Many manufacturers today are striving to offer high value-added product-related services (PRS) due to increasing competition and environmental pressure. PRS can reduce the negative impact on the environment, because it extends the life of products and minimizes the cost. Product and service planning has been considered as the critical factor to the success of PRS. Quality function deployment (QFD) has been recognized as an efficient planning tool which can convert customer needs (CNs) into design attributes of PRS involving product attributes (PAs) and service attributes (SAs). However, the subjective and vague information in the design of PRS with QFD may lead to inaccurate priority of PAs and SAs. To solve this problem, a novel rough VIKOR- (VIseKriterijumska Optimizaciji I Kompromisno Resenje-) based QFD is proposed. The proposed approach integrates the strength of rough number (RN) in manipulating vague concepts with less a priori information and the merit of VIKOR in structuring framework of compromise decision-making. Finally, an application in compressor-based service design is presented to illustrate the potential of the proposed method.
Product-related services (PRS) are services that are closely associated with goods in products. Expanding the service content of products has been for years a major trend in business strategy [
To solve the above problems, this work proposes a new approach for prioritizing PAs and SAs of PRS by integrating VIKOR (VIseKriterijumska Optimizaciji I Kompromisno Resenje) and rough number (RN). In the rough QFD, the relationships among CNs, PAs, and SAs are mapped, and VIKOR and RN are used to convert the rough CN importance into the rough PA importance and then into the rough SA importance. Thus, designers can make reasonable decisions with vague, subjective, and limited information.
The rest of this paper is organized as follows. Section
Some researchers have applied the conventional QFD to the field of service design. An et al. [
Therefore, to deal with vague and subjective information in the conventional QFD for service design, the fuzzy set theory is utilized. Geng et al. [
Pawlak [
Lower approximation:
Upper approximation:
Boundary region:
For a concept
Zhai et al. [
Rough number:
Interval of boundary region:
The arithmetic operations of interval analysis can also be used in RNs as follows [
VIKOR (VIseKriterijumska Optimizaciji I Kompromisno Resenje) is an effective tool in multicriteria decision-making (MCDM). It is proposed by Opricovic [
In the VIKOR method,
The VIKOR method is suitable for the situation where the decision-maker is not able, or does not know, to express his/her preference at the early stage of solution selection [
Although VIKOR is a simple and straightforward MCDM technique, it cannot well reflect the vague and subjective information contained in the process of QFD analysis for PRS; that is, it lacks the capability of capturing and reflecting the subjective perceptions of designers in the analyzing process. Thus, a new method should be developed to effectively manipulate the vague and subjective information in the QFD.
In order to solve the problem of vagueness and subjectivity in the early design of PRS, a QFD framework based on rough VIKOR is proposed, as shown in Figure
The proposed QFD framework based on rough VIKOR.
In order to improve customer satisfaction of new products, CNs are collected and classified. Meanwhile, experts identify PAs and SAs.
CNs are the crucial inputs for the success of new product development. A CN is a description, in the customer’s own words, of the benefit to be fulfilled by the product or service [
To satisfy CNs, PAs are identified. Then SAs are also identified to improve the design. They are expressed as follows:
In the rough QFD, the importance of PAs and SAs is calculated by integrating VIKOR and RN. The process is as follows.
Customers evaluate the CN importance with the 9-point subscale (1-3-5-7-9). Scores of 1, 3, 5, 7, and 9 are define as very low, low, moderate, high, and very high importance, respectively. Similarly, experts evaluate the CN-PA relationship and the PA-SA relationship with the 9-point subscale. Scores of 1, 3, 5, 7, and 9 represent very weak, weak, moderate, strong, and very strong relationship. The CN importance, the CN-PA relationship, and the PA-SA relationship are obtained.
