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POLITECNICO DI TORINO - ITALYDIGEP – Department of Management and Production Engineering
Prioritization of Engineering Characteristics on QFD: old problems and new approaches7TH GALILEE QUALITY CONFERENCE, “QUALITY – THEORY AND
PRACTICE”
ORT BRAUDE COLLEGE OF ENGINEERING IN KARMIEL
MAY 1ST 2014Fiorenzo FranceschiniMaurizio Galetto
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“QFD is a method to transform user demands into design quality, to deploy the functions forming quality, and to deploy methods for achieving the design quality into subsystems and component parts, and ultimately to specific elements of the manufacturing process”. Akao (1988)
Quality Function Deployment (QFD)
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From Customer Requirements to new products
NEW PRODUCT
COMPANY
CUSTOMERS
I want …I like …I like .
I want …I want …I like … I wa
I want …I like …
I want …
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Phases of QFD
QFD PLANNING STRUCTURE
PRODUCTPLANNING MATRIX
PART / SUBSYSTEMDEPLOYMENT MATRIX
PROCESS PLANNINGMATRIX
PROCESS / QUALITYCONTROL MATRIX
Customerrequirements
CriticalProduct
Requirement
CriticalProduct
Requirement
CriticalComponents
Characteristics
CriticalProcess
Steps
CriticalProcess
Step
Process &Quality Control
Parameters
CriticalComponents
Characteristics
Phase I
Phase II
Phase III
Phase IV
EngineeringCharacteristics
CustomerRequirements
EngineeringCharacteristics
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The main pillars of the House of Quality (HoQ)
1. C
usto
mer
Req
uire
men
ts
6. Relationship Matrix
3. C
ompe
titive
Ben
chm
arki
ng
8. Prioritization of Engineering Characteristics
5. Engineering Characteristics
7. Correlation Matrix
2. P
rioriti
zatio
n of
Cus
tom
er
Requ
irem
ents
4. C
ompe
titive
Prio
ritiza
tion
of
Cust
omer
Req
uire
men
ts
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Example: design of a pencil (Customer Requirements)
• Easy to hold• Does not smear• Point lasts• Does not roll• …
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Identification of Engineering Characteristics
Customer Requirements
Engineering Characteristics
QFD work group
Lf
• hexagonality,• erasure residue,• dust,• …
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The pencil exampleCustomer Requirements
(CRs)Engineering Characteristics
(ECs)
Easy to hold • length• hexagonality
Does not smear• time between sharpening• lead dust generated• erasure residue
Point lasts• length• time between sharpening• lead dust generated• erasure residue
Does not roll • length• hexagonality
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The pencil example
Engineering Characteristics(HOWS)
Length
Time between sharpening
Lead dust generated
Hexagonality
Erasure residue
Customer Requirements (WHATS)
Easy to hold O X
Does not smear O X X
Point lasts O X X
Does not roll X
-> weak relationshipO -> medium relationshipX -> strong relationship
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Two prioritization problems
• CRs prioritization (are all CRs equally important?)
• ECs prioritization.
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The pencil exampleEngineering Characteristics
(HOWS)
Priorities of
WHATS
Length
Time between sharpening
Lead dust generated
Hexagonality
Erasure residue
Customer Requirements (WHATS)
Easy to hold 3rd O X
Does not smear 2nd O X X
Point lasts 1st O X X
Does not roll 3rd X
Priorities of HOWS
Can CRs prioritization influence ECs prioritization?
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Steps:
1. assign a numerical importance to each CR;
2. convert the relationships symbols between CRs and ECs into “equivalent” numeric values;
3. determine the numerical importance of each EC using the ISM algorithm.
The Independent Scoring Method (ISM)
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The pencil example: 1st STEPEngineering Characteristics
(HOWS)
Importance of
WHATS
Length
Time between sharpening
Lead dust generated
Hexagonality
Erasure residue
Customer Requirements (WHATS)
Easy to hold 2 O X
Does not smear 3 O X X
Point lasts 5 O X X
Does not roll 2 X1 -> not important at all2 -> minor importance3 -> some importance4 -> strong importance5 -> very strong importance
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The pencil example: 2nd STEP
empty box -> 0 -> 1O -> 3X -> 9
Engineering Characteristics (HOWS)
Importance of
WHATS
Length
Time between sharpening
Lead dust generated
Hexagonality
Erasure residue
Customer Requirements (WHATS)
Easy to hold 2 3 0 0 9 0
Does not smear 3 0 3 9 0 9
Point lasts 5 1 3 9 0 9
Does not roll 2 1 0 0 9 0
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The pencil example: 3rd STEPEngineering Characteristics
(HOWS)
Importance of
WHATS
Length
Time between sharpening
Lead dust generated
Hexagonality
Erasure residue
Customer Requirements (WHATS)
Easy to hold 2 3 0 0 9 0
Does not smear 3 0 3 9 0 9
Point lasts 5 1 3 9 0 9
Does not roll 2 1 0 0 9 0
Priorities of HOWS 13 24 72 36 72
1
2
2
2 3 3 0 5 1 2 1 132 0 3 3 5 3 2 0 24...
