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Using Vector Projection Method to evaluate maintainability of mechanical system in design review
Reliability Engineering and System Safety 81 (2003) 147–154 www.elsevier.com/locate/ress
Using Vector Projection Method to evaluate maintainability of mechanical system in design review Lu Chen*, Jianguo Cai Department of Industrial Engineering and Management, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200030, People’s Republic of China Received 18 November 2002; accepted 15 March 2003
Abstract Maintainability of a mechanical system is one of the system design parameters that has a great impact in terms of ease of maintenance. In this article, based on the definition of the terms of maintenance and maintainability, an important tool of Design for Maintenance is developed as a way to improve maintainability through design. A set of standard and organized guidelines is provided and maintainability factors in terms of physical design, logistics support and ergonomics are identified. As a specific application of design review, a methodology so called Vector Projection Method is developed to evaluate the maintainability of the mechanical system. Lastly, an example is discussed. q 2003 Elsevier Science Ltd. All rights reserved. Keywords: Maintainability; Design for Maintenance; Guidelines; Factors; Vector Projection Method
1. Introduction Maintainability is recognized as being highly significant factor in the economic success of engineering systems and products. Also, design is the stage at which the eventual characteristics of future systems and products are determined. Therefore, it is important that designers should take maintainability into account during their work. However, there is much to consider at the design stage; a designer should be provided with simple and logical measure qualitatively or quantitatively to evaluate and predict the maintainability. Prediction facilitates an early assessment of the maintainability of the design and enables decisions concerning the compatibility of a proposed design with specified maintenance requirements or the choice of better alternatives. There are a number of excellent specialist papers and text books in maintainability. The problem for designers is that they are mainly written from the perspective of the dedicated maintainability engineer. These papers and books contain in-depth analytical methods that require information that is not available at the design stage. Therefore, they are of limited use to designers. * Corresponding author. Tel.: þ 86-21-629-321-15. E-mail address: [email protected] (L. Chen).
This paper is written entirely from a design perspective. In this article, an important tool, Design for Maintenance (DFMAIN) is firstly introduced in Section 2. Also in Section 2, a set of standard and organized guidelines is provided. Section 3 introduces some general concepts of design review. Then, as a method of design review, maintainability evaluation methods are discussed in detail in Section 4. A specific methodology so called Vector Projection Method (VPM) is developed to evaluate the maintainability of the system. Section 5 presents a stepwise evaluation procedure. In Section 6, a case demonstration is carried out, while Section 7 concludes the paper.
2. Design for Maintenance DFMAIN is concerned with achieving good designs that consider the general care and maintenance of equipment and the repair actions that follow a failure. 2.1. Maintenance and maintainability Traditionally, people think that maintenance is only a kind of guaranteed technical job made by a few of technicians, and has nothing with the design and production of the product. In fact, nowadays, mechanical or electronic
0951-8320/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0951-8320(03)00075-9
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products are becoming more and more complicated. As a result, the content and meaning of maintenance are richer than ever. The Chinese Standardization Department publication of ‘Definition of Terms for Reliability and Maintainability’, GJB451-90 defines maintenance as “all the activities that are intended to retain or restore the product to a specified condition”. With respect to maintainability, the designer has to take a different view from that of the maintenance manager. Some definitions lead to mathematical analyses using repair rates in a similar manner to reliability analyses. Although useful to the maintenance manager in the analysis of data accumulated in service, this approach is not very useful in design. The designer should consider those factors which are under his/her control. The US military publication MIL-STD-721 [1] defines maintainability as follows: Maintainability: The measure of the ability of an item to be retained or restored to specific conditions when maintenance is performed by personnel having specified skill levels, using prescribed procedures and resources at each prescribed level of maintenance and repair. The maintainability definition has fostered the development of many maintainability prediction procedures for providing an assessment of system maintainability. Rather than predicting how the system will fail, the effort of maintainability is to make manufacturing systems and products that require minimal maintenance and that are easy and inexpensive to fix when they fail. Consequently, manufacturers strive to design maintainability into the products and their manufacturing processes.
2.3. DFMAIN guidelines A general rule for DFMAIN is to reduce the possibility of damage to the product or equipment during maintenance and servicing or better yet to eliminate the need for maintenance. To assist in establishing a solid foundation for implementing DFMAIN in the early stage of design, a set of standard and organized guidelines is provided. Use of these guidelines can help improve maintainability and enhance product quality [2]. B
B
B
B
B
B
2.2. Design for Maintenance DFMAIN is an important part of product/system design. Design changes during production are very costly, but if DFMAIN is implemented early in the design stage, a great number of benefits would be realized including: † † † †
Longer life of systems and products. Lower operation costs, by performing at high efficiency. Lower unscheduled downtime, by preventing failures. Lower scheduled downtime, by decreasing the time required to perform a particular maintenance task.
B
B
B
Keep the functional and physical characteristics as simple as possible. Complexity of design has a direct bearing on production and maintenance cost. To reduce the number of components and assemblies including redundant components is helpful in lowering the skill of technicians and the requirement of the equipment and maintenance tools. There is adequate access for visual and manipulative tasks, including the assembly of parts and any required tooling during assembly, inspection, repair, or replacement. Use standardized parts to simplify the maintenance work, especially for those parts that are mostly like to fail. Because standard parts are easy to find and be replaced. Select modular design so that subassemblies could be tested and maintained at that level and not at the final assembly. Design for ease of assembly and disassembly with a minimum number of parts. A product that is easily assembled and disassembled is also easily maintainable. Provide easy diagnosability. Diagnosability could be assured by provide functional sharing, monitoring parameters for failure including alarms, build-in test equipment facility and indication signal for failure including fault isolation. Test points are available for needed test pertaining to maintenance action. Provide identification to eliminate accident in maintenance. Critical components should be identified; test points and arrows should be well marked. Minimize weight and awkwardness in handling of parts that must be removed. Provide safety guards to prevent contact with moving parts, high temperature, high voltage lines or gaseous leakage. Provide appropriate manuals for maintenance instructions and procedures.
