed to
provide ventilation of the janitor’s closet on each floor.
(8)
Duct Distribution System: A duct distribution system should be improved to prevent air
leakage.
(9)
Duct Plenums and Fans: Duct plenums and fans should be cleaned.
10
(10) Direct Digital Control (DDC) System: The existing standard profile control system should
be replaced with a DDC system for more efficient air control and delivery.
(11) HVAC Louvers: All damper motors, existing insect screens, and the vestibule ventilation
exhaust fan should be replaced with new units.
(12) Carbon Dioxide Sensor System: A CO2 monitoring station with sensors should be installed
in the return air plenum.
(13) Housekeeping: BT janitorial services should be reviewed and improved to ensure the
building is clean at all times. In addition, any chemical cleaning detergents should be
removed from the building.
4.2 Numerical Results
To determine the priorities of implementing the above recommendations, the new HOQ
prioritization process described in Section III was employed.
A customer study involved
assessing the judgments of department secretaries in their views on the significance of problems
caused by poor indoor air quality.
The customer study was conducted using a pairwise
comparison method in the AHP data collection process. Since a group of eight secretaries
working daily in the BT building participated in the survey, a geometric mean which is an 8-th
root of the product of judgments provided by eight individuals was used to combine group
judgments. It should be noted that the secretaries are good surrogates for those who use the
building because they spend more time in the building than anyone else.
11
Table 1 shows the results of the customer study done, using a pairwise comparison method in the
AHP data collection process, and a geometric mean approach to combining group judgments.
Eigenvalues of the judgment matrix in Table 1, which are the importance weights of CRs, are
then calculated as .202, .187, .085, .152, .157, .132, and .084, respectively. Since the consistency
ratio turns out to be 0.04, judgments of the importance of problems are acceptable. It should be
noted that the value of consistency ratio should be around 10% or less to be acceptable. (Saaty
and Kearns, 1985)
Table 1. An Importance Matrix for CRs Obtained Using Pairwise Comparison.
The numbers indicate geometric means of judgments of eight secretaries.
Stuffiness
Temperature
Dust Particles
Temp.
Dust
Ventil.
Odors
House
Flies
1.0
2.7
2.2
1.1
1.1
2.4
3.5
1.2
1.2
1.6
1.2
.82
.54
.63
1.4
1.8
1.3
1.8
2.0
1.7
Ventilation
Odors
Housekeeping
2.4
Figure 3 presents an HOQ matrix for the BT building indoor air quality problem, including (1)
degrees of importance of CRs as obtained from the AHP analysis, (2) normalized relationship
ratings between CRs and DRs obtained using Swing Method and normalization of relationship
ratings by Equation (2) in Section II, (3) correlation between DRs, and (4) cost required to install
the DRs.
12
According to the results of prioritization of DRs, it is found that upgrading an air delivery system
(i.e., air supply/return fans) is most important for improving building occupants’ satisfaction with
indoor air quality in the BT building, and the installation of a CO2 monitoring station with
sensors is least important. If a repair budget is enough to complete all recommendations, the
problem will become very trivial. As mentioned earlier, however, when available organizational
resources (e.g., budget and time) are limited, as in our BT indoor air quality problem, a further
analysis is necessary to select which DRs should be completed.
Each cost shown in Figure 3 is required to complete an individual DR alone. However, there
may be some cost savings when two DRs are installed at the same time. For example, upgrading
air plenum walls (i.e., DR1) and replacing all fan plenum door seals with new ones (i.e., DR2)
require $18,000 and $12,000, respectively, when each of them is completed separately. When
both of them are included in a repair contract, $4500 out of $30,000 is discounted because of
savings in time. Table 2 illustrates cost savings from simultaneous installation of two DRs.
Wasserman (1993) presented a simple linear cost function under a limitation of a given target
cost as follows: c1 x1 +

+ cn xn - B, where cj is cost required to include DRj, and B is a given
total target cost. In the case where dependencies (i.e., correlations) exist among some DRs, some
savings in resource consumption are most likely expected when two or more correlated DRs are
simultaneously installed into a product or service design. It is more appropriate to express the
n
cost function in a quadratic form such that y (X) =
n
n
c x - s
j
j=1
j
ij
x i x j - B , where sij is
i=1 j>i
saving of resource (e.g., cost) usage associated with simultaneous implementation of i-th and j-th
DRs.
13










DR1
DR2
DR3
DR4
DR5
DR6
DR7
DR8
DR9 DR10 DR11 DR12 DR13 DR14 DR15 DR16
e
nc
rta
po
Im
Degree of