www
,1
n
j i i ji
w d r
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• Intuitional.• Easy to use.• Easy to interpret.• Use of standard Mathematical operators.• Largely diffused.• …
Advantages of the ISM
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• Are customers really able to express CRs importance on ratio scales (cardinal properties)?
• What is the correct symbol codification in the relationship matrix (1-2-3, 1-3-5, 1-3-9, …)?
• How to select the right scale for importance and symbol codification?
• Is there any arbitrariness in scale definition (zero point, graduation, unit, …)?
Drawbacks/Criticalities
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Example: effect of different codifications of symbols in the relationship matrix
EC1 EC2 EC1 EC2
CR1 X X CR1 X XCR2 X CR2 XCR3 O X CR3 O XCR4 O CR4 OCR5 O CR5 O
CR6 O CR6 O
Importance 18 15 Importance 22 27
Codification 1-3-5 Codification 1-3-9
EC1 > EC2 EC1 < EC2
All CRs have the same importance d = 1.
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Techniques based on 5-levels rating scales
• The response scale has ordinal properties:
• Arbitrary promotion of results from ordinal to interval or ratio scales.
Scale level Description1 Not important at all2 Minor importance3 Some importance4 Strong importance5 Very strong importance
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Individual response scales are not aligned
Can we sentence that the mean value of the
sample is ? 3 2 5 10
3 3x
1 52 43
1 5432
1 5432
3
2
5
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Example of arbitrary promotion of results from ordinal to interval or ratio scales.
CRs 1 2 3 4 5CR1 XCR2 XCR3 X
We can sentence:• CR1 is better than CR2
We cannot sentence:• CR1 is evaluated twice CR2 (ratio scale)• the distance between CR3 and CR1 is 3 scale
units (interval scale).
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Fusion of CRs importance evaluated by linear orderings
• Respondents’ orderings:1) CR3 > CR1 > CR2
2) CR1 > CR2 > CR3
3) ...
• How operate a fusion of respondents’ orderings?
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The first problem: prioritization of CRs1.
Cus
tom
er R
equi
rem
ents
6. Relationship Matrix
3. C
ompe
titive
Ben
chm
arki
ng
8. Prioritization of Engineering Characteristics
5. Engineering Characteristics
7. Correlation Matrix
2. P
rioriti
zatio
n of
Cus
tom
er
Requ
irem
ents
4. C
ompe
titive
Prio
ritiza
tion
of
Cust
omer
Req
uire
men
ts
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Finding the right way
• In some cases we assist to a violation of scale properties on which CRs are evaluated.
• In the scientific literature there are many approaches for prioritizing CRs.
• Some of them may lead to misleading results.
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Analytic Hierarchy Process (AHP)
• The AHP is a technique of Multiple Criteria Decision Making developed by Thomas L. Saaty (1980).
• It is based on the paired comparison of CRs.
• The result is a global ordering of the CRs.
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Conceptual scheme of AHP
12 1
12 2
1 2
1 ...
1/ 1 ...
... ... ... ...
1/ 1/ ... 1
n
n
n n
a a
a a
a a
A
1 1 1 2 1
2 1 2 2 2
1 2
/ / /
/ / /
/ / /
n
n
n n n n
d d d d d d
d d d d d d
d d d d d d
1
n
d
d
d
PAIRED COMPARISON MATRIX
PRIORITY VECTOR
maxA d d
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The comparison matrix for the pencil example
CR1 (Easy to hold)
CR2 (Does not smear)
CR3 (Point lasts)
CR4 (Does not roll)
CR1 (Easy to hold) 1 5 6 7
CR2 (Does not smear) 1/5 1 4 6
CR3 (Point lasts) 1/6 1/4 1 4
CR4 (Does not roll) 1/7 1/6 1/4 1
CRs Importance
0.61
0.24
0.10
0.05
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Criticalities of AHP approach
• Not always the consistency of paired comparisons is guaranteed.
• Respondents usually do not have a common reference scale.