3. Design review Maintainability is one of the system design parameters that has a great impact in terms of ease of maintenance. System failure is inevitable no matter how reliably this is built-in, so its ability to be quickly restored is therefore the most important. To fully realize part or all of these benefits, some maintainability guidelines are presented next.
The design review may be defined as: [3] The quantitative and qualitative examination of a proposed design to ensure that it is safe and has optimum performance with respect to maintainability, reliability
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149
Table 1 Design review procedure Activity
Purpose
Timing
Review of the design specification
To ensure that the significance of all the points contained within the design specification is understood (1) To identify critical areas of the design that may affect plant availability and to comment on the advisability of pursuing projects with a high risk content (2) To examine equipment groups to maximize uniformity and suitability and to maximize the reliability systems formed by manufacturing and process consideration To evaluate quantitatively critical items of functional unit and to undertake qualitative reviews of functional unit generally To check that certain important sets of components will not give rise to, say, maintainability problems in service
Prior to the commencement of any design activity
System level design
Functional unit evaluation
Component analysis
and those performance variables needed to specify the equipment. The review is much more than the scrutiny of design work in the manner that an examiner checks a student exercise. It should help the designer and enrich design activity. It is an integral part of design activity and not a ‘bolt-on’ extra. The specific benefits associated with a good design review methodology include:
Prior to the start of functional unit design
After the completion of the first functional unit design
After the completion of the first detail design After the completion of the first detail design
Usually, there are different kinds of review work at different levels of design, such as design specification review, system review, functional unit evaluation, component analysis. A comprehensive design review is summarized in Table 1. Evaluation is a normal part of design activity, which is to evaluate the status of emerging designs against customer-driven criteria prior to proceeding forward to the next phase of a project.
† Added assurance that the voice of the customer has been heard correctly † Reductions in design cost and time-to-market † Reduced likelihood of program delay due to unexpected problems † Improved overall design integrity † Prevention of problems and associated downstream costs † Increased standardization † Improved customer satisfaction † Increased program structure and control.
4. Maintainability evaluation
Given these benefits, it is no surprise that the design review methodology is widely used and endorsed in commercial industry. In fact, 89% of the companies surveyed in a recent benchmarking study of 72 leading companies in seven basic industries reported using design review as a design assurance tool [4]. So, as we can see, the design review is one of the most important ways of achieving good maintainability. It should contribute to those problem areas such as maintainability and reliability which may not have been fully taken into account during the search for cost-effective feasible solutions.
Various attempts have been made by researchers in developing procedures for evaluation of the maintainability. Takata and Saito [5] have proposed a structure of the facility model for a computer-assisted life cycle maintenance system. It provides a flexible representation scheme for technical information as well as for the physical structure of the facility, and could be used to do deterioration evaluation of the facility. Vujosevic and Raskar [6] have developed procedures for identification of disassembly sequence, animation of human technicians while carrying out the disassembly sequence. Based on these, the maintainability of the systems is evaluated. Wani and Gandhi [7] developed
As a specific application of functional unit evaluation in design review activity, maintainability evaluation is discussed in this section. In this way alternatives can be systematically reviewed from the perspective of maintainability view to make them robust and suitable for further design work. 4.1. Literature review
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a procedure based on a digraph and matrix method to evaluate the maintainability index of mechanical systems. The department of highway in Chaoyang, Liaoning province, China [8] has evaluated the automobile maintainability base on the respective calculation of maintenance time and maintenance fee. In all these methods, the maintainability characteristics of the system affecting the maintainability have not been fully identified. Here, a methodology so called VPM is proposed to evaluate the maintainability of the system which is a multi-objective assessment. The concepts of fuzzy set theory and multiple-criteria decision analysis are widely used to solve this kind of problem in which a source of vagueness is involved. A fuzzy decisionmaking method integrates various linguistic or, in other word, qualitative assessment and weights to evaluate different alternatives. Details on this technique could be found in Refs. [14,15]. Chen [16] used this method to solve the distribution center location selection problem under fuzzy environment. Karasak and Tolga [17] proposed a fuzzy decision algorithm to select the most suitable advanced manufacturing system alternative from a set of mutually exclusive alternatives. Ammar and Wright [18] even applied this method in social science, such as performance measurement, namely to evaluate the state government performance and to survey client satisfaction. Even though fuzzy set theory is proved to be very effective in multi-objective evaluation, it has certain limitations. For example, when comparing two alternatives, only comparative goodness can be obtained. Therefore, in this paper, a methodology so called VPM is developed based on fuzzy set theory. With this method, a more absolute evaluation result could be obtained. And at the same time, the algorithm complexity is not increased. 4.2. Evaluation factors In maintainability evaluation, assessment criteria are defined in terms that are suitable for concept evaluation. For example, a repair time would be inappropriate because the repair time could not be calculated form the information available at the concept stage. Similarly, mean time to failure or mean failure rate calculations cannot be made. Instead, criteria should be used that refer to such factors as: simplicity and elegance of the design; minimum number of parts; suitability for modular construction, etc. Maintainability evaluation factors Vj in terms of design factors, logistics support, ergonomic factors are defined in a hierarchical structure as in Table 2. Under different circumstances, some or all of these factors are chosen to be the evaluation criterion. It depends on which of them are more important for a certain evaluation task.
