Replacing target setting by value models in the ‘house of quality’ for value-based requirements specifications

Abstract

Setting targets for engineering characteristics is common practice in the ‘house of quality’ for establishing requirements specifications. However, if deployed arbitrarily, this practice is prone to errors and can often yield irrational results. Three potential methodological problems have been identified, regarding the setting of independent targets for each engineering characteristic, setting fixed targets and cascading down targets from the system level to the component level have been identified. In this article, targets are categorised as constraints and goals because of their different implications for value trade-offs. Then, a ‘multi-attribute utility theory’ based approach is proposed, in which a system value model is developed in order to replace the setting of targets for system engineering characteristics and component value models are further derived to replace the setting of targets for component engineering characteristics. These value models enhance the traditional approach to requirements specification so that value-based requirements specifications can be developed. A case study is deployed to demonstrate the applicability of the approach in the civilian aerospace context for the development of requirements for commercial aircraft. The benefits of the proposed approach are twofold: (1) value becomes an explicit construct and (2) value can be rationally modelled and simulated in the ‘house of quality’ in order to establish value-based requirements specifications. Furthermore, identified methodological problems in terms of setting engineering characteristic targets at any level are mitigated.

Keywords

House of quality targets multi-attribute utility theory value model requirements specification

Introduction

It is currently well recognised that customer-perceived value is the source of competitive advantage in the 21st century.^1,2 It is desirable to establish value-based requirement specifications that are based on customers’ value perceptions, which promotes value to become an explicit construct that can be rationally qualified and quantified. Proactive and reactive application of value-based requirements specifications in the engineering design process can significantly enhance the capability of the designers to develop systems with higher value, as perceived by customers. This, in turn, is likely to translate into sustainable competitive advantage of the manufacturers that apply the proposed approach.

The ‘house of quality’ is a conceptual map that can be used to derive requirements specifications from customer needs based on competitive, technical and cost considerations.^3–5 The derived requirements specifications are typically text-based with some quantified targets, and they are usually stored and managed using various Commercial Off the Shelf (COTS) software such as IBM DOORS or Microsoft Excel. Design solutions are then developed to satisfy the requirements in the specification, and trade-offs between multiple design alternatives (if applicable) are analysed in detail against these requirements.

Although the ‘house of quality’ is a useful tool for understanding customer needs and for deriving requirements specifications, it suffers from a set of metho-dological problems with respect to a tool to derive value-based requirements specifications.^6–10 Especially, setting independent targets for each engineering characteristic (EC) could lead to value trade-offs between the ECs that are inconsistent with the customer value model and the system value model. Additionally, the fixed targets are unable to cope with the uncertain performance levels of ECs. In some instances, it could finally lead to a system with a sub-optimised system value when these targets are used for generating and evaluating design alternatives. In addition, when the targets of system ECs are derived into the targets of component ECs through a hierarchical flow down, it could also result in sub-optimised system designs, even though the system designs achieve all the targets. It this article, a ‘multi-attribute utility theory’ based approach is proposed to replace target setting by value models in the ‘house of quality’ towards deriving value-based requirements specifications. System value model is developed to replace targets setting for system ECs, while component value models are derived from system value model to replace target settings for component ECs.

The rest of the article is organised as follows. In section ‘Foundations’, foundations of the article are introduced, including definitions of key concepts and multi-attribute utility theory. In section ‘Methodological problems of setting targets in the ‘house of quality’, methodological problems of setting targets in the ‘house of quality’ are identified. In section ‘Substituting value models for setting targets’, a system value model and component value models are developed to encapsulate the value-based requirements specifications. In section ‘Case study’, a case study is presented. Finally, conclusions and future directions are given in section ‘Conclusion’.

Foundations

Definitions of key concepts

Definitions of a list of key concepts are given in Table 1. These concepts include value, customer value, value model and others. Definitions are given according to the development in this article. Customer value is a customer’s perceived preference for product attributes, consequences of use and purposes in use situations. Product attributes are means to influence consequence of use and consequences of use implement the purposes in use situation. Therefore, customer value is usually in different levels with means–ends relationships.

Table 1.

Definitions of key concepts presented in this article.

Concept	Definition
Value	Value is thought in a broad sense, including preference under certainty (value in a narrow sense) and preference under uncertainty (utility).
Customer value	Customer value is a customer’s perceived preference for product attributes, attribute performances, consequences of use, goals and purposes in use situation.¹
Value model	A ‘value model’ enables the assessment of the value for every design option so that options can be rationally compared and a choice taken.^11,12 In this article, value model is in the form of a multi-attribute utility function.
Customer value model	A customer value model is a value model based on customer attributes.
System value model	A system value model is a value model based on system attributes (or system-level ECs).
Component value model	A component value model is a value model based on component attributes (or component-level ECs).
Value-based requirements specification	A value-based requirements specification describes how value becomes an explicit construct and can be reasonably qualified and quantified.

