Methodological problems in QFD and directions for future development

Customers are usually not able to voice their demands with respect to products they do not know or have no experience with. This problem has in fact been recognized in the literature on QFD: customers are hardly able to voice their demands with respect to new products. Therefore, it has been advised in the QFD literature to focus on the improvement of existing products (Sarlemijn and Boddendijk 1995; Vairaktarakis 1999). Nevertheless, QFD has also been used to develop new products (Bergquist and Abeysekera 1996, p. 270). The above also implies that the choice for a certain product, and in fact also the choice for a certain group of customers, precedes the use of QFD.

QFD presupposes that overall customer satisfaction (S) can be represented by a linear additive value function of the degree of attainment (s _i ) of the individual customer demands:

How are we to interpret this function S? The most plausible interpretation, I think, is to interpret S as a multi-attribute value function that corresponds with certain customer preferences over options. Each option consists of m attributes A ₁,…,A _m that correspond with the user demands. Different options are characterized by different bundles of values x ₁,…,x _m for these attributes. These values can be chosen in such a way that they correspond to the degree of attainment of the user demands s _i ,…,s _m . Now the fact that a customer prefers an option x(x ₁,x ₂,…,x _m ) over another option y(y ₁,y ₂,…,y _m ) corresponds with a value function v so that v(x ₁,x ₂,…,x _m ) > v(y ₁,y ₂,…,y _m ) if certain conditions are met (see, e.g. French 1988, pp. 74–82, 103–106). Thus, given that d _i is fixed for a given i, the value function S corresponds with the preferences of a customer as follows:

In QFD, S is represented as an additive linear value function with weighing factors d ₁,…,d _m . This representation is valid if three axioms are met (French 1988, p. 130):Of these conditions, the assumption of constant relative tradeoffs is the strongest. It supposes that the trade-off ratio between two different customer demands is constant. In general, this is not a plausible assumption. An example might illustrate the point (Fig. 4). Suppose that there are two relevant customer demands with respect to cars: safety and costs. Now in the “House of Quality”, the relative importance of the demands has to be indicated; for example that costs are considered twice as important as safety. It is, however, unlikely that people’s judgement about the relative importance of safety versus costs is completely independent of the achieved levels of safety and costs. It seems likely that many people will consider safety the most important consideration up to a certain level of safety and will consider cost more important above that level. When this is the case, QFD might result in a misrepresentation of the preferences of customers.

Proponents of QFD might react to this objection in two ways. One reaction would be to argue that QFD usually focuses on limited improvements of existing products. It might be argued that in the range of products actually considered the customer demands can adequately represented by an additive value function (cf. Fig. 4). This might be true at least for some products and for some improvements. It is, however, something that needs to be checked, not something that can be taken for granted as happens in most of the QFD literature.

Another reply would be to adapt the QFD method and to represent customer preferences not as a linear additive value function, but in another, mathematically more complex, way. One attractive representation would be a non-linear additive value function. For such a representation to be possible, the customers demands—corresponding with the attributes A ₁,…,A _m —have to be preferentially independent (Keeney and Raiffa 1993, p. 111).⁹ A set of attributes X is preferentially independent of its complement Y if, and only if, the preference relation between options that differ only in the attributes X and are similar in the attributes Y, does not depend on the exact values of the attributes Y. For example, the preferred cost for a car should not depend on its safety, and the desirable degree to which the point of a pencil lasts should not depend on how easy the pencil is to hold.

We have seen that under certain, albeit rather strong, conditions customer preferences can be represented as a linear additive value function. This representation presupposes that the customer is able to weakly order any pair of options (axiom 1 in Sect. 3.2). One could, for example, ask a customer to make comparisons between a range of options and, on that basis, construct a value function representing the preferences of the customer. Under certain conditions, this value function has the form of a linear additive value function.

This procedure, however, does not work for a group of customers who have at least some conflicting preferences. In such cases, we cannot ask the group for its preferences. Rather, we are confronted with the problem of how to translate preferences of individual customers into collective preferences of the entire group of customers. I think that the best way to present this problem here is to cast it in terms of Arrow’s Impossibility Theorem. This theorem, proved by Arrow (1950), shows that—in cases of at least two individuals and at least three options—it is impossible to find a function or decision procedure that meets a number of minimally reasonable conditions to translate individual into collective preferences. These minimal conditions are:¹⁰ Arrow’s theorem means that no general procedure exist to translate individual preferences into a collective preference ordering unless one is willing to breach one of the above-mentioned conditions.¹¹ The absence of a collective preference ordering over the options implies that these preferences cannot be represented by a value function (French 1988, p. 75). Therefore it is, in general, not possible to represent collective customer preferences by a value function S as in done in QFD. It should be stressed that Arrow’s Impossibility Theorem only shows that such a representation is not possible in general; it might still be possible in specific cases; for example if all customers have the same preferences.