Stuffiness
.202
.039
.040
0
.044
0
.280
.044
0
.039
.023
.185
0.224
0
.039
.031
.013
Temperature
.187
0
0
0
.028
0
.361
.042
0
.046
0
.279
.217
0
0
.028
0
Dust Particles .085 .384
.209
0
.037
0
0
0
0
.037
.321
0
.011
0
0
0
0
Ventilation
.152
.015
.021
.020
.099
.017
.255
.059
.017
.039
0
.155
.251
0
.020
.032
0
Odors
.157
.003
.010
0
0
.150
.033
.332
.196
.033
0
.010
.100
0
0
0
.133
Housekeeping .132 .128
.128
.337
0
0
0
0
0
.027
.061
0
.051
0
0
.168
.101
0
0
.174
0
0
0
0
0
0
0
.130
.435
0
.261
0
Flies
.084
Absolute Importance
Cost
0
.0602 .0475 .0475 .0469 .0261 .1680 .0778 .0334 .0343 .0400 .1147 .1583 .0365 .0109 .0605 .0368
18000 12000 12000 12000 18000 45000 25000 15000 15000 50000 240000 25000
8000
8000 10000
0
[NOTE] DR1: Air plenum walls upgrade
DR2: Air plenum doors seals
DR3: Coils condensation collection
DR4: Air dampers upgrade
DR5: Sewer and vent. lines pressure test
DR6: Supply fan/return fan air delivery upgrade
DR7: Janitor closets exhaust system addition
DR8: Janitor closet trap primer addition
DR9: Duct leakage
DR10: Cleaning of duct, plenums, and fans
DR11: Terminal boxes conversion to DDC system
DR12: Air balancing
DR13: Air louvers screen
DR14: CO2 detection
DR15: Stairwell vestibule’s shaft cleaning and door seal
DR16: Chemical/detergents type and storage
Figure 3. An HOQ Matrix for the Indoor Air Quality Problem for the BT building at SJSU.
14
Table 2. Cost Savings Occurring When Two DRs are Completed
at the Same Time.
Pair of DRs
Cost Saving from Simultaneous Installation
DR1 & DR2
$4,500
DR1 & DR10
$10,200
DR2 & DR9
$4,050
DR6 & DR11
$28,500
DR6 & DR12
$10,500
DR12 & DR15
$5,250
Thus, the BT building indoor air quality problem is to achieve two objectives: maximization of a
total absolute technical importance rating and minimization of total costs by solving the
following a quadratic integer programming with the desirability function approach:
Maximize D = (d1d2)1/2
subject to
16
ŷ1 =
 AI X
i
i
i =1
ŷ 2 = c1 x1 +    + c16 x16 - s1,2 x1 x2 - s1,10 x1 x10 - s2,9 x2 x9 - s6,11 x6 x11 - s6,12 x6 x12 - s12,15 x12 x15
ŷ 2  B
Xi = 0 or 1,  i = 1, …, 16.
where Xi = 0-1 decision variable for the i-th DR,
d1 = a desirability function for ŷ1 , defined by Equation (4) with r = 0.3,
d2 = a desirability function for ŷ 2 , defined by Equation (3) with r = 0.3,
B = budget ($500,000) available for improving indoor air quality.
15
The above quadratic integer programming with a repair budget of $500,000 is solved using the
Solver module in Microsoft Excel, and the following solution is found:
(1) Objective function value of the total technical importance rating: 0.7743.
(2) Objective function value of the total cost: $157700.
(3) Decision variables: DR1 =    = DR4 = 1, DR5 = 0, DR6 = DR7 = 1, DR8 = 0, DR9 = 1,
DR10 = DR11 = 0, DR12 = DR13 = 1, DR14 = 0, DR15 = DR16 = 1.
(4) Desirability function value (d1) for the total technical importance rating: 0.9263,
(5) Desirability function value (d2) for the total cost: 0.9197,
(6) An optimal overall desirability (D): 0.923.
The optimal solution remains the same even with different r values of o.6 and 1.0.
5. CONCLUSIONS
A multiple-objective mathematical programming using a prioritization process in QFD and
desirability function is presented in this paper to determine an optimal set of design requirements
that will be included in a new product or service. The new integrative decision approach with
multiple objectives has been applied to a building indoor air quality problem. Results of the
application show that its step-by-step structured decision process can help practitioners
understand the entire decision process easily and implement it to their industrial problems which
will usually have more than one objective. Although the proposed comprehensive model involves
more effort (e.g., data collection, mathematical model building, and computation) in comparison
to the conventional HOQ process, it is worthwhile to invest such effort during the design stage in
order to determine an optimal set of DRs.
16
REFERENCES
1)
Akao, Y., 1990, Quality Function Deployment: Integrating Customer Requirements into
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