Table 2 Maintainability evaluation factors Vj Physical design
Logistics support
Ergonomics
Simplicity
Test equipment
Accessibility
Assembly/disassembly tool or maintenance tool
Fault and operation indicators Skills of maintenance personnel Maintenance environment
Assembly/ disassembly Standardization Modularization Test points layout
Documentation
Other ergonomics factors
4.3. Weight calculation As we all know that not all the factors are equally important, in other words, weights must be assigned to these factors when evaluation work is done. Here we use Analytical Hierarchy Process (AHP) method to calculate the weight. AHP is a decision-aiding method developed by Saaty [9]. It is one of the extensively used multicriteria decision making methods. It aims at quantifying relative priorities for a given set of alternatives on a ratio scale. Numerous applications of the AHP have been made since its development and it has been applied to many types of problems [10 –13]. In this case, the factors are in one level, so the calculation is compared simple, the following steps are developed for applying the AHP: 1. A pair-wise comparison matrix (size n £ n) is constructed for each factor by using the relative scale measurement shown in Table 3. The pair-wise comparisons are done in terms of which factor dominates the other. 2. There are n ðn 2 1Þ judgements required to develop the matrix in step 1, reciprocals are automatically assigned in each pair-wise comparison. 3. Calculate the eigenvectors, the eigenvalue, consistency index. Judgement consistency can be checked by the consistency ratio (CR), given by CR ¼
CI RIðnÞ
where CI is the consistency index given by CI ¼ ðlmax 2 nÞðn 2 1Þ; RIðnÞ is the random consistency Table 3 Pair-wise comparison scale for AHP preferences Numerical rating
Verbal judgments of preferences
9 7 5 3 1
Extremely preferred Very strongly preferred Strongly preferred Moderately preferred Equally preferred 2, 4, 6, 8 are in the middle scale.
L. Chen, J. Cai / Reliability Engineering and System Safety 81 (2003) 147–154 Table 4 Average random consistency (RI) Size of matrix 1 2 3 4 5 6 7 8 9 10 Random 0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45 1.49 consistency
index (refer to Table 4) for matrices of size n and lmax is the principal eigenvalue of the matrix. The CR value is acceptable, if it does not exceed 0.10. If it is more, the judgement matrix is inconsistent. To obtain a consistent matrix, judgements should be retrieved and improved. For example, if we consider the following five factors: simplicity, assembly/disassembly, standardization, tools, and skills of maintenance personal, the factor set V ¼ {V1 ; V2 ; V3 ; V4 ; V5 }: A pair-wise comparison matrix (size 5 £ 5) is constructed as described in step1 and 2 as follows: V1
V1 V2 V3 V4 V5
1 0:5 0:33 0:33 0:25
V2
V3
V4
2
3
3
1
3
3
0:33
1
2
0:33
0:5
1
0:25
0:33
0:5
which means the factor has a fixed optimized value; scope type which means the factor has a range of optimized value. For example, if we use system component number to describe the attribute of simplicity, then it is a profit type factor. One thing must be considered, that is different value has different unit. In order to ensure the fairness of the evaluation, all the value must be processed on a unitary scale. To different type of the factor, different processing ways are developed. Only the factors of profit type and cost type are covered in this paper, so just two processing method are discussed. To profit type factor: bij ¼
aij 2 amin j i ¼ 1; 2; …; m min amax 2 a j j
ð4Þ
To cost type factor
V5 4 3 3 2 1
bij ¼
amax 2 aij j i ¼ 1; 2; …; m max aj 2 amin j
ð5Þ
where amax ; amin is the maximum and minimum value, j j respectively, of the factor Vj : After the value translation, we get a new attribute matrix B ¼ ðbij Þm£k : Apparently, the bigger the bij ; the better, and to an ideal alternative Pp ; its attribute value is
The eigenvector of this matrix is (0.33, 0.28, 0.16, 0.13, 0.10)T, which is also the weight vector W: While the consistency is checked by calculating CR with the expression given in step 3. Here CR ¼ 0.067.
