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 k

n

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.