ECs: engineering characteristics.

A schema can be used to intuitively illustrate informal relationships between these concepts, as presented in Figure 1. Customer value is usually made explicit when it is expressed through customer statements, although there are some cases in which customer value should be uncovered through observation or other means. These initial customer statements are then transformed into customer needs that are independent from any particular solution developed to address them.¹³ Customer needs are then transformed into system requirements and in turn into component requirements. All these together represent a traditional requirements specification for system development. A value-based requirements specification enhances traditional requirements specification with three kinds of value models: customer value model, system value model and component value models. A customer value model is a particular value model constructed from a set of customer attributes while customer attributes are attributes for measuring the attainment of customer needs. A system value model is derived from a customer value model by combining the customer value model together with function forms of customer attributes that are functions of system-level ECs. Component value models are further derived from the system value model, which are value models based on component attributes. These value models make value as explicit construct in the requirements specification, so that value can be reasonably modelled and simulated.

Figure 1.

Informal relationships between the concepts.

Multi-attribute utility theory

Multi-attribute utility theory is a systematic approach for composing a set of usually conflicting attributes with different incommensurable units into one common unit, which is called the utility. It helps customers to think hard about various value trade-offs and about the risk attitude towards uncertainty in achieving these attributes.¹⁴

Given a set of $n$ attributes $X = (X_{1}, \dots, X_{n})$ with $n \geq 2$ , if $X_{i}, i = 1, \dots, n$ is the utility independence of the other attributes, then a multi-linear utility function

u (x) = \sum_{i = 1}^{n} w_{i} u_{i} (x_{i}) + \sum_{i = 1}^{n} \sum_{j > i}^{n} w_{ij} u_{i} (x_{i}) u_{j} (x_{j}) + \sum_{i = 1}^{n} \sum_{j > i}^{n} \sum_{m > j > i}^{n} w_{ijm} u_{i} (x_{i}) u_{j} (x_{j}) u_{m} (x_{m}) + \dots + w_{123 \dots n} Π_{i = 1}^{n} u_{i} (x_{i})

(1)

is appropriate to compose the attributes together in order to derive their utility. Here, $u_{i}$ is a single-attribute utility function over attribute $i$ scaled from 0 to 1 and ws are scaling constants. Equation (1) reduces to

1 + wu (x) = Π_{i = 1}^{n} [1 + w w_{i} u_{i} (x_{i})]

(2)

when mutual utility independence holds among $X$ and $\sum_{i = 1}^{n} w_{i} \neq 1$ (or $w \neq 0$ ). Furthermore, when $\sum_{i = 1}^{n} w_{i} = 1$ (or $w = 0$ ), equation (2) reduces to the additive utility function

u (x) = \sum_{i = 1}^{n} w_{i} u_{i} (x_{i})

(3)

Multi-attribute utility theory is employed as the theoretical foundation for developing value models in this article.

Methodological problems of setting targets in the ‘house of quality’

The structure of ‘house of quality’ is shown in Figure 2.

Figure 2.

The structure of the ‘house of quality’.

In step 7 of ‘the house of quality’ as shown in Figure 2, targets are usually independently set for each EC. For example, ECs and their targets of one cordless drill may be ‘tool mass should be 1.25 kg’, ‘battery mass should be between 0.2 and 0.4 kg’ and ‘work output should be more than 25 kJ’, respectively. These targets represent acceptable or ideal measures for ECs to be achieved by design alternatives.⁴ There are also cases that targets only mean ideal fixed threshold to be achieved.³ In this article, targets include acceptable measures (constraints) and ideal measures (goals). A goal is an ideal level of an EC for orientation of preference, which is either achieved or not. One alternative that fails to achieve one or more goals may still be acceptable. A constraint defines an acceptable level of an EC and unacceptable design alternatives are eliminated. Setting constraints imply special value judgment that if an alternative fails to achieve one or more constraints, it is unacceptable even if the alternative had perfect achievement in other ECs. Usually, there are five types of targets,⁴ including no smaller ( $EC \geq X$ ), no larger ( $EC \leq X$ ), exact value ( $EC = X$ ), range ( $X \leq EC \leq Y$ ) and a discrete list ( $E C_{1}, E C_{2}, \dots$ ). Hauser and Clausing³ proposed only using the type of exact value ( $EC = X$ ) to avoid the possibility of being risk averse towards the least desirable achievement of ECs. All these situations can lead to unexpected traps or methodological problems and result in irrational target-based decision-making.