One important reason for Arrow’s theorem is that interpersonal comparison of preferences is not deemed possible (French 1988, pp. 288–298). This means—among other things—that it is not meaningful to add up the relative weights of the different customer demands given by the individual customers and to derive—by taking the mean or otherwise—the collective relative weights of the customer demands.

This fundamental difficulty in translating individual customer preferences into a collective preference ordering may be a reason why so much of the literature on QFD is silent on how individual preferences are to be translated into a collective preference ordering. Many publications simply presuppose that the relative importance of the customer demands is given or has been obtained in a further unspecified way. If it is mentioned how individual customer preferences have been attained and how these have been translated into a collective ordering of the customer demands, no justification is given for the chosen method (e.g. Bergquist and Abeysekera 1996; Park and Kim 1998).

In the relationship matrix in the House of Quality the correlation between customer demands and engineering characteristics in indicated. QFD presupposes that the (relative) weight of the engineering characteristics (w _j ) can be expressed as a linear additive function of the (relative) importance of the customer demands:

In this formula, a _ij is the correlation between the attainment of the jth engineering characteristic and the attainment of the ith customer demand. QFD presupposes that a _ij is always non-negative (see Sect. 2). This assumption can cause problems, as can be illustrated with the following example. One of the customer demands for cars is “fuel consumption”. This can, for example, be achieved through the engineering characteristic “weight of the car”, i.e. lighter cars have lower fuel consumption ceteris paribus. However, lighter cars get a higher relative acceleration in collisions with heavier cars and, therefore, are more dangerous to the driver and passengers.¹² So, while the engineering characteristic “weight of the car” correlates positively with the customer demand “safety for the driver and for the passengers”, it correlated negatively with the customer demand “fuel consumption”. There are two ways to adapt the original QFD approach to deal with this type of situation.

One way is to take the absolute value of the correlation between the jth engineering characteristic and the attainment ith customer demand in determining a _ij . The effect would be that an engineering characteristic that correlates positively with one customer demand and negatively with another becomes overall more important. This might be considered desirable in as far as that both the positive and the negative correlation are an indication that this is indeed an important engineering characteristic. The disadvantage, however, is that it becomes unclear what the optimal value of the engineering characteristic is or even in what direction the optimal value should be sought—in this case: more weight or less weight—while the target setting approach in QFD that I discussed in Sect. 2 presupposes that it is clear what the optimal value of an engineering characteristic is. This approach thus increases the methodological problem that will be discussed in Sect. 4.3: target values are unclear or meaningless.

Another approach would be to introduce negative a _ij for situations in which the correlation between the jth engineering characteristic and the attainment of the ith customer demand is negative.¹³ One effect of introducing negative a _ij might be that the overall importance of some engineering characteristics becomes negative or 0. This seems undesirable.¹⁴

Another issue is that QFD presupposes that all a _ij are constant. This seems not always adequate. In the pencil example (Fig. 2), for example, a medium correlation between “easy to hold” and “length of pencil” is presupposed. It might, however, be the case that the correlation is much stronger for rather short pencils of, say, 3–4 centimetres than for “normal” medium-sized pencils. If the engineering characteristic is understood in the sense of “more is better”, it might even be the case that above some length the correlation becomes negative because longer pencils become less easy to hold.

Presuppositions that are similar to those made with respect to a _ij are made in QFD with respect to the tradeoffs z _jk between the engineering characteristics. Also these presuppositions are often not realistic: not only the intensity of trade-offs between engineering characteristics may change over the domain of the engineering characteristics, even the direction—positive versus negative trade-offs—may change (Ramaswamy and Ulrich 1992).

The methodological problem attached to translating customer demand weights in weights for the engineering characteristics is deeper than the presumption that all a _ij are non-negative and constant. It might even be doubted if this translation is possible at all.

At first sight, the step from customer demands to engineering characteristics seems less subjective than the step in which the relative importance of customer demands is determined. Engineering judgement plays an important role in this step. As Fung et al. write “The determination of…[engineering characteristics] and relation ratings depends to a great extent on the expert’s knowledge of the specified product and the designer’s experience” (Fung et al. 2003, p. 252).