The crisp importance and crisp relationships are converted into RNs with formula (
The group RN is aggregated as follows:
The rough importance and rough relationships are normalized as follows:
The importance of PAs is calculated with rough VIKOR as follows [
For any two interval numbers If the interval of a RN is not strictly contained by another if if If the interval of a RN is strictly contained by another if if if If if if
Acceptable advantage: Acceptable stability in decision-making:
If (C1) or (C2) is not satisfied, a set of PAs is proposed as follows:
Therefore, the ranking order of PAs is determined by the aggregating function
Similarly, the SA-PA relationship matrix is the rough decision matrix, and the PA importance is the evaluation criterion. According to Step
In this section, the design of the compressor-related services is taken as an example to illustrate the application of the proposed method. The compressor is the heart of refrigeration system. It can compress and transport refrigerant vapor and make the refrigerant work. The design of the compressor affects the performance of a refrigerator directly. The information of the compressor is provided by company A, who has developed the compressor for more than 40 years. It mainly provides the compressor and related services to its customers.
Before developing the compressor, a team consisting of 20 investigators in company A take more than two months to collect CNs. These investigators are divided into five groups. Three groups interview key customers, one group communicates with their vendors, and the other exchanges the information of the compressor with the relevant enterprises. After collecting CNs, the team refines them and six key CNs are determined. They are safety (CN1), lower energy consumption (CN2), lower noise (CN3), lower failure rate (CN4), being easy to maintain (CN5), and environmental protection (CN6).
To satisfy the six key CNs, design team identifies PAs of the compressor. In the concurrent and collaborative design, all groups can work together at the same time. For example, one group involving 25 persons designs the parts or components, one group including 10 people develops the power system, and another group consisting of 8 people designs the hydraulic system. According to the existing knowledge, experience, and CNs, these designers exchange the information and then identify seven key PAs, that is, refrigerating capacity (PA1), cylinder volume (PA2), rated power (PA3), performance coefficient (PA4), structure (PA5), noise (PA6), and air discharge (PA7). Similarly, service team consisting of 22 people identify SAs to improve the design of the compressor. Seven key SAs are determined depending on the existing knowledge, CNs, PAs, and so forth. The final determined SAs are diagnosing failure timely (SA1), less repair time (SA2), lower repair cost (SA3), supplying spare parts timely (SA4), supplying spare parts with lower cost (SA5), professional cleaning (SA6), and timely lubrication (SA7).
The PA importance and SA importance are calculated in the following steps.
Five key customers are invited to evaluate the CN importance of the compressor with the 9-point subscale, as shown in Table
The crisp ratings for the CN importance.
CN | C1 | C2 | C3 | C4 | C5 |
---|---|---|---|---|---|
CN1 | 9 | 7 | 9 | 9 | 9 |
CN2 | 5 | 9 | 7 | 7 | 7 |
CN3 | 5 | 7 | 9 | 5 | 7 |
CN4 | 7 | 9 | 7 | 9 | 9 |
CN5 | 3 | 3 | 5 | 3 | 5 |
CN6 | 5 | 5 | 7 | 5 | 7 |
The crisp ratings for the relationships between CNs and PAs.
PA1 | PA2 | PA3 | PA4 | PA5 | PA6 | PA7 | |
---|---|---|---|---|---|---|---|
CN1 | 7, 3, 7, 5, 5 | 1, 1, 1, 1, 1 | 5, 7, 7, 5, 7 | 9, 7, 9, 9, 9 | 5, 5, 5, 3, 5 | 3, 1, 1, 3, 1 | 1, 1, 3, 1, 1 |
CN2 | 9, 9, 7, 9, 7 | 0, 0, 0, 0, 0 | 5, 1, 3, 3, 3 | 7, 9, 7, 7, 9 | 3, 1, 1, 1, 1 | 0, 0, 0, 0, 0 | 3, 1, 1, 3, 1 |
CN3 | 3, 1, 3, 3, 5 | 0, 0, 0, 0, 0 | 3, 3, 1, 5, 1 | 7, 5, 7, 9, 5 | 5, 3, 5, 7, 5 | 9, 9, 9, 9, 9 | 1, 1, 1, 3, 1 |
CN4 | 5, 5, 5, 5, 3 | 0, 0, 0, 0, 0 | 3, 1, 5, 3, 5 | 5, 3, 7, 7, 7 | 5, 3, 3, 3, 3 | 1, 3, 1, 3, 1 | 1, 3, 1, 1, 1 |
CN5 | 0, 0, 0, 0, 0 | 5, 3, 5, 5, 3 | 0, 0, 0, 0, 0 | 0, 0, 0, 0, 0 | 7, 5, 5, 5, 3 | 0, 0, 0, 0, 0 | 0, 0, 0, 0, 0 |
CN6 | 7, 5, 5, 3, 5 | 0, 0, 0, 0, 0 | 0, 0, 0, 0, 0 | 3, 5, 3, 7, 5 | 3, 3, 3, 1, 1 | 5, 1, 3, 5, 3 | 3, 1, 3, 3, 1 |
The crisp ratings for the relationships between PAs and SAs.