One of the methodological problems stems from independently setting targets for each EC. It can lead to value trade-offs between ECs inconsistent with the customer value model or the system value model. For example, assume customers consider only two ECs when they evaluate and select a cordless drill, these are as follows: (1) ‘work output should be larger than $25 kJ$ ’ and (2) ‘tool life should be larger than $1000 h$ ’. These two targets define a rectangular region as the target region, which is shown in Figure 3.

Figure 3.

Target region with two ECs.

According to this target setting, any cordless drill whose performance of these two ECs is within the target region is satisfactory, and any cordless drill whose performance of these two ECs is outside of the target region is unsatisfactory. For example, point A ( $25 kJ, 1000 h$ ) is satisfactory and C ( $40 kJ, 990 h$ ) is unsatisfactory. Precisely, point A is preferred to all points outside of the target region even if the points, for example, point C, have much higher achievement in work output with just a little less achievement in tool life. Therefore, less achievement of one EC is not compensated by higher achievement of another EC in this case. Straightforward as it may be, this kind of target setting poses serious problems, and it possibly eliminates all cordless drills outside the target region, which is an undesirable feature of setting independent targets.

Assume an indifference curve between these two ECs has been elicited from the customer as presented in Figure 4. All points in the curve then have the same perception of value to the customer. For example, the customer will be indifferent between point B ( $35 kJ, 1000 h$ ) and point C. Then, compared with C, less achievement of B in terms of work output ( $5 kJ$ ) is compensated by a higher achievement of tool life ( $1000 h$ ). As point B with higher achievement of work output is preferred to point A, point C is then preferred to point A according to transitivity of preference. Thus, there are points that are outside of the target region but are preferred to points inside the target region. Point C with a higher perception of value is rationally selected compared with point A, although it is not in the target region.

Figure 4.

Target region with two ECs and their indifference curve.

These two observations of setting targets seem contradictory. They represent two kinds of value trade-offs: compensation and non-compensation. There is not any compensation among the ECs when the targets are constraints, while there is compensation among the ECs when the targets are goals. Great attention should be paid to verifying whether the targets are real constraints or goals.

The second methodological problem of setting targets is that it fails to resolve the situations when the design alternatives have uncertain achievement of ECs and/or when targets of ECs are uncertain. For example, if a cordless drill has a $90 %$ chance of tool life of $900 h$ or tool life of $1200 h$ with an average tool life of $1170 h$ , it may also be an unsatisfactory alternative as there is $10 %$ chance of failure. However, this may not be a real response of customer value. Furthermore, targets may be set according to the performance of ECs of competitors’ cordless drills, which is a normal practice when setting targets for ECs in the traditional ‘house of quality’. However, competitors’ performance on these ECs may be uncertain before their cordless drills are finally launched in the market. In this case, setting fixed targets for a cordless drill in development might make it suffer from losing competitive advantages.

In addition, when targets are reasonably set according to customer value, competitive advantage and technical capability for system-level ECs, they are usually used for deriving targets of component-level ECs. Specially, when the targets of system-level ECs are the sum of targets of component-level ECs, such as mass, cost, volume and power consumption, a budget allocation process is used. This process may tend to be irrational. A hypothetical example can illustrate the problem, and similar examples can also be found about preference conflicts.¹¹ An originally allocated aircraft wing target with regard to cost and mass is $(c_{w}, m_{w})$ and an originally allocated landing gear target with regards to cost and mass is $(c_{g}, m_{g})$ . After design activities, the designed wing has attained the level of $(c_{w} + 10, m_{w} - 20)$ and the designed landing gear has attained the level of $(c_{g} - 20, m_{g} + 3)$ . Thus, the two designs are not desired as they are beyond the limit of allocated component-level targets, although the two together $(c_{w} + c_{g} - 10, m_{w} + m_{g} - 17)$ satisfy the overall system target $(c_{w} + c_{g}, m_{w} + m_{g})$ . In order to improve the design of the wing, a new design solution is proposed that reduces the cost to $(c_{w} - 1)$ with an addition of weight to $(m_{w} - 15)$ . In order to improve the design of the landing gear, a new design solution is proposed that reduces the cost to $(c_{g} - 5)$ with an addition of weight to $(m_{g} - 1)$ . Then, the two improved design solutions will all satisfy their targets and they together attain the level of $(c_{w} + c_{g} - 6, m_{w} + m_{g} - 16)$ . However, after a simple check, the improved attainment in the two components with regard to cost and weight is worse than the first design ( $c_{w} + c_{g} - 10, m_{w} + m_{g} - 17$ ).