It could reasonably be argued, I think, that usually the following determinations can more or less “objectively” be made on the basis of engineering judgement:These points imply that the engineering characteristics can be ordered on a weak ordinal scale with respect to their importance for the individual customer demands. Such a weak ordinal scale, however, is not enough to achieve what QFD aims at: an ordering of the importance of the engineering characteristics on the basis of their importance for a number of customer demands. This is so because the choice situation is analogous to the choice situation for which Arrow originally developed his Impossibility Theorem (cf. Franssen 2005). Arrow considered a situation in which individual preferences are to be translated into a collective preference ordering; here we have the individual preferences replaced by collective customer demands and the collective preference ordering replaced by an ordering of the engineering characteristics.¹⁵ Like in Arrow’s original case, the input information is ordered on a weak ordinal scale. Like in the translation of individual customer demands into collective ones, all Arrow requirements (collective rationality, unrestricted domain, Pareto principle, independence of irrelevant alternatives, absence of a dictator) seem quite reasonable (cf. Franssen 2005).

The condition that is not met by the conventional QFD approach is that of “independence of irrelevant alternatives,” which here means that the ordering of two engineering characteristics may not depend on the inclusion or the exclusion of a third one. In the pencil example, leaving out the engineering characteristic “hexagonality” has the effect that the engineering characteristic “length of pencil”, which was first the least important engineering characteristic (Fig. 3) now becomes the most important (Fig. 5), at least in terms of the technical weights.

In the light of this example, one might cast some doubts on the reasonableness of the condition “independence of irrelevant alternatives”. Given the fact that the engineering characteristics “length of pencil” and “hexagonality” fulfil more or less the same customer demands, it seems not unreasonable that when one of these two characteristics is not taken into account the other becomes relatively more important. However, the fact that “length of pencil” now becomes the most important engineering characteristic would mean—if improvement efforts would first focus on the engineering characteristics with the highest technical importance—that the efforts would first focus on the two customer demands, viz. “easy to hold” and “does not roll”, which are considered the least important, whereas in the original situation (Fig. 3) efforts would first focus on the other two customer demands. If we look at the resource weight of the engineering characteristics the picture is somewhat different; “length of pencil” is now the third important characteristic. However, the original target value for “length of pencil” was 0.13 (Fig. 3). In the new situation this target value would probably become 1 and the target value for “time between sharpening” would probably drop below 1. Again this implies more emphasis on the customer demands “easy to hold” and “does not roll” at the cost of the other customer demands.

Apart from what might be said about the pencil example, it does not seem desirable in general that the ordering of two engineering characteristics depends on the inclusion or exclusion of a third one. The condition “independence of irrelevant alternatives,” moreover, forbids the use of non-ordinal information (Sen 1970, pp. 89–92), while QFD presuppose that the numbers in the relationship matrix can be measured on a ratio scale (cf. Otto 1995). As I have argued above, it is not very likely that such a measurement is possible. Typically, in the literature on QFD no arguments are given why or how a measurement of relationships on a ratio scale that is uniform over the various engineering characteristics and customer demands would be possible or meaningful.

In the approach for setting targets proposed by Bode and Fung (1998), target values are expressed as a fraction of the optimal meeting of an engineering characteristic. In many cases, however, it is not clear what this means. Take for example the engineering characteristic “lead dust generated” for a pencil. It is already difficult to determine what it would mean to optimally meet this requirement, but without some measurement scale, a target liking meeting this requirement for 70% is meaningless. It should be noted that even if a measurement scale is available for some engineering characteristics, this scale is usually not uniformly related to meeting customer demands, while that is presupposed by the formula used for customer satisfaction:

Take for example the engineering characteristic “length of pencil”. This length can be expressed in centimetres. Now suppose that the optimal value is 15 cm. What does it mean to meet this requirement by 50%? One way to construct a measurement scale for degree of attainment is to calculate it as the quotient of the actual length and the optimal length (15 cm). So, 7.5 cm is equivalent to meeting this target with 50 and 20% corresponds with 3 cm. This scaling, however, has no obvious connection to customer satisfaction. A decrease from 100 to 80% in the value of “length of pencil” might not have the same value for a customer as the decrease from 80 to 60%. As can be seen from the formula above a decrease in e _k , i.e. the attainment of engineering characteristic k, from 1 (100%) to 0.8 (80%) has the same impact on overall customer satisfaction as a decrease from 0.8 (80%) to 0.6 (60%). For the reasons outlined, this presupposition will usually not hold.