SA1 | SA2 | SA3 | SA4 | SA5 | SA6 | SA7 | |
---|---|---|---|---|---|---|---|
PA1 | 5, 3, 3, 7, 5 | 7, 5, 5, 7, 7 | 5, 7, 5, 7, 5 | 0, 0, 0, 0, 0 | 0, 0, 0, 0, 0 | 1, 3, 1, 3, 1 | 3, 1, 3, 3, 1 |
PA2 | 1, 3, 1, 5, 3 | 5, 5, 5, 7, 5 | 9, 7, 9, 9, 7 | 3, 3, 1, 3, 3 | 9, 5, 7, 7, 5 | 0, 0, 0, 0, 0 | 0, 0, 0, 0, 0 |
PA3 | 5, 7, 5, 5, 7 | 7, 7, 7, 7, 5 | 7, 5, 7, 9, 7 | 0, 0, 0, 0, 0 | 0, 0, 0, 0, 0 | 0, 0, 0, 0, 0 | 5, 3, 5, 7, 3 |
PA4 | 3, 3, 3, 5, 3 | 5, 3, 5, 3, 5 | 5, 7, 5, 5, 7 | 3, 1, 3, 5, 3 | 7, 5, 5, 3, 5 | 7, 7, 5, 5, 7 | 5, 5, 7, 9, 7 |
PA5 | 5, 3, 5, 5, 7 | 7, 5, 7, 7, 7 | 9, 9, 9, 7, 9 | 5, 3, 3, 3, 3 | 9, 7, 5, 9, 7 | 5, 3, 5, 5, 3 | 5, 7, 5, 7, 7 |
PA6 | 5, 3, 1, 3, 5 | 3, 3, 5, 5, 5 | 7, 5, 5, 5, 3 | 0, 0, 0, 0, 0 | 0, 0, 0, 0, 0 | 0, 0, 0, 0, 0 | 3, 3, 7, 5, 5 |
PA7 | 1, 5, 1, 3, 3 | 5, 3, 5, 5, 3 | 5, 5, 7, 3, 5 | 0, 0, 0, 0, 0 | 0, 0, 0, 0, 0 | 5, 7, 5, 7, 5 | 5, 7, 5, 7, 3 |
The crisp ratings are converted into RNs with formula (
According to (
The group rough importance and group rough relationships are normalized with formula (
According to Step
The rough decision matrix of PAs.