bpj ¼ max{bij li ¼ 1; 2; …; m} ¼ 1 j ¼ 1; 2; …; k
The relationship between maintainability and the 13 variables (see Table 1) discussed earlier is represented mathematically as:
ð7Þ
Then we can get a weighted unified attribute matrix, which is written as V1 P1
ð1Þ
where M is system maintainability and V1 ; V2 ; …; V13 are variables of the system. Here a so called VPM is developed to analysis this problem which is a multi-objective assessment. In this multi-objective assessment, the factor set is defined as:
ð6Þ
The weights of these factors could be obtained by using AHP method: W ¼ {W1 ; W2 ; …; Wk } k ¼ 1; 2; …; 13
4.4. Vector Projection Method
M ¼ f ðV1 ; V2 ; …; V13 Þ
151
P2 C¼
.. . Pm
2
w1 b11
6 6w b 6 1 21 6 6 6 ··· 6 6 6 w1 bm1 4 w1
Pp
V2
···
Vk
w2 b12
···
wk b1k
w2 b22
···
···
···
w2 bm2
···
w2
···
3
7 wk b2k 7 7 7 7 ··· 7 7 7 wk bmk 7 5
ð8Þ
wk
where V1 ; V2 ; …; Vk are some or all of the 13 variables of the system. The alternative set is:
In this matrix, each row vector can be treated as an alternative, and the last row vector is an ideal alternative. Then there is an angle ai between each alternative and the ideal alternative, the cosine of this angle is
P ¼ {P1 ; P2 ; …; Pm };
ri ¼ cos ai ¼
V ¼ {V1 ; V2 ; …; Vk }; k ¼ 1; 2; …; 13
ð2Þ
ð3Þ
aij (i ¼ 1; 2; …; m; j ¼ 1; 2; …; k) is the factor value of alternative Pi to factor Vj : Matrix A ¼ ðaij Þm£k is developed as the attribute matrix of alternative set P to factor set V: In general, there are four types of factors: profit type which means the bigger the factor value the better; cost type which means the less the factor value the better; fix type
Pi £ P p kPi k £ kPp k
Xn
w b £ wj j¼1 j ij ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiqffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ qX ; Xn n ½wj bij 2 ½wij 2 j¼1 j¼1 i ¼ 1; 2; …; m; j ¼ 1; 2; …; k
ð9Þ
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Fig. 1. Representations of ri ; di ; Ti :
the module of each alternative is vffiffiffiffiffiffiffiffiffiffiffiffiffi uX un i ¼ 1; 2; …; m; j ¼ 1; 2; …; k di ¼ t ½wj bij 2
ð10Þ
Use AHP method to calculate the weight of these k factors expressed as W ¼ {W1 ; W2 ; …; Wk }; k ¼ 1; 2; …; 13; Step 5 Derive the weighted unified attribute matrix C as described in Eq. (8) Section 4.4; Step 6 Calculate ri ; di ; Ti for each alternative Pi ; i ¼ 1; 2; …; m: Refer to Eqs. (9) –(11) Section 4.4; Step 7 Compare the maintainability of each alternative based on the Step 6, and identify the best alternative form the maintenance point of view.
j¼1
the projection of each row vector on the ideal alternative vector is
6. Case study
Ti ¼ di £ ri i ¼ 1; 2; …; m
An example of mechanisms of valve-driving system is considered for illustrating the earlier procedure. The two design alternatives of the valve-driving system are: rocker mechanisms and jib mechanisms under hydraulic pressure shown in Fig. 2. First of all it is necessary to study the system details as step 1, Section 5. After identifying the critical component from maintenance point of view, the identification of maintainability factors is carried out, which are: design simplicity, assembly/disassembly, standardization, tools and skills of maintenance personnel. In this case, some factors like design simplicity and assembly/disassembly attribute are described in system components and assembly/disassembly time obtained from the experiment. Value of other factors like standardization, tool and skills of maintenance personnel, cannot be obtained directly from experiment. These factors are therefore assigned a value with reference to MIL-HDBK-472 [19]. Here only the scoring criteria for maintenance tools is given in Table 5 for a better understanding. The value of all these five factors are shown in Table 6 [20]. Then we get the attribute matrix written as
ð11Þ
where Ti represents the consistency of each alternative and the ideal alternative, as shown in Fig. 1. Apparently the bigger the value of Ti ; the better the maintainability of the system. While the ideal alternative has a value of T p equal to 1.
5. Steps for maintainability evaluation With the above methods, the evaluation procedure can be described as follows: Step 1 Consider the given system and its various design alternatives P ¼ {P1 ; P2 ; …; Pm }: Study functions, structure details, and design features from maintenance point of view. Identify the maintainability evaluation factors V ¼ {V1 ; V2 ; …; Vk } ðk # 13Þ in the given situation. This step could be much easier by choosing from thirteen evaluation factors introduced in Section 4.2; Step 2 For each alternative Pi ; i ¼ 1; 2; …; m; assign a value aij for each factor Vj ; j ¼ 1; 2; …; k; k # 13; according to the system attribute. For those factors that can not be quantitatively represented, The values can be assigned on appropriate scale e.g. 0 –4 based on the system design features for the attribute and using MIL-HDBK-472 [19], which includes design check lists and scoring criteria for physical design factors, design dictates-facilities and design dictates-maintenance skills. The attribute takes value 4, if the system features favor maintainability to the maximum extent. Then the attribute matrix A ¼ ðaij Þm£k is developed; Step 3 Identify the type of each factor Vj ; j ¼ 1; 2; …; k; k # 13; out of altogether four different types, namely profit type, cost type, fix type and scope type. Then using Eqs. (4) and (5) to translate attribute matrix A ¼ ðaij Þm£k to matrix B ¼ ðbij Þm£k ; Step 4
" A¼
30
12
2 3
2
21
8
2 2
4
#
Fig. 2. Two kinds of mechanisms of valve-driving system.