Flowing down the targets of system-level ECs to targets of component-level ECs sets constraints to the development of components. When these constraints are used, the design space is then constrained. And the final design that satisfies the targets might not be optimised in terms of value. Different aspects of components’ design also influence targets setting in the component level. That is, in different components’ design, to achieve the same level of improvement in one attribute, different compensations in other attributes need to be made.

Therefore, traditional practice of setting targets in the ‘house of quality’ at least suffers from three kinds of possible methodological problems: (1) setting independent targets for each EC may lead to irrational design decisions, (2) setting fixed targets for ECs fails to resolve uncertainty in performance of ECs and uncertainty in targets themselves and (3) deriving targets of system-level ECs into targets of component-level ECs tend to result in sub-optimal design solutions.

Substituting value models for setting targets

In this section, a multi-attribute utility theory–based approach is proposed to resolve or avoid the aforementioned methodological problems in the house-of-quality. More precisely, a system value model is developed to compose a set of system-level ECs, which enable meaningful value trade-off between ECs and resolution of uncertainty. Component value models are derived from the system value model as a substitute for setting targets for component-level ECs.

However, developing a system value model directly from system-level ECs is always difficult for the following two reasons:

It could result in double counting. For example, there are usually a set of ECs provided by manufacturers, say, torque, horsepower and acceleration for cars.¹⁵ Means–ends relationships among them are verified after performing an initial means–ends analysis. Torque and horsepower are the means to influence the achievement of acceleration. Therefore, an additive function form as a conjoint measurement to compute value is problematic, resulting in double counting the importance of torques and horsepower. In fact, it is difficult to verify possible independence assumptions between ECs, and it will be difficult to identify special utility functions for modelling their relationship with value. From this view, the weighted sum of ECs as a way to calculate customer satisfaction in the ‘house of quality’ might also be problematic.

It needs three steps to perceive meaningfully value of special performances of ECs. ECs are usually the means the designer use to influence the achievement of customer needs that are the fundamental reasons of customer in the interests of system development. And, it is much easier for customers to perceive the value of customer needs. Therefore, a sophisticated three-step process is needed to assess a single-attribute utility function over ECs. First, the influence relationships between an EC and customer needs are established. Single-attribute utility functions over customer needs are then assessed. Finally, these two kinds of functions are combined together to establish the single-attribute utility function over the EC. However, it is not so trivial to judge the quantitative influence of one EC on a specific customer need when a set of ECs has influence on that customer need.

In order to avoid these difficulties, a system value model is derived from a customer value model that is a multi-attribute utility function of customer attributes. However, different procedures of assessment are needed for the case of goals and constraints. It is then necessary to clearly distinguish one from the other at first. Some heuristic questions can be useful for this task:

Whether it is a real constraint that cannot be violated or it is a desirable goal that is exciting if it is achieved?

Asking value trade-offs questions. For example, if a target of one performance criterion is finally achieved with a very small deviation, could this deviation be offset by a much higher achievement in another performance criterion? If it is not possible, this indicates a real constraint.

Asking the original source of a target. Does it come from external organisations, regulatory bodies, government policies, current legislature or decision maker’s subjective preference? If it comes from outside with compelling characteristics, it is a real constraint.

After carefully questioning, goals and targets are separated into two different sets, which should be used differently. All the targets can be deleted and are not used in value models and optimisation to reflect the flexibility of requirements if they all are finally verified as goals, but they are still stored and maintained for validation, verification and other purposes. If this is the case, a three-step procedure to develop a system value model is the following:

1. A customer value model is developed based on customer needs. Assume customer needs have been carefully identified by performing means–ends analysis and part–whole analysis,^9,12 and assume there is one attribute for each lowest-level customer need in a hierarchy of customer needs. $X = (X_{1}, \dots, X_{n})$ is the set of attributes. $u (x)$ can be assessed based on the verified independence assumptions. Empirically, Keeney shows that it is appropriate to determine an additive function form, for example, equation (3), when the set of lowest-level customer need indicates fundamental reasons of interest and the customer needs satisfy a set of desired properties.^12,16 Single-attribute utility functions are assessed according to the attributes’ types (no smaller, no larger or others) and perception of customer’s preference. This developed customer value model is an approximation of customer’s subjective preference. In the ‘house of quality’, an additive linear function form is used to calculate the degree of customer satisfaction,¹⁰ which is a special case of equation (3) when single-attribute utility function $u_{i}$ is of linear form. Multi-attribute utility functions of equations (1)–(3) thus provide a more comprehensive framework to measure customer value and satisfaction.