CN1 | CN2 | CN3 | CN4 | CN5 | CN6 | |
---|---|---|---|---|---|---|
PA1 | [0.48, 0.69] | [0.89, 1.00] | [0.22, 0.39] | [0.63, 0.75] | [0.00, 0.00] | [0.74, 1.00] |
PA2 | [0.11, 0.11] | [0.00, 0.00] | [0.00, 0.00] | [0.00, 0.00] | [0.65, 0.83] | [0.00, 0.00] |
PA3 | [0.63, 0.74] | [0.23, 0.41] | [0.16, 0.35] | [0.32, 0.62] | [0.00, 0.00] | [0.00, 0.00] |
PA4 | [0.92, 1.00] | [0.84, 0.95] | [0.63, 0.74] | [0.69, 1.00] | [0.00, 0.00] | [0.64, 0.95] |
PA5 | [0.46, 0.55] | [0.12, 0.17] | [0.46, 0.62] | [0.47, 0.55] | [0.74, 1.00] | [0.27, 0.45] |
PA6 | [0.13, 0.23] | [0.00, 0.00] | [1.00, 1.00] | [0.18, 0.31] | [0.00, 0.00] | [0.37, 0.73] |
PA7 | [0.12, 0.17] | [0.14, 0.23] | [0.12, 0.17] | [0.16, 0.23] | [0.00, 0.00] | [0.27, 0.45] |
The best
CN1 | CN2 | CN3 | CN4 | CN5 | CN6 | |
---|---|---|---|---|---|---|
| 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| 0.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
The
| | | Weight | Rank | ||||
---|---|---|---|---|---|---|---|---|
| Rank | | Rank | | Rank | |||
PA1 | [1.29, 2.32] | 2 | [0.38, 0.65] | 2 | [0.15, 0.44] | 2 | [0.73, 0.96] | 2 |
PA2 | [3.76, 4.52] | 7 | [0.92, 1.00] | 7 | [0.84, 1.00] | 7 | [0.00, 0.20] | 7 |
PA3 | [2.38, 3.60] | 4 | [0.59, 0.70] | 3 | [0.40, 0.65] | 4 | [0.40, 0.65] | 4 |
PA4 | [0.60, 1.56] | 1 | [0.37, 0.47] | 1 | [0.00, 0.20] | 1 | [0.84, 1.00] | 1 |
PA5 | [2.00, 2.95] | 3 | [0.58, 0.75] | 4 | [0.35, 0.60] | 3 | [0.60, 0.86] | 3 |
PA6 | [2.62, 3.53] | 5 | [0.80, 0.98] | 5 | [0.60, 0.86] | 5 | [0.35, 0.60] | 5 |
PA7 | [3.28, 4.25] | 6 | [0.86, 0.99] | 6 | [0.73, 0.96] | 6 | [0.15, 0.44] | 6 |
Similarly, the rough decision matrix of SAs is determined (shown in Table
The rough decision matrix of SA.
PA1 | PA2 | PA3 | PA4 | PA5 | PA6 | PA7 | |
---|---|---|---|---|---|---|---|
SA1 | [0.54, 0.80] | [0.17, 0.31] | [0.73, 0.86] | [0.40, 0.47] | [0.47, 0.63] | [0.37, 0.73] | [0.23, 0.44] |
SA2 | [0.85, 1.00] | [0.59, 0.65] | [0.86, 0.96] | [0.47, 0.60] | [0.70, 0.78] | [0.65, 0.82] | [0.58, 0.74] |
SA3 | [0.80, 0.94] | [0.89, 1.00] | [0.86, 1.00] | [0.68, 0.80] | [0.92, 1.00] | [0.74, 1.00] | [0.70, 0.90] |
SA4 | [0.00, 0.00] | [0.23, 0.33] | [0.00, 0.00] | [0.26, 0.46] | [0.34, 0.40] | [0.00, 0.00] | [0.00, 0.00] |
SA5 | [0.00, 0.00] | [0.67, 0.89] | [0.00, 0.00] | [0.54, 0.73] | [0.71, 0.92] | [0.00, 0.00] | [0.00, 0.00] |
SA6 | [0.18, 0.30] | [0.00, 0.00] | [0.00, 0.00] | [0.73, 0.86] | [0.41, 0.52] | [0.00, 0.00] | [0.85, 1.00] |
SA7 | [0.22, 0.38] | [0.00, 0.00] | [0.50, 0.80] | [0.75, 1.00] | [0.63, 0.74] | [0.64, 0.95] | [0.69, 0.99] |
The best
PA1 | PA2 | PA3 | PA4 | PA5 | PA6 | PA7 | |