ð12Þ
L. Chen, J. Cai / Reliability Engineering and System Safety 81 (2003) 147–154 Table 5 Scoring criteria for maintenance tools
153
Table 7 Calculation result
Description of scoring criteria
Scoring
Parameter
Mechanism (a)
Mechanism (b)
No supplementary materials are needed to perform task No more than two pieces of supplementary materials is need to perform task Three or more pieces of supplementary materials are needed
4
d r T
0.299 0.969 0.290
0.399 0.980 0.391
2
0
where the first row represents mechanism (a), the second row represents mechanism (b). This completes step 2. After data translation to a unified scale by using Eqs. (4) and (5), matrix A becomes as " # 0:45 0:77 0:5 0:75 0:5 B¼ ð13Þ 0:86 0:85 0:5 0:5 1 max min Here, we set ðamax ; amin ; aj Þlj¼2 ¼ j j Þlj¼1 ¼ ð40; 18Þ; ðaj ð52; 0Þ from the empirical data of design engineers and some skilled maintenance technicians; and ðamax ; amin j j Þlj¼3 ¼ max min max min ð4; 0Þ; ðaj ; aj Þlj¼4 ¼ ð4; 0Þ; ðaj ; aj Þlj¼5 ¼ ð4; 0Þ according to the 0 –4 scale adopted by MIL-HDBK-472 [19]. This completes step 3. Using AHP method, we can get the weight of these five factors (see calculation steps in Section 4.3), W ¼ {0:33; 0:28; 0:16; 0:13; 0:10}; which completes step 4. Then the weighted unified attribute matrix C is obtained as per the step 5 as: 2 3 0:15 0:22 0:08 0:10 0:05 6 7 7 C¼6 ð14Þ 4 0:28 0:24 0:08 0:07 0:1 5
0:33 0:28 0:16
0:13
0:10
r1 ; d1 ; T1 and r2 ; d2 ; T2 are obtained from expressions (9) – (11) as per step 6, and the result of the calculation is shown in Table 7. Where in Table 7, d; r; T mean the module of each alternative, the cosine of the angle between each alternative and the ideal alternative, and the projection of each alternative, respectively. From the result we see that mechanism (b) is better. This result is perfectly identical Table 6 The value of the maintainability factors of the two systems Maintainability factors
Mechanism (a)
Mechanism (b)
Simplicity (in terms of system components) Assembly/disassembly (in terms of assembly/disassembly time (min)) Standardization Tools Skills
30
21
12
8
2 3 2
2 2 4
with the experiment we made. Alternative (a) is composed by rocker shaft, rocker shaft spring, rocker and valve. It takes a long time to disassemble and to conduct maintenance. Instead of rocker mechanism, alternative (b) uses the jib mechanism, then its maintenance is rather easy compared with alternative (a). This procedure provides a convenient method to determine the best design alternative from maintenance point of view.
7. Conclusion DFMAIN is introduced as a way to improve maintainability through design. Maintenance, maintainability of mechanical system is defined. A number of maintainability guidelines have been presented. These guidelines are used to develop a set of maintainability factors. An evaluation method called VPM is presented in this paper as a specific application of design review to assess and comprise the system maintainability. The proposed procedure is useful for designers and practicing engineers to compare various alternatives of a system from a maintainability point of view.
Acknowledgements Sponsored by National Science Foundation of China (Granted No. 59935120).
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[8] Gong L. Study on the evaluation of automobile maintainability. Liaoning Transportation Technol 1999;8:46–8. [9] Saaty TL. The fundamentals of decision making and priority theory with the analytic hierarchy process. Pittsburgh, PA: RWS Publications; 1994. [10] Al-subhi KM, Al-Harbi. Application of the AHP in project management. Int J Project Manage 2001;(19):19–27. [11] Byun DH, Suh EH. A methodology for evaluating EIS software packages. J End User Comput 1996;8(2):21 –31. [12] Lai VS, Trueblood RP, Wong BK. Software selection: a case study of the application of the analytic hierarchical process to the selection of a multimedia authoring system. Information Manage 1999;36:221– 32. [13] Yang T, Kuo C. A hierarchical AHP/DEA methodology for the facilities layout design problem. Eur J Oper Res 2003;147:128–36.
[14] Kaufmann A, Gupta MM. Introduction to fuzzy arithmetic: theory and applications. New York: Van Nostrand Reinhold; 1985. [15] Zadeh LA. Fuzzy sets. Inform Control 1965;8:338– 53. [16] Chen CT. A fuzzy approach to select the location of the distribution center. Fuzzy Sets Syst 2001;118:65–73. [17] Karsak EE, Tolga E. Fuzzy multi-criteria decision-making procedure for evaluating advanced manufacturing system investments. Int J Prod Econ 2001;69:49–64. [18] Ammar S, Wright R. Applying fuzzy-set theory to performance evaluation. Socio-Econ Plann Sci 2000;34:285 –302. [19] Military Standardization Handbook MIL-HDBK-472. Maintainability Prediction, US Department of Defense. 1966. [20] Fu H. Design for disassembly and recycling. PhD Dissertation, Shanghai Jiaotong University, Shanghai, China. 2000.
Using Vector Projection Method to evaluate maintainability of mechanical system in design review Lu Chen*, Jianguo Cai Department of Industrial Engineering and Management, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200030, People’s Republic of China Received 18 November 2002; accepted 15 March 2003
Abstract Maintainability of a mechanical system is one of the system design parameters that has a great impact in terms of ease of maintenance. In this article, based on the definition of the terms of maintenance and maintainability, an important tool of Design for Maintenance is developed as a way to improve maintainability through design. A set of standard and organized guidelines is provided and maintainability factors in terms of physical design, logistics support and ergonomics are identified. As a specific application of design review, a methodology so called Vector Projection Method is developed to evaluate the maintainability of the mechanical system. Lastly, an example is discussed. q 2003 Elsevier Science Ltd. All rights reserved. Keywords: Maintainability; Design for Maintenance; Guidelines; Factors; Vector Projection Method
1. Introduction Maintainability is recognized as being highly significant factor in the economic success of engineering systems and products. Also, design is the stage at which the eventual characteristics of future systems and products are determined. Therefore, it is important that designers should take maintainability into account during their work. However, there is much to consider at the design stage; a designer should be provided with simple and logical measure qualitatively or quantitatively to evaluate and predict the maintainability. Prediction facilitates an early assessment of the maintainability of the design and enables decisions concerning the compatibility of a proposed design with specified maintenance requirements or the choice of better alternatives. There are a number of excellent specialist papers and text books in maintainability. The problem for designers is that they are mainly written from the perspective of the dedicated maintainability engineer. These papers and books contain in-depth analytical methods that require information that is not available at the design stage. Therefore, they are of limited use to designers. * Corresponding author. Tel.: þ 86-21-629-321-15. E-mail address: [email protected] (L. Chen).