2. Concurrently, a function form is established for $X_{i}, i = 1, \dots, n$ , to model the influence relationships between $X_{i}$ and ECs

x_{i} = f_{i} (y_{1}, \dots, y_{m}), i = 1, \dots, n

(4)

where $y_{j}, j = 1, \dots, m$ is a special level of the jth EC $Y_{j}$ ; $Y = (Y_{1}, \dots, Y_{m})$ ; $f_{i}$ maps special achievement of ECs to $x_{i}$ . This type of model, called consequence model in decision analysis, is different from a value model that incorporates the value or value trade-offs and risk tolerances to evaluate consequences. The construction of consequence model should collate data objectively rather than subjectively in order to assign parameters in the function form of equation (4). Ideally, these kinds of function forms could be established with identified physical laws, such as physics, mechanics and economics. Practically, surrogate models are more appropriate as substitutes to approximate full response functions.

The relationship matrix in the house quality is usually used to model the influence relationships. However, it oversimplifies the relationships with linear functions and only focuses on the first-order effects. In order to model the interactions between ECs and second-order effects, a second-order model is introduced as an appropriate approximation to equation (4), which is very flexible and works well in solving real response surface problems.¹⁷ For the case of $m$ numbers of ECs, the second-order model is

x_{i} \approx β_{i 0} + \sum_{j = 1}^{m} β_{ij} y'_{ij} + \sum_{j = 1}^{m} β_{ijj} {(y'_{ij})}^{2} + \sum_{j = 1}^{m} \sum_{l > j}^{m} β_{ijl} y'_{ij} y'_{il}

(5)

Here, $β_{ij}$ are regression coefficients for the first-degree terms, $β_{ijj}$ are coefficients for the quadratic terms, $β_{ijl}$ are coefficients for the cross-product terms and $β_{i 0}$ is the intercept term. If $β_{ijj}$ are set to 0, then the second-order model reduces to the first-order model with interactions. If $β_{ijj}$ and $β_{ijl}$ are both set to 0, then the model reduces to main effects model that is similar to the equation used in the ‘house of quality’.

3. A system value model is found by combining together the customer value model developed in step 1, and the function forms developed in step 2 gives

u_{Y} (y_{1}, \dots, y_{m}) = u (x_{1}, \dots, x_{M}) = \sum_{i = 1}^{M} k_{i} u_{i} (f_{i} (y_{1}, \dots, y_{m}))

(6)

However, if some of the targets are finally verified as constraints, the first step of the procedure will then be different and the second and third steps are the same. Even if means–ends and part–whole analysis were carefully performed, the assumption of additive independence may not be satisfied, because joint distribution of attribute utility is apparent in customer’s preference. Therefore, additive function form is not appropriate as a utility function to compose together the set of customer attributes. Independence assumptions should be carefully verified for identifying special utility functions. Usually, a multi-linear function form will be appropriate as a utility function in this situation. While the assessment procedure for multi-linear function form is the same as in the literature,¹⁴ there are still two further points that can make a difference. One is about the single-attribute utility function over the attribute with constraint, which may change from a range utility function into a step utility function. Assume in this case the constraint for $x_{i}$ is $x_{il} \leq x_{i} \leq x_{iu}, i = 1, 2, \dots, n$ and the constraint for the $y_{j}$ is $y_{jl} \leq y_{j} \leq y_{ju}, j = 1, \dots, m$ . Then, the final constraint of $x_{i}$ will be $[c_{il}, c_{iu}] = [x_{il}, x_{iu}] \cap [min (f_{i} (y_{1}, \dots, y_{m})), max (f_{i} (y_{1}, \dots, y_{m}))]$ . The utility function over $X_{i}$ may be assessed as

u_{i} (x_{i}) = {\begin{matrix} 1, x_{i} \in [c_{il}, c_{iu}] \\ 0, x_{i} \notin [c_{il}, c_{iu}] \end{matrix}

(7)

The other is that $u (\dots, x_{i}, \dots) = 0, x_{i} \notin [c_{il}, c_{iu}]$ . That is, if the constraint of $x_{i}$ is not achieved, any higher level of achievement in other attributes cannot compensate this.

After a system value model is developed through application of these three steps, an optimisation study is finally deployed, which is to optimise expected utility of design alternatives. $E (u_{Y} (y_{1}, \dots, y_{m}))$ is maximised and the design alternatives are rationally compared in terms of value with choice taken. This approach thus resolves the first two identified methodological problems. In fact, it eliminates unnecessary targets (goals) and substitutes system value model for targets in order to provide focus for generating and evaluating design alternatives.

