Prioritization of Engineering Characteristics on QFD : old problems and new approaches

1. Prioritization of Engineering Characteristics on QFD: old problems and new approaches 7th Galilee Quality Conference, “Quality – Theory and Practice” ORT Braude College of Engineering in Karmiel May 1st 2014 Fiorenzo Franceschini Maurizio Galetto

2. Quality Function Deployment (QFD) “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)

3. From Customer Requirements to new products I want … I like … I like . I want … I like … I want … I want … I like … I wa I want … NEW PRODUCT CUSTOMERS COMPANY

4. Phases of QFD Phase IV Phase III Phase II Phase I Engineering Characteristics Customer Requirements Engineering Characteristics

5. 7. Correlation Matrix The main pillars of the House of Quality (HoQ) 5. Engineering Characteristics 4. Competitive Prioritization of Customer Requirements 3. Competitive Benchmarking 2. Prioritization of Customer Requirements 6. Relationship Matrix 1. Customer Requirements 8. Prioritization of Engineering Characteristics

6. Example: design of a pencil (Customer Requirements) • Easy to hold • Does not smear • Point lasts • Does not roll • …

7. Identification of Engineering Characteristics Customer Requirements Engineering Characteristics f QFD work group L • hexagonality, • erasure residue, • dust, • …

8. The pencil example

9. The pencil example  -> weak relationship O-> medium relationship X-> strong relationship

10. Two prioritization problems • CRs prioritization (are all CRs equally important?) • ECs prioritization.

11. The pencil example Can CRs prioritization influence ECs prioritization?

12. The Independent Scoring Method (ISM) Steps: • assign a numerical importance to each CR; • convert the relationshipssymbols between CRs and ECs into “equivalent” numeric values; • determine the numerical importance of each EC using the ISM algorithm.

13. The pencil example: 1stSTEP 1 -> not important at all 2-> minor importance 3 -> some importance 4 -> strong importance 5 -> very strong importance

14. The pencil example: 2nd STEP empty box -> 0  -> 1 O-> 3 X-> 9

15. The pencil example: 3rdSTEP

16. Advantages of the ISM • Intuitional. • Easy to use. • Easy to interpret. • Use of standard Mathematical operators. • Largely diffused. • …

17. Drawbacks/Criticalities • Are customers really able to express CRs importance on ratio scales (cardinal properties)? • What is the correct symbolcodification 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 arbitrarinessin scale definition (zero point, graduation, unit, …)?

18. Example: effect of different codifications of symbols in the relationship matrix All CRs have the same importance d = 1.

19. Techniques based on 5-levels rating scales • The response scale has ordinal properties: • Arbitrary promotion of results from ordinal to interval or ratio scales.

20. Individual response scales are not aligned Can we sentence that the mean value of the sample is ?

21. Example of arbitrary promotion of results from ordinal to interval or ratio scales. 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).

22. Fusion of CRs importance evaluated by linear orderings • Respondents’ orderings: • CR3 > CR1 > CR2 • CR1> CR2> CR3 • ... • How operate a fusion of respondents’ orderings?

23. 7. Correlation Matrix The first problem: prioritization of CRs 5. Engineering Characteristics 4. Competitive Prioritization of Customer Requirements 3. Competitive Benchmarking 2. Prioritization of Customer Requirements 6. Relationship Matrix 1. Customer Requirements 8. Prioritization of Engineering Characteristics

24. Finding the right way • In the scientific literature there are many approaches for prioritizing CRs. • Some of them may lead to misleading results. • In some cases we assist to a violation of scaleproperties on which CRs are evaluated.

25. 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.

26. Conceptual scheme of AHP PAIRED COMPARISON MATRIX PRIORITY VECTOR

27. The comparison matrix for the pencil example

28. 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’sscale for paired comparison has ratio scale properties. • It is “effective” only with small numbers of CRs.

29. 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 .

30. 7. Correlation Matrix The second problem: prioritization of ECs 5. Engineering Characteristics 4. Competitive Prioritization of Customer Requirements 3. Competitive Benchmarking 2. Prioritization of Customer Requirements 6. Relationship Matrix 1. Customer Requirements 8. Prioritization of Engineering Characteristics

31. The state of the art The scientific literature proposes manytechniques 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 ECsin the relationship matrix (linear, weighted, …).

32. Principal techniques • 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]. • ...

33. What is the most appropriate? Interactive Design Requirement Ranking (IDRR) Multiple Criteria Decision Aid (MCDA) Independent Scoring Method (ISM) Paired Comparison Method (PC) Ordinal Prioritization Method (OPM)

34. A novel taxonomy

35. 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: • Construction and reorganization of decision-makers’ preference vectors. • Definition of the reading sequence. • Generation of the fused ordering.

36. OPM (Phase 1) Reorganized vectors for the pencil example (CR3 > CR2 > CR1 CR4)

37. OPM(Phases 2 and 3) The ordering algorithm FINAL ORDERING

38. OWA methods • Ordered Weighted Average (OWA) emulator of arithmetic mean was first introduced by Yager (1993). • This operator is typically used with ordinal scales. ORDERED ELEMENT OF THE SAMPLE SAMPLE SIZE LINGUISTIC QUANTIFIER

39. The pencil example S1-> not important at all S2-> minor importance S3 -> some importance S4 -> strong importance S5 -> very strong importance  -> weak relationship O-> medium relationship X-> strong relationship

40. The linguistic quantifier • is the average linguistic quantifier (the weights of the OWA operator), with ; • is the f(k)-thlevel of the linguistic scale (for example Sf(k)= S1if 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.

41. 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.

42. Graphical representation of OWA

43. The end Thank you for your attention! … any questions?

44. Major references (1) • RossettoS., 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.

45. 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.

46. 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.