This paper is written entirely from a design perspective. In this article, an important tool, Design for Maintenance (DFMAIN) is firstly introduced in Section 2. Also in Section 2, a set of standard and organized guidelines is provided. Section 3 introduces some general concepts of design review. Then, as a method of design review, maintainability evaluation methods are discussed in detail in Section 4. A specific methodology so called Vector Projection Method (VPM) is developed to evaluate the maintainability of the system. Section 5 presents a stepwise evaluation procedure. In Section 6, a case demonstration is carried out, while Section 7 concludes the paper.
2. Design for Maintenance DFMAIN is concerned with achieving good designs that consider the general care and maintenance of equipment and the repair actions that follow a failure. 2.1. Maintenance and maintainability Traditionally, people think that maintenance is only a kind of guaranteed technical job made by a few of technicians, and has nothing with the design and production of the product. In fact, nowadays, mechanical or electronic
0951-8320/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0951-8320(03)00075-9
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products are becoming more and more complicated. As a result, the content and meaning of maintenance are richer than ever. The Chinese Standardization Department publication of ‘Definition of Terms for Reliability and Maintainability’, GJB451-90 defines maintenance as “all the activities that are intended to retain or restore the product to a specified condition”. With respect to maintainability, the designer has to take a different view from that of the maintenance manager. Some definitions lead to mathematical analyses using repair rates in a similar manner to reliability analyses. Although useful to the maintenance manager in the analysis of data accumulated in service, this approach is not very useful in design. The designer should consider those factors which are under his/her control. The US military publication MIL-STD-721 [1] defines maintainability as follows: Maintainability: The measure of the ability of an item to be retained or restored to specific conditions when maintenance is performed by personnel having specified skill levels, using prescribed procedures and resources at each prescribed level of maintenance and repair. The maintainability definition has fostered the development of many maintainability prediction procedures for providing an assessment of system maintainability. Rather than predicting how the system will fail, the effort of maintainability is to make manufacturing systems and products that require minimal maintenance and that are easy and inexpensive to fix when they fail. Consequently, manufacturers strive to design maintainability into the products and their manufacturing processes.
2.3. DFMAIN guidelines A general rule for DFMAIN is to reduce the possibility of damage to the product or equipment during maintenance and servicing or better yet to eliminate the need for maintenance. To assist in establishing a solid foundation for implementing DFMAIN in the early stage of design, a set of standard and organized guidelines is provided. Use of these guidelines can help improve maintainability and enhance product quality [2]. B
B
B
B
B
B
2.2. Design for Maintenance DFMAIN is an important part of product/system design. Design changes during production are very costly, but if DFMAIN is implemented early in the design stage, a great number of benefits would be realized including: † † † †
Longer life of systems and products. Lower operation costs, by performing at high efficiency. Lower unscheduled downtime, by preventing failures. Lower scheduled downtime, by decreasing the time required to perform a particular maintenance task.
B
B
B
Keep the functional and physical characteristics as simple as possible. Complexity of design has a direct bearing on production and maintenance cost. To reduce the number of components and assemblies including redundant components is helpful in lowering the skill of technicians and the requirement of the equipment and maintenance tools. There is adequate access for visual and manipulative tasks, including the assembly of parts and any required tooling during assembly, inspection, repair, or replacement. Use standardized parts to simplify the maintenance work, especially for those parts that are mostly like to fail. Because standard parts are easy to find and be replaced. Select modular design so that subassemblies could be tested and maintained at that level and not at the final assembly. Design for ease of assembly and disassembly with a minimum number of parts. A product that is easily assembled and disassembled is also easily maintainable. Provide easy diagnosability. Diagnosability could be assured by provide functional sharing, monitoring parameters for failure including alarms, build-in test equipment facility and indication signal for failure including fault isolation. Test points are available for needed test pertaining to maintenance action. Provide identification to eliminate accident in maintenance. Critical components should be identified; test points and arrows should be well marked. Minimize weight and awkwardness in handling of parts that must be removed. Provide safety guards to prevent contact with moving parts, high temperature, high voltage lines or gaseous leakage. Provide appropriate manuals for maintenance instructions and procedures.
3. Design review Maintainability is one of the system design parameters that has a great impact in terms of ease of maintenance. System failure is inevitable no matter how reliably this is built-in, so its ability to be quickly restored is therefore the most important. To fully realize part or all of these benefits, some maintainability guidelines are presented next.