However, if a system value model replaces targets of system-level ECs, then it is naturally expected that component value models replace targets of component-level ECs. Component value models are then derived from the system value model through sensitivity analysis, which can mitigate the third methodological problem and there is no need to flow down targets of system-level ECs to targets of component-level ECs.

Assume the system has a set of $P$ components, and the pth component $p$ has a set of $m_{p}$ attributes, $p = 1, \dots, P$ expressed as a vector $z_{p}$ . All component attributes are concatenated into a vector z. And assume there is a vector function $h$ such that $y = h (z)$ . The objective then is to maximise $u_{y} (y) = u_{y} (h (z))$ , which makes the component designs consistent with system design to maximise system value. Because attribute spaces tend to be sufficiently smooth, $u_{y} (h (z))$ can be linearised by a Taylor’s series expansion¹⁸ in the vicinity of the preliminary design $y'$ , corresponding to component design attributes $z'$ . The component value model for the component $p$ can be approximated by

u_{cp} \approx \sum_{k = 1}^{m_{p}} (\sum_{j = 1}^{m} \frac{d u_{y}}{d y_{j}} | y'_{j} \cdot \frac{d y_{j}}{d z_{pk}} | z'_{pk}) \cdot z_{pk}

(8)

or equivalently by

u_{cp} \approx \sum_{k = 1}^{m_{p}} (\sum_{j = 1}^{m} (\sum_{i = 1}^{n} \frac{du}{d x_{i}} | x'_{i} \cdot \frac{d x_{i}}{d y_{j}} | y'_{j}) \cdot \frac{d y_{j}}{d z_{pk}} | z'_{pk}) \cdot z_{pk}

(9)

which replaces targets of component-level ECs of the component $p$ and is used for generating and evaluating the component design alternatives.

These value models are integrated into traditional requirements specification and a value-based requirements specification is established. The main benefits of the approach and value-based requirements specifications are the following:

Value becomes an explicit construct that can be qualified and quantified to some extent enabling value modelling and simulation.

The methodological problems in the ‘house of quality’ are mitigated.

Value-based requirements specifications are used for evaluating design alternatives, which helps selecting one or a subset of design alternatives with high value to customers. It is a reactive way of using value-based requirements specifications. Value-based requirement specifications can also be used for designing for value in the life cycle of products. Important value dimensions and value drivers are identified as pointers for designing. It is a proactive way of using value-based requirements specifications.

Case study

Context

In commercial aircraft development programmes, systems engineering processes and standards are widely used. However, they do not address ‘value’ in much detail in the requirements engineering stage.¹⁹ Losing a holistic, value-focused viewpoint is also obvious in the aircraft design and evaluation process.^20,21 For example, when the aircraft design alternatives are in a target region of the solution space that is given by the independently set targets for top-level aircraft requirements, aircraft design alternatives are traditionally evaluated in terms of recurring and non-recurring cost by aircraft manufacturers, and direct and indirect operating costs by the airlines or other operators. Therefore, it naturally eliminates the design alternatives that are outside of the target regions but with higher multi-dimensional value as perceived by customers (and in fact by other external and internal stakeholders). Furthermore, a design alternative that lies in the target region and achieves best results in terms of lowest costs may not be the alternative that offers the highest overall value, because in this case no value trade-offs were conducted that were based on multiple value dimensions. Value models in this case study are developed to revise this situation as a complement to traditional requirements specification.

Application

A process underlying the house of quality has been systematically deployed in our case study and customer needs, ECs and their relationship matrix have been elicited, which were inputs for the application of the proposed approach. A customer (an airline company) is currently interested in purchasing a number of long- and medium-range commercial aircrafts for its intended routes. A simplified set of three airline needs is identified: (1) maximise profitability, (2) maximise maintainability and (3) comply with emission standards and airworthiness authorities’ directives and safety requirements. Correspondingly, attributes for measuring each customer need are as follows: (1) X ₁: surplus value measured in 2012 million dollars, (2) X ₂: mean maintenance man-hours per flight hour and (3) X ₃: yes or no, respectively. More surplus value is preferred than less, and an increasing utility function $u_{2} (x_{2})$ is assessed in a specified interval, which is shown in Figure 5. For mean maintenance time, less is preferred and a decreasing utility function is assessed. Targets specified for these two attributes are verified as goals. However, the commercial aircrafts are either complying with emission and safety standards or not, and the standards specified by national and international regulations have to be achieved. If one design alternative of a commercial aircraft fails to achieve the emission and safety standards, it is unacceptable and is eliminated in the evaluation and selection process. The third customer need and its attributes thus define a constraint with a step utility function.