In the literature on QFD, a whole range of more sophisticated approaches has been proposed. Some of these are intended to deal with the methodological problems I have sketched; others mainly aim at a more precise and mathematically sophisticated formulation of QFD. My aim is not to give a complete overview, but only to sketch some current developments and to indicate whether these are promising for eventually overcoming the earlier sketched methodological problems or not.

A first development is the integration of Kano’s model for customer satisfaction into QFD (Matzler and Hinterhuber 1998). Kano’s model makes a distinction between three types of user demands:This distinction can be seen as an attempt to address the methodological problem that tradeoffs between customer demands are usually not constant (Sect. 3.2). Distinguishing between these three types of requirements helps to avoid this oversimplified assumption. Matzler and Hinterhuber (1998) propose different indexes for customer satisfaction and customer dissatisfaction for customer demands. They do, however, not offer a method for translating these into priorities among the engineering characteristics or into target values. Still, although Kano’s model does not address the more fundamental methodological problems in QFD, it goes some way in addressing the issues described in Sect. 3.2.

A second development is the use of more sophisticated rating scales for the relation between customer demands and engineering characteristics. Park and Kim (1998), for example, criticize the choice of rating scales like 1–3–9. They propose to use a cardinal scale instead of an ordinal scale for these ratings, and so try to address the methodological issue discussed in Sect. 4.1. They fail to argue, however, how it would be possible to measure the correspondence between customer demands and engineering characteristics on a cardinal scale and on one that is uniform for all the different correspondences. Another proposal to deal with this methodological problem is sensitivity analysis (e.g. Shen et al. 1999). Again, this does not solve the fundamental problem. Sensitivity analysis applies different rating scales and tests whether this results in different outcomes. In doing so, it presupposes that the (relative) weight of the engineering characteristics can be expressed as a linear additive function of the (relative) importance of the customer demands. However, the distorting effect of this assumption might well be larger than the mere choice of the rating scale. For such reasons, the added value of sensitivity analysis is limited.

A third development is more sophisticated methods for target setting (e.g. Fung et al. 1998, 2003, Kim et al. 2000; Tang et al. 2002). Such more sophisticated methods, for example, try not simply to maximize customer satisfaction given a budget constraint, but also introduce additional constraints, for example a minimum degree to which each engineering characteristic has to be met. Some methods also try to differentiate between different types of resources instead as just overall costs. Finally, a number of approaches use fuzzy models to deal with impreciseness and uncertainty. Sophisticated as they approaches might be, they neither address the more fundamental methodological problems that are due to Arrow’s Impossibility Theorem nor the more specific problems with respect to target setting I have sketched. Some in fact seem to increase the methodological problems by making more or stronger assumptions than conventional QFD approaches do.

QFD is usually not understood as a method for choosing between different design concepts, but as a method for setting engineering targets. Nevertheless, the outcomes of QFD can be used to choose between different designs. It is therefore interesting to see if alternative selection procedures exist that can help to overcome the methodological problems of QFD. In the literature, a number of approaches has been proposed that claim, sometimes implicitly, to overcome the methodological problems that arise due to Arrow’s Impossibility Theorem.

Franceschini and Rossetto (1995) have proposed multi criteria analysis, in combination with outranking, as an alternative to the relationship matrix in QFD for setting the relative importance of the engineering characteristics. However, this does not overcome Arrow’s Impossibility Theorem, even if Scott and Antonsson (1999) claim that multi criteria analysis is not plagued by Arrow’s Impossibility Theorem. Franssen (2005), however, has shown that their arguments beg the question because they presuppose that an aggregate order among the multiple criteria exists, while that is just what is at stake.

Dym et al. (2002) have proposed pairwise comparison charts for comparing alternative designs, a method that could also be used to rank design criteria or engineering characteristics by importance. As they show, their approach is equivalent to the Borda count, i.e. it gives the same outcome. The Borda count is known to violate the condition “independence of irrelevant alternatives” of Arrow. Saari has argued that the Borda count is nevertheless superior to others methods of aggregation because it uses all relevant available information (Dym et al. 2002). It is, however, contestable what information exactly is relevant and available (cf. Franssen 2005, p. 48).

A third category of alternatives focuses on market segmentation. To understand the importance of market segments, it is useful to look at an example presented by Hazelrigg (1996) to show how Arrow’s theorem can result in erroneous QFD results. Suppose a product has three attributes: colour, size and shape, and suppose that each attribute has two possible options: red or green (colour), large or small (size) and flat or bumpy (shape). Suppose that there are three groups of customers, whose preferences are represented in Table 2.