The design review may be defined as: [3] The quantitative and qualitative examination of a proposed design to ensure that it is safe and has optimum performance with respect to maintainability, reliability
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Table 1 Design review procedure Activity
Purpose
Timing
Review of the design specification
To ensure that the significance of all the points contained within the design specification is understood (1) To identify critical areas of the design that may affect plant availability and to comment on the advisability of pursuing projects with a high risk content (2) To examine equipment groups to maximize uniformity and suitability and to maximize the reliability systems formed by manufacturing and process consideration To evaluate quantitatively critical items of functional unit and to undertake qualitative reviews of functional unit generally To check that certain important sets of components will not give rise to, say, maintainability problems in service
Prior to the commencement of any design activity
System level design
Functional unit evaluation
Component analysis
and those performance variables needed to specify the equipment. The review is much more than the scrutiny of design work in the manner that an examiner checks a student exercise. It should help the designer and enrich design activity. It is an integral part of design activity and not a ‘bolt-on’ extra. The specific benefits associated with a good design review methodology include:
Prior to the start of functional unit design
After the completion of the first functional unit design
After the completion of the first detail design After the completion of the first detail design
Usually, there are different kinds of review work at different levels of design, such as design specification review, system review, functional unit evaluation, component analysis. A comprehensive design review is summarized in Table 1. Evaluation is a normal part of design activity, which is to evaluate the status of emerging designs against customer-driven criteria prior to proceeding forward to the next phase of a project.
† Added assurance that the voice of the customer has been heard correctly † Reductions in design cost and time-to-market † Reduced likelihood of program delay due to unexpected problems † Improved overall design integrity † Prevention of problems and associated downstream costs † Increased standardization † Improved customer satisfaction † Increased program structure and control.
4. Maintainability evaluation
Given these benefits, it is no surprise that the design review methodology is widely used and endorsed in commercial industry. In fact, 89% of the companies surveyed in a recent benchmarking study of 72 leading companies in seven basic industries reported using design review as a design assurance tool [4]. So, as we can see, the design review is one of the most important ways of achieving good maintainability. It should contribute to those problem areas such as maintainability and reliability which may not have been fully taken into account during the search for cost-effective feasible solutions.
Various attempts have been made by researchers in developing procedures for evaluation of the maintainability. Takata and Saito [5] have proposed a structure of the facility model for a computer-assisted life cycle maintenance system. It provides a flexible representation scheme for technical information as well as for the physical structure of the facility, and could be used to do deterioration evaluation of the facility. Vujosevic and Raskar [6] have developed procedures for identification of disassembly sequence, animation of human technicians while carrying out the disassembly sequence. Based on these, the maintainability of the systems is evaluated. Wani and Gandhi [7] developed
As a specific application of functional unit evaluation in design review activity, maintainability evaluation is discussed in this section. In this way alternatives can be systematically reviewed from the perspective of maintainability view to make them robust and suitable for further design work. 4.1. Literature review
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a procedure based on a digraph and matrix method to evaluate the maintainability index of mechanical systems. The department of highway in Chaoyang, Liaoning province, China [8] has evaluated the automobile maintainability base on the respective calculation of maintenance time and maintenance fee. In all these methods, the maintainability characteristics of the system affecting the maintainability have not been fully identified. Here, a methodology so called VPM is proposed to evaluate the maintainability of the system which is a multi-objective assessment. The concepts of fuzzy set theory and multiple-criteria decision analysis are widely used to solve this kind of problem in which a source of vagueness is involved. A fuzzy decisionmaking method integrates various linguistic or, in other word, qualitative assessment and weights to evaluate different alternatives. Details on this technique could be found in Refs. [14,15]. Chen [16] used this method to solve the distribution center location selection problem under fuzzy environment. Karasak and Tolga [17] proposed a fuzzy decision algorithm to select the most suitable advanced manufacturing system alternative from a set of mutually exclusive alternatives. Ammar and Wright [18] even applied this method in social science, such as performance measurement, namely to evaluate the state government performance and to survey client satisfaction. Even though fuzzy set theory is proved to be very effective in multi-objective evaluation, it has certain limitations. For example, when comparing two alternatives, only comparative goodness can be obtained. Therefore, in this paper, a methodology so called VPM is developed based on fuzzy set theory. With this method, a more absolute evaluation result could be obtained. And at the same time, the algorithm complexity is not increased. 4.2. Evaluation factors In maintainability evaluation, assessment criteria are defined in terms that are suitable for concept evaluation. For example, a repair time would be inappropriate because the repair time could not be calculated form the information available at the concept stage. Similarly, mean time to failure or mean failure rate calculations cannot be made. Instead, criteria should be used that refer to such factors as: simplicity and elegance of the design; minimum number of parts; suitability for modular construction, etc. Maintainability evaluation factors Vj in terms of design factors, logistics support, ergonomic factors are defined in a hierarchical structure as in Table 2. Under different circumstances, some or all of these factors are chosen to be the evaluation criterion. It depends on which of them are more important for a certain evaluation task.
Table 2 Maintainability evaluation factors Vj Physical design
Logistics support
Ergonomics
Simplicity
Test equipment
Accessibility
Assembly/disassembly tool or maintenance tool
Fault and operation indicators Skills of maintenance personnel Maintenance environment
Assembly/ disassembly Standardization Modularization Test points layout
Documentation
Other ergonomics factors
4.3. Weight calculation As we all know that not all the factors are equally important, in other words, weights must be assigned to these factors when evaluation work is done. Here we use Analytical Hierarchy Process (AHP) method to calculate the weight. AHP is a decision-aiding method developed by Saaty [9]. It is one of the extensively used multicriteria decision making methods. It aims at quantifying relative priorities for a given set of alternatives on a ratio scale. Numerous applications of the AHP have been made since its development and it has been applied to many types of problems [10 –13]. In this case, the factors are in one level, so the calculation is compared simple, the following steps are developed for applying the AHP: 1. A pair-wise comparison matrix (size n £ n) is constructed for each factor by using the relative scale measurement shown in Table 3. The pair-wise comparisons are done in terms of which factor dominates the other. 2. There are n ðn 2 1Þ judgements required to develop the matrix in step 1, reciprocals are automatically assigned in each pair-wise comparison. 3. Calculate the eigenvectors, the eigenvalue, consistency index. Judgement consistency can be checked by the consistency ratio (CR), given by CR ¼
CI RIðnÞ
where CI is the consistency index given by CI ¼ ðlmax 2 nÞðn 2 1Þ; RIðnÞ is the random consistency Table 3 Pair-wise comparison scale for AHP preferences Numerical rating
Verbal judgments of preferences
9 7 5 3 1
Extremely preferred Very strongly preferred Strongly preferred Moderately preferred Equally preferred 2, 4, 6, 8 are in the middle scale.