Figure 5.

Utility function over surplus value.

After verifying the independence relationships between these three attributes, a multi-linear utility function similar to equation (1) is appropriate as a multi-attribute utility function. And the weights $u (x_{1}^{0}, x_{2}^{0}, x_{3}^{0})$ , $u (x_{1}^{*}, x_{2}^{0}, x_{3}^{0})$ , $u (x_{1}^{0}, x_{2}^{*}, x_{3}^{0})$ and $u (x_{1}^{*}, x_{2}^{*}, x_{3}^{0})$ are assessed as 0, where $x_{i}^{0}$ is the lower level of $x_{i}$ , $x_{i}^{*}$ is the upper level of $x_{i}, i = 1, 2, 3$ . This assessment reflects the fact that the aircraft is of no value to the airline if it cannot achieve the constraint of emission and safety standards. Also, the airline believes that meeting the constraint is not sufficient to provide value, which indicates $u (x_{1}^{0}, x_{2}^{0}, x_{3}^{*}) = 0$ . The assessed airline value model then is

u (x) = {\begin{matrix} 0.7 u_{1} (x_{1}) + 0.3 (x_{2}) if x_{3} = yes \\ 0 otherwise \end{matrix}

(10)

An evaluation of five alternatives using the airline value model is then carried out. The approach distinguishes goals and constraints first, and only reserves real constraints of emission and safety in the value model. This quickly eliminates option 3 and reduces the set of alternatives to options 1, 2, 4 and 5, as shown in Table 2. The performances of these four options are entered into the airline value model that provides the value for each of the options. Options 4 and 5 are identified as the most favourable options. However, they slightly violate the given targets and would have been eliminated directly had a target-based evaluation been applied. This approach then allows to search in a broader solution space and to find alternatives with higher value to airlines.

Table 2.

Target-based evaluation and value model-based evaluation.

Customer need/attribute	Attribute range	Target	Option 1	Option 2	Option 3	Option 4	Option 5
Profitability/ $X_{1}$	[1000, 8000]	>5000	6300	5700	7500	7500	4980
Maintainability/ $X_{2}$	[0.1, 0.3]	<0.2	0.19	0.13	0.2	0.21	0.1
Emission, safety/ $X_{3}$	0,1	1	1	1	0	1	1
Target-based approach			Ok	Ok	No	No	No
Proposed approach			0.7710	0.7789	0	0.8011	0.7889

With this value model, it is possible to identify a list of 11 aircraft top-level requirements (system ECs) $Y = (Y_{1}, Y_{2}, \dots Y_{11})$ , such as ‘manufacturing cost’, ‘gross weight’, ‘field length’, ‘time to climb’, ‘dispatch reliability’, ‘airport noise’, ‘range’, ‘speed’ and ‘payload weight’. The surrogate models between customer attributes $(X_{1}, X_{2}, X_{3})$ and system ECs $(Y_{1}, Y_{2}, \dots Y_{11})$ are then found through experience or response surface modelling, which are combined together with equation (10) to find the aircraft system value model $u_{Y} (y_{1}, \dots, y_{11})$ . An implementation of the aircraft system value model in Vanguards Studio²² is shown in Figure 6. It is then possible to use this model to calculate the influence of ECs on system value. Different ECs have different degree of influence on system value model as indicated by the different colours in Figure 6. Designers can be clearly informed through this kind of value visualisation. Most importantly, value trade-offs are made possible among all the attributes: customer attributes and aircraft ECs. For example, one unit of change to ‘range’ or ‘dispatch reliability’ results in different change of value and a special trade-off, and all these different value trade-offs are implied in the implemented system value model.

Figure 6.

The system value model of a commercial aircraft.

While traditional fixed targets are unable to resolve uncertain achievement of system ECs, system value model is more appropriate. When performance of ECs is uncertain with respective probability distributions, values for the design alternatives are still measurable. For example, if ‘Dispatch Reliability’ is of a normal distribution with a mean value of 0.98 and standard deviation of 0.1, then ‘Utilisation’ will be also of a normal distribution, which finally results in an uncertain surplus value. A Monte Carlo simulation of the model as shown in Figure 7 can be easily performed.

Figure 7.

Expected utility of one design alternative.