---|---|---|---|---|---|---|---|
| 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| 0.00 | 0.00 | 0.00 | 0.26 | 0.34 | 0.00 | 0.00 |
The
| | | Weight | Rank | ||||
---|---|---|---|---|---|---|---|---|
| Rank | | Rank | | Rank | |||
SA1 | [1.33, 3.00] | 4 | [0.60, 0.81] | 5 | [0.36, 0.64] | 4 | [0.36, 0.64] | 4 |
SA2 | [0.77, 1.82] | 2 | [0.45, 0.72] | 2 | [0.20, 0.49] | 2 | [0.51, 0.85] | 2 |
SA3 | [0.29, 1.13] | 1 | [0.23, 0.43] | 1 | [0.00, 0.22] | 1 | [0.60, 1.00] | 1 |
SA4 | [2.80, 4.80] | 7 | [0.73, 1.00] | 7 | [0.60, 1.00] | 7 | [0.00, 0.22] | 7 |
SA5 | [1.95, 3.72] | 6 | [0.73, 0.96] | 6 | [0.51, 0.85] | 6 | [0.20, 0.49] | 6 |
SA6 | [1.86, 3.44] | 5 | [0.51, 0.79] | 4 | [0.36, 0.71] | 5 | [0.22, 0.58] | 5 |
SA7 | [0.94, 2.45] | 3 | [0.45, 0.75] | 3 | [0.22, 0.58] | 3 | [0.36, 0.71] | 3 |
To reveal the advantages of the proposed method, the conventional QFD (using precise numbers) and fuzzy QFD (using symmetrical triangular fuzzy numbers) are applied (see Tables
Ranking of CNs with precise, fuzzy, and rough numbers.
CN | Precise numbers | Fuzzy numbers | Rough numbers | |||
---|---|---|---|---|---|---|
| Rank | | Rank | | Rank | |
CN1 | 1.00 | 1 | [0.79, 1.00] | 1 | [0.92, 1.00] | 1 |
CN2 | 0.80 | 3 | [0.61, 0.83] | 3 | [0.70, 0.85] | 3 |
CN3 | 0.75 | 4 | [0.56, 0.78] | 4 | [0.63, 0.83] | 4 |
CN4 | 0.95 | 2 | [0.75, 0.96] | 2 | [0.86, 0.97] | 2 |
CN5 | 0.43 | 6 | [0.28, 0.49] | 6 | [0.37, 0.47] | 6 |
CN6 | 0.67 | 5 | [0.49, 0.70] | 5 | [0.59, 0.70] | 5 |
Ranking of PAs in the conventional, fuzzy, and rough QFD
PA | Conventional QFD | Fuzzy QFD | Rough QFD | |||
---|---|---|---|---|---|---|
| Rank | | Rank | | Rank | |
PA1 | 0.92 | 2 | [0.64, 0.95] | 2 | [0.73, 0.96] | 2 |
PA2 | | 7 | [0.00, 0.33] | 7 | [0.00, 0.20] | 7 |
PA3 | 0.53 | 4 | [0.35, 0.68] | 4 | [0.40, 0.65] | 4 |
PA4 | 1.00 | 1 | [0.70, 1.00] | 1 | [0.84, 1.00] | 1 |
PA5 | 0.78 | 3 | [0.53, 0.90] | 3 | [0.60, 0.86] | 3 |
PA6 | 0.45 | 5 | [0.32, 0.65] | 5 | [0.35, 0.60] | 5 |
PA7 | 0.21 | 6 | [0.15, 0.52] | 6 | [0.15, 0.44] | 6 |
Ranking of SAs in the conventional, fuzzy, and rough QFD
SA | Conventional QFD | Fuzzy QFD | Rough QFD | |||
---|---|---|---|---|---|---|
| Rank | | Rank | | Rank | |
SA1 | 0.64 | 4 | [0.31, 0.82] | 4 | [0.36, 0.64] | 4 |
SA2 | 0.83 | 2 | [0.47, 0.87] | 2 | [0.51, 0.85] | 2 |
SA3 | 1.00 | 1 | [0.53, 1.00] | 1 | [0.60, 1.00] | 1 |
SA4 | | 7 | [0.00, 0.40] | 7 | [0.00, 0.22] | 7 |
SA5 | 0.29 | 6 | [0.27, 0.65] | 6 | [0.20, 0.49] | 6 |
SA6 | 0.35 | 5 | [0.25, 0.64] | 5 | [0.22, 0.58] | 5 |
SA7 | 0.61 | 3 | [0.36, 0.78] | 3 | [0.36, 0.71] | 3 |
Comparison of the importance of CN, PA, and SA.