On the basis of this table, one might be tempted to think that the group preference is a red, large, bumpy product. It might be the case, however, that customer 1 dislikes a bumpy product so much that is has no value to him, while customer 2 dislikes large products so much that they have no value to her; for customer 3, finally, red products may have no value at all. What seems to be the most preferred product is actually disliked by all customers.

Lowe and Ridgway (2000) present two possible solutions to the example presented by Hazelrigg. The first has to do with how the preferences of the three individuals are aggregated. Hazelrigg presupposes a kind of majority voting on each attribute separately. However, we might also ask each of the customers to rate the importance of each attribute on a scale from 0 to 1 and then calculate the weighted average importance of each attribute. Even if this procedure gives a better solution in this particular case, as Lowe and Ridgway argue, it does obviously not solve the fundamental issues that arise due to Arrow’s Impossibility Theorem.¹⁶ In other situations, it might be Lowe and Ridgway’s aggregation method instead of Hazelrigg’s one that leads to “erroneous” results.

The second solution presented by Lowe and Ridgway is to supply not a single product but a number of products, each of which would satisfy some customer group; in this case, this would imply the supply of three different products. In terms of Arrow’s Impossibility Theorem, the choice of a specific customer segment can be seen as way to introduce domain restrictions, so weakening the second condition (unrestricted domain) on which the theorem rests: we only count certain customers as members of a market segment if their preferences meet certain domain restrictions.

It is known that under certain domain restrictions Arrow’s Impossibility Theorem does not apply. One such a restriction is single-peakedness. This condition implies that there is one underlying criterion alongside which all the individuals order the options. An example is the left–right distinction in politics. The idea is that while individuals will prefer different options on the left–right axis, their preferences will fall monotonically to both the left and the right side of their most-preferred option on the left–right axis. A similar restriction does not seem reasonable in QFD, however. If customer preferences are eventually determined by only one criterion, what is the point in distinguishing different customer demands in QFD? This seems to presuppose that there is in fact not one underlying criterion, and there are, I think, good reasons for this presupposition.

Nevertheless, the use of market segments may introduce domain restrictions that even if they do not avoid Arrow’s Impossibility Theorem, at least alleviate the consequences of it. It can be shown, for example, that under reasonable domain restrictions for market segments, QFD results in a Pareto improvement among the customers in that market segment, so avoiding the erroneous results suggested by Hazelrigg.

To show this, I start with supposing that the preferences of each customer in a market segment can be represented by an ordinal value function. This is usually possible if the preferences of each customer over the options form a weak order. Note that in this case, the options are formed by some combinations of the values of the customer demands s _i as discussed in Sect. 3.2. In contrast to there, I do not presuppose that the value function takes the form of a linear additive value function. This supposition can be written as: Now also suppose that the value function v _x of each customer x in market segment m has the following two properties: These conditions could be used to define market segments, so that these conditions are by definition met in each market segment. (Note that in different market segments s _i ,…,s _m can be different). In this situation, an improved meeting of the customer demands will result in a Pareto improvement, in the sense that no customer in the market segment is worse off and at least one customer is better off.

Now suppose that it is also possible to find a set of engineering characteristics meeting the following conditions:

If conditions 4, 5 and 6 are met, better meeting one of the engineering characteristics—without doing worse on any of the other engineering characteristics—automatically implies a Pareto improvement among the customer demands. If conditions 1, 2 and 3 are also met, this also implies a Pareto improvement for the customers.

Note that in traditional QFD, it is presupposed that γ _i can be written as

Under this presupposition, conditions 4, 5 and 6 are indeed met. Note, however, that conditions 4, 5 and 6 are much weaker than what is usually presupposed in QFD. It is, for example, not presupposed that each γ _i can be written as a linear additive value function of e _j , so avoiding a number of the methodological problems discussed in Sect. 4.1. (Note, however, that condition 5 and 6 are a kind of reformulation of the presupposition in QFD that a _ij is always non-negative.) It should also be noted that condition 4 is not plagued by Arrow’s Impossibility Theorem. The reason is that condition 4 requires the solution of a single criterion instead of a multiple criteria problem.¹⁷ Condition 4 requires that it is possible to weakly order different combinations of engineering characteristics e _j ,…,e _n with respect to one specific customer demand s _i ; it does not require weakly ordering combinations of engineering characteristics e _j ,…,e _n with respect to combinations of customer demands s _i ,…,s _m . So, we only have one “voter”, i.e. customer demand i, while Arrow’s Impossibility Theorem only applies to two or more “voters”.