With the aircraft system value model, component value models can be derived using equations (8) or (9). The premise is that functions between component ECs and system ECs are established through experience and response surface modelling. In this case, the functions between engine ECs and aircraft ECs are identified in order to derive an engine value model. A set of nine engine ECs that significantly influence aircraft ECs are chosen, such as ‘engine manufacturing cost’, ‘take-off thrust performance’, ‘engine weight’, ‘specific fuel consumption’ and ‘engine reliability’. The functions are in the form of

dispatch reliability \approx 99.5 % \times engine reliability

aircraft manufacturing cost \approx $ 20 million + 2 \times engine manufacturing cost

It is then straightforward to derive the engine value model by multiplying the first-order partial derives of the aircraft system value model with respect to the aircraft ECs and the first-order partial derives of aircraft ECs with respect to engine ECs. With the derived mathematical engine value model, the same procedures are used to develop engine value model in Vanguards Studio as those for aircraft value model. An engine value model derived from the aircraft system value model in the vicinity of a special aircraft design $y'$ corresponding to engine design $z'_{Engine}$ is shown in Figure 8. This engine design alternative is of negative value, and performance of engine ECs can be adjusted to certain extent to maximise the engine value model, which might also be negative. However, when engine is maximised in terms of this value model and combined with other maximised component design, the aircraft is optimised in the vicinity of a special aircraft design $y'$ . Then $y$ can be changed again and in turn performance of engine ECs for value optimisation.

Figure 8.

The derived engine model from the aircraft system value model.

These computerised value models will be used for generating and evaluating aircraft and engine alternatives and they are a necessary complement to traditional requirements specification. When the approach and this case study are presented to senior managers and engineers in the research and technology community that are working towards preparation of future aircraft programmes in an aircraft manufacturer, their feedback is really positive and there is a strong need for value models from the industry to provide the best possible solution to their customers. They are actually investigating and applying it at low industrial maturity in order to enhance their early conceptual work. They believe that this and other innovative approaches should be followed up because they offer high potential to improve the quality of future aircraft programmes. The suggested approach is considered as one of a small number of complementary value-related approaches that are actively followed up by a company-wide research initiative that aims to provide a mature set of value generation methodologies for a specific future aircraft programme. Furthermore, while applicability of the approach at the customer and aircraft level is obvious, it is also recognised that an application of the approach at a component level or sub-component level in an enterprise context is needed, and a comparison between the approach and requirements flowing down in real context is necessary. This work will be reported in the near future.

Conclusion

In this article, three methodological problems are identified with regard to setting targets in the ‘house of quality’. When targets are set independently for each EC, with fixed value or flowed down through a decomposition process, they may not be aligned with overall value optimisation, which cause difficulty in establishing rational requirements specifications.

In order to mitigate these three possible methodological problems of setting targets and establishing value-based requirements specifications on a theoretical foundation, a multi-attribute utility theory–based approach is proposed. A system value model is developed to replace targets. By this replacement, there is no need for setting targets like the traditional way, and probability measurement is naturally incorporated in the multi-attribute utility functions. Importantly, the system value model also provides focus and motivation for design engineers, because it provides a composition function among ECs, which can model the value influence of ECs and their value trade-offs. Another effect of this replacement is that there is no need to flow down targets of system ECs, which would bring about problems when establishing requirements specifications at component levels. Component value models are derived from system value model through sensitivity analysis, instead of the traditional process of setting targets at the component levels. These mathematical value models enable rational value modelling and simulation at the requirements development stage and during the later change management over time. It will promote value-driven design²¹ to experience a transformation from merely economic-based to true multi-dimensional value-based optimisation and model-based development. This approach has potential applicability for developing complex systems of high value to customers, such as commercial aircraft, space and defence systems. However, more applications or experiments are needed to check its applicability in different contexts and corresponding comparisons between the proposed approach and the target setting approach in terms of value achievement are to be deployed.

From another perspective, setting targets is a well-recognised practice in the ‘house of quality’ and sometimes designers and customers do not feel inclined to develop sophisticated value models. It would then be useful to set targets but just to comply with rational decision-making. In the literature, equivalence between target-oriented preference function and multi-attribute utility function in certain assumptions has been presented.^23,24 Therefore, targets in the house of quality can be set in a rational way, which needs to be explored in future studies.

Footnotes

Acknowledgements

The authors thank CRESCENDO WP2.2 partners for invaluable discussions during model development.

Declaration of conflicting interests

The authors declare that there is no conflict of interest.

Funding

The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) () under grant agreement no. 234344, the Humanity and Social Science Youth Foundation of Ministry of Education of China (14YJCZH213) and from Northwestern Polyetchnical University (13GH 0311, RW201305, W016228).

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