Comparison of the CNs’ importance
Comparison of the PAs’ importance
Comparison of the SAs’ importance
Although the three methods produce the same rankings, they have different mechanisms of decision-making information manipulation. Firstly, different from the conventional QFD, both fuzzy QFD and rough QFD consider the subjectivity and vagueness in the decision-making process. Secondly, compared with fuzzy QFD, rough QFD does not need much a priori information, for example, pre-set membership function in the fuzzy methods. More importantly, rough QFD uses flexible intervals to describe vague and subjective information, while fuzzy QFD uses fixed intervals. The weights from the former have smaller intervals than that of the latter, which indicates that the result of rough QFD is more precise. In fact, the precise weights of design attributes are important in the design decision-making process. Designers always set different threshold values of weights to determine whether the design attributes can be considered in the next stage of development. For example, PA2 will be not considered in the next stage of conventional QFD, because its weight is 0.00. However, PA2 will be still considered in the fuzzy QFD and rough QFD, because the weights in the two methods are [0.00, 0.33] and [0.00, 0.20], respectively.
The differences of the three methods are summarized in Table
Main differences between the rough QFD, conventional QFD, and fuzzy QFD.
Method | Manipulation of uncertainty | Reliance on much prior information | Flexibility |
---|---|---|---|
Conventional QFD | No | No | Low |
Fuzzy QFD | Partial | Yes | Low |
Rough QFD | Yes | No | High |
This paper presents an improved QFD method for PRS design based on the rough set theory and VIKOR. The proposed approach uses rough VIKOR to prioritize design attributes of PRS in the vague and subjective situation. The validation of the proposed method in compressor-related service shows that it is an effective decision support tool for design of PRS. To sum up, the approach reveals the following features.
The proposed QFD method provides a progressive mapping process for PRS design. That is, mapping relationships between CNs and PAs and then mapping relationships between PAs and SAs, which is not presented in previous literature of PRS. PRS designers can systematically make reasonable planning of product and service in the early design of PRS.
RN with flexible boundary is used to manipulate the vagueness and subjectivity in the QFD analysis process to reduce lost information, because it can comprehensively reflect decision-maker’s subjective judgment and preference.
The rough VIKOR provides a structured framework of compromise decision-making in PRS design under vague and subjective environment.
The proposed approach for PRS planning can be implemented without large amount of data and much a priori information (e.g., pre-set membership function).
Although the rough VIKOR-based QFD has merits in dealing with vagueness and subjectivity, it does not consider different weights of decision-makers in the QFD group. Therefore, to better reflect the actual situation of decision-making in QFD implementation process, it is necessary to develop suitable aggregation operators for judgments aggregation. The aggregation operators’ influence on the rough VIKOR-based QFD would also be explored in future researches. Besides, more testing work is necessitated to gain external validity.
The authors declare that there are no competing interests regarding the publication of this paper.
The work described in this paper was supported by the National Natural Science Foundation of China (Grant no. 71501006). It was also partially supported by the National Natural Science Foundation of China (Grants nos. 71332003, 71632003, and 71420107025) and the Fundamental Research Funds for the Central Universities.