• It is based on the assumption that Saaty’s scale for paired comparison has ratio scale properties.
• It is “effective” only with small numbers of CRs.
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Paired Comparison Method
• It may lead to inconsistencies in judgment.
Example:If CR1 > CR2 and CR2 > CR3 , it can happen for some individuals that CR3 > CR1 .
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The second problem: prioritization of ECs1.
Cus
tom
er R
equi
rem
ents
6. Relationship Matrix
3. C
ompe
titive
Ben
chm
arki
ng
8. Prioritization of Engineering Characteristics
5. Engineering Characteristics
7. Correlation Matrix
2. P
rioriti
zatio
n of
Cus
tom
er
Requ
irem
ents
4. C
ompe
titive
Prio
ritiza
tion
of
Cust
omer
Req
uire
men
ts
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The state of the art
The scientific literature proposes many techniques which differ for:• typology of data,• properties of data and scales,• mathematical models for
synthesis/aggregation of the information collected from the customers (mean, median, standard deviation, …),
• models linking CRs and ECs in the relationship matrix (linear, weighted, …).
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• Independent Scoring Method (ISM) [Akao, 1988],• Multiple Criteria Decision Aid (MCDA) methods
(Electre II, …) [Roy, 1991].• Interactive Design Requirement Ranking (IDRR)
algorithm [Franceschini, 2002].• Paired Comparison Method (PC) [Thurstone,
1927].• Ordinal Prioritization Method (OPM)
[Franceschini, 2014].• ...
Principal techniques
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What is the most appropriate?
Multiple Criteria Decision Aid
(MCDA) Independent
Scoring Method (ISM)
Paired Comparison Method (PC)
Interactive Design Requirement
Ranking (IDRR)
Ordinal Prioritization
Method (OPM)
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A novel taxonomy
CRs importance
cardinal scale ordinal scale ordering
Coefficients of
Relationshi
p matri
x
cardinal scale
Independent Scoring Method
(ISM)
Thurstone scaling+
Independent Scoring Method
(ISM)
ordinal scale
Multiple Criteria Decision Aid
(MCDA) methods
Thurstone scaling+
Multiple Criteria Decision Aid
(MCDA) methods
Ordinal Prioritization
Method (OPM)
orderingOrdered
Weighted Averaging (OWA)
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Ordinal Prioritization Method (OPM)
• It is a variant of Yager’s algorithm (2001).
• Each EC is evaluated according to any CR, a preference vector corresponding to each CR can be defined.
• There are 3 fundamental phases:1. Construction and reorganization of
decision-makers’ preference vectors.2. Definition of the reading sequence.3. Generation of the fused ordering.
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OPM (Phase 1)
Reorganized vectors for the pencil example (CR3 > CR2 > CR1 CR4)
CR3 CR2 CR1CR4
{EC3,EC5} {EC3,EC5} {EC4,EC4}{EC2} {EC2} {EC1}{EC1} Null {EC1}
{EC4} {EC1,EC4} {EC2,EC2,EC3,EC3,EC5,EC5}
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OPM (Phases 2 and 3)The ordering algorithm
Pass Element (I) Cumulative Occurrences (Ok) Residual elements (R) Gradual Ordering
EC1 EC2 EC3 EC4 EC5 (Tk = 1) (Tk = 1)
0 - 0 0 0 0 0 {EC1, EC2, EC3, EC4, EC5} -
1 {EC3,EC5} 0 0 1 0 1 {EC1, EC2, EC4} EC3 EC5
2 {EC3,EC5} 0 0 2 0 2 {EC1, EC2, EC4} EC3 EC5
3 {EC4,EC4} 0 0 2 2 2 {EC1, EC2} EC3 EC5 > EC4
4 {EC2} 0 1 2 2 2 {EC1} EC3 EC5 > EC4 > EC2
5 {EC2} 0 2 2 2 2 {EC1} EC3 EC5 > EC4 > EC2
6 {EC1} 1 2 2 2 2 - EC3 EC5 > EC4 > EC2> EC1
7 {EC1} 2 2 2 2 2 - EC3 EC5 > EC4 > EC2> EC1
8 Null 2 2 2 2 2 - EC3 EC5 > EC4 > EC2> EC1
9 {EC1} 3 2 2 2 2 - EC3 EC5 > EC4 > EC2> EC1
10 {EC4} 3 2 2 3 2 - EC3 EC5 > EC4 > EC2> EC1
11 {EC1,EC4} 4 2 2 4 2 - EC3 EC5 > EC4 > EC2> EC1
12 {EC2,EC2,EC3,EC3,EC5,EC5} 4 4 4 4 4 - EC3 EC5 > EC4 > EC2> EC1
FINAL ORDERING
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OWA methods
• Ordered Weighted Average (OWA) emulator of arithmetic mean was first introduced by Yager (1993).