Market segmentation can thus be used to introduce certain domain restrictions. A minimal result that can be achieved by market segmentation is to avoid that some customers are actually less satisfied with the new product than with the current product. It might be possible to introduce even stricter, but still plausible, domain restrictions than those suggested above in defining market segments, so that Arrow’s theorem can be avoided.¹⁸ This is, however, beyond the scope of this article.

Another interesting development is demand modelling to predict the demand for products with certain features. On the basis of such predictions, the desirable characteristics of products can be chosen. Some authors have also attempted to introduce such considerations into QFD. I will discuss at some length a proposal developed by Cook and Wu (2001).

Cook and Wu use the so-called S-model to predict user demand. This is a phenomenological model for predicting demand, expressed in terms of the values and prices of products. The demand is taken to be equal to the total amount of a product sold over a period of time, assuming that there is no scarcity of supply. The value of a product is a measure for the amount of money people are willing to spend on that product. The assumption is that people buy a product if its value is higher than its price. If demands and prices are known for a range of competing products, the value of these products can be calculated.

Using the S-model, predictions of future demand can be made if prices and values of a new product are known. The difficult part, of course, is to predict the value of a new product. Cook and Wu propose the direct value (DV) method to this end. In this method, customers are asked to compare a baseline product with an imaginary alternative product in which one or more of the values of the product attributes have been modified. The customers are asked to choose between the baseline and the alternative product for a series of prices of the alternative product. Next, the fraction of respondents choosing the alternative is plotting against the price of the alternative. On basis of this plot, a so-called neutral price P _N is determined; this is the price at which half of the respondents chooses the alternative product and half the baseline product. On basis of the S-model, it can now be shown that:

In this formula V ₀ is the value of the baseline product and P ₀ is the price of the baseline product. V is the value of the new product. If V ₀ and P ₀ are known, and P _N has been determined, V can easily be calculated.

The DV method is usually used for one attribute change at the time. Note that this supposes that the attributes are preferentially independent: the change in value due to changes in one attribute does not depend on the values of the other attributes. As discussed earlier, this might be a problematic assumption (Sect. 3.2). The DV method also presupposes that people can compare non-existing products with current ones, which might be problematic (cf. Sect. 3.1).

Another methodological issue with respect to the DV method is that, from earlier research, it is known that there is a gap between the maximum price for which someone is willing to buy a product and the minimum price for which that person is willing to sell it. Most people want a higher minimum price for selling a product than they are prepared to pay for buying the same product. Usually this phenomenon is phrased in terms of Willingness to Pay (WTP) versus Willingness to Accept (WTA). Cook and Wu interpret this phenomenon in terms of uncertainty. Even if this would be a right interpretation, an implication seems to be that the DV method will probably yield different values for the same product if different baselines are chosen. In general, it might seems reasonable to use the current product as baseline; however, in reality consumers will not choose between the current product and the new product but between a number of—new—products of competitors and the newly developed product.

Cook and Wu integrate the S-model in QFD in order to increase the profit of the company. Their proposed QFD approach proceeds as follows. Customer demands are listed and related to engineering characteristics. The engineering characteristics for the current (baseline) product are measured. A range of alternative products is devised with other engineering characteristics. With the DV method, the changes in customer value for these alternative products are measured. Using the S-model, the expected additional demand given a certain price for the alternatives is calculated. By also estimating the expected additional costs for developing and producing each alternative, the added profit for each alternative can easily be calculated. The option with the highest additional profits is chosen.

Some people would probably argue that the approach proposed by Cook and Wu is no longer a QFD approach. It does, for example, not set target values for the engineering characteristics. Although, they use a kind of House of Quality, they do not make any of the calculations mentioned in Table 1. However, by not making these calculations they avoid most of the methodological problems that were discussed in Sect. 3.3 and in Sect. 4. This is not to say that their approach is completely without methodological problems; some of these have been indicated above.

What is perhaps most important is that Cook and Wu’s approach avoids Arrow’s Impossibility Theorem because it does not try to aggregate individual preferences into collective ones, but just models how many people would probably buy a product with certain features. This seems more generally true for demand modelling approaches. Wassenaar et al. (2005), for example, write about their demand modelling approach that it “aggregates the customer choices (not preferences) by summing the choice probabilities across individual decision makers (customers), thus avoiding the paradox associated with aggregating the utility or preference of a group of customers” (Wassenaar et al. 2005, p. 522).