• This operator is typically used with ordinal scales.
1
,n
kkOWA Max Min Q k b
ORDERED ELEMENTOF THE SAMPLELINGUISTIC QUANTIFIERSAMPLE SIZE
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The pencil exampleEngineering Characteristics
(HOWS)
Importance of
WHATS
Length
Time between sharpening
Lead dust generated
Hexagonality
Erasure residue
Customer Requirements (WHATS)
Easy to hold S2 O X
Does not smear S3 O X X
Point lasts S5 O X X
Does not roll S2 XS1 -> not important at allS2 -> minor importanceS3 -> some importanceS4 -> strong importanceS5 -> very strong importance
-> weak relationshipO -> medium relationshipX -> strong relationship
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• is the average linguistic quantifier (the weights of the OWA operator),
with ;
• is the f(k)-th level of the linguistic scale (for example Sf(k) = S1 if f(k) = 1);
• Int(a) is a function which gives the integer closest to a;
• t is the number of scale levels;
• n is the sample size.
The linguistic quantifier
, 1,2,...,fkQ k S k n
11
tfk Int kn
fkS
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An example of OWA
• Number of scale levels: t = 5 (S1, S2, S3, S4, S5).
• Sample size: n = 10.
• Ordered elements: S5, S5, S5, S4, S4 , S3, S3, S3, S2, S1.
• The weights are:Q(1) = S1,Q(2) = Q(3) = S2,Q(4) = Q(5) = Q(6) = S3,Q(7) = Q(8) = S4,Q(9) = Q(10) = S5.
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Graphical representation of OWA
1 5 2 5 2 5 3 4 3 4
3 3 4 3 4 3 5 2 5 1 3
OWA= Max Min S , ,Min S , ,Min S , ,Min S , ,Min S , ,
Min S , ,Min S , ,Min S , ,Min S , ,Min S ,
S S S S S
S S S S S S
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Thank you for your attention!
The end
… any questions?
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Major references (1)
• Rossetto S., Franceschini F., “Quality and innovation: A conceptual model of their interaction”, Total Quality Management, v. 6 n. 3, 1995, pp. 221-229.
• Franceschini F., Rossetto S., “The problem of comparing technical/engineering design requirements”, Research in Engineering Design, v. 7, 1995, pp. 270-278.
• Franceschini F., Rossetto S., “Design for Quality: selecting product's technical features”, Quality Engineering, v. 9, n. 4, 1997, pp. 681-688.
• Franceschini F., Zappulli M., “Product's technical quality profile design based on competition analysis and customer requirements: an application to a real case”, International Journal of Quality and Reliability Management, v. 15, n. 4, 1998, pp. 431-442.
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Major references (2)
• Franceschini F., Rossetto S., “QFD: how to improve its use”, Total Quality Management, v. 9 n. 6, 1998, pp. 491-500.
• Franceschini F., Terzago M., “An application of Quality Function Deployment to industrial training courses”, International Journal of Quality and Reliability Management, v. 15, n. 7, 1998, pp. 753-768.
• Franceschini F., Rupil A., “Rating scales and prioritization in QFD”, Total Quality Management, v. 16, n. 1, 1999, pp. 85-97.
• Franceschini F., Rossetto S., “QFD: an interactive algorithm for the prioritization of product's technical characteristics”, Integrated Manufacturing Systems, v. 13, n. 1, 2002, pp. 69-75.
• Franceschini F., Advanced Quality Function Deployment, St. Lucie Press/CRC Press LLC, Boca Raton, FL, 2002.
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Major references (3)
• Franceschini, F., Galetto, M., Varetto, M., “Qualitative ordinal scales: the concept of ordinal range”, Quality Engineering, v. 16, n. 4, 2004, pp. 515-524.
• Franceschini, F., Galetto, M., Varetto, M., “Ordered samples control charts for ordinal variables”, Quality and Reliability Engineering International, v. 21, n. 2, 2005, pp. 177-195.
• Franceschini, F., Brondino, G., Galetto, M., Vicario, G., “Synthesis maps for multivariate ordinal variables in manufacturing”, International Journal of Production Research, v. 44, n. 20, 2006, pp. 4241-4255.
• Franceschini F., Galetto M., Maisano D., Management by Measurement: Designing Key Indicators and Performance Measurements. Springer, Berlin, 2007.