L. Chen, J. Cai / Reliability Engineering and System Safety 81 (2003) 147–154 Table 4 Average random consistency (RI) Size of matrix 1 2 3 4 5 6 7 8 9 10 Random 0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45 1.49 consistency
index (refer to Table 4) for matrices of size n and lmax is the principal eigenvalue of the matrix. The CR value is acceptable, if it does not exceed 0.10. If it is more, the judgement matrix is inconsistent. To obtain a consistent matrix, judgements should be retrieved and improved. For example, if we consider the following five factors: simplicity, assembly/disassembly, standardization, tools, and skills of maintenance personal, the factor set V ¼ {V1 ; V2 ; V3 ; V4 ; V5 }: A pair-wise comparison matrix (size 5 £ 5) is constructed as described in step1 and 2 as follows: V1
V1 V2 V3 V4 V5
1 0:5 0:33 0:33 0:25
V2
V3
V4
2
3
3
1
3
3
0:33
1
2
0:33
0:5
1
0:25
0:33
0:5
which means the factor has a fixed optimized value; scope type which means the factor has a range of optimized value. For example, if we use system component number to describe the attribute of simplicity, then it is a profit type factor. One thing must be considered, that is different value has different unit. In order to ensure the fairness of the evaluation, all the value must be processed on a unitary scale. To different type of the factor, different processing ways are developed. Only the factors of profit type and cost type are covered in this paper, so just two processing method are discussed. To profit type factor: bij ¼
aij 2 amin j i ¼ 1; 2; …; m min amax 2 a j j
ð4Þ
To cost type factor
V5 4 3 3 2 1
bij ¼
amax 2 aij j i ¼ 1; 2; …; m max aj 2 amin j
ð5Þ
where amax ; amin is the maximum and minimum value, j j respectively, of the factor Vj : After the value translation, we get a new attribute matrix B ¼ ðbij Þm£k : Apparently, the bigger the bij ; the better, and to an ideal alternative Pp ; its attribute value is
The eigenvector of this matrix is (0.33, 0.28, 0.16, 0.13, 0.10)T, which is also the weight vector W: While the consistency is checked by calculating CR with the expression given in step 3. Here CR ¼ 0.067.
bpj ¼ max{bij li ¼ 1; 2; …; m} ¼ 1 j ¼ 1; 2; …; k
The relationship between maintainability and the 13 variables (see Table 1) discussed earlier is represented mathematically as:
ð7Þ
Then we can get a weighted unified attribute matrix, which is written as V1 P1
ð1Þ
where M is system maintainability and V1 ; V2 ; …; V13 are variables of the system. Here a so called VPM is developed to analysis this problem which is a multi-objective assessment. In this multi-objective assessment, the factor set is defined as:
ð6Þ
The weights of these factors could be obtained by using AHP method: W ¼ {W1 ; W2 ; …; Wk } k ¼ 1; 2; …; 13
4.4. Vector Projection Method
M ¼ f ðV1 ; V2 ; …; V13 Þ
151
P2 C¼
.. . Pm
2
w1 b11
6 6w b 6 1 21 6 6 6 ··· 6 6 6 w1 bm1 4 w1
Pp
V2
···
Vk
w2 b12
···
wk b1k
w2 b22
···
···
···
w2 bm2
···
w2
···
3
7 wk b2k 7 7 7 7 ··· 7 7 7 wk bmk 7 5
ð8Þ
wk
where V1 ; V2 ; …; Vk are some or all of the 13 variables of the system. The alternative set is:
In this matrix, each row vector can be treated as an alternative, and the last row vector is an ideal alternative. Then there is an angle ai between each alternative and the ideal alternative, the cosine of this angle is
P ¼ {P1 ; P2 ; …; Pm };
ri ¼ cos ai ¼
V ¼ {V1 ; V2 ; …; Vk }; k ¼ 1; 2; …; 13
ð2Þ
ð3Þ
aij (i ¼ 1; 2; …; m; j ¼ 1; 2; …; k) is the factor value of alternative Pi to factor Vj : Matrix A ¼ ðaij Þm£k is developed as the attribute matrix of alternative set P to factor set V: In general, there are four types of factors: profit type which means the bigger the factor value the better; cost type which means the less the factor value the better; fix type
Pi £ P p kPi k £ kPp k
Xn
w b £ wj j¼1 j ij ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiqffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ qX ; Xn n ½wj bij 2 ½wij 2 j¼1 j¼1 i ¼ 1; 2; …; m; j ¼ 1; 2; …; k
ð9Þ
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Fig. 1. Representations of ri ; di ; Ti :
the module of each alternative is vffiffiffiffiffiffiffiffiffiffiffiffiffi uX un i ¼ 1; 2; …; m; j ¼ 1; 2; …; k di ¼ t ½wj bij 2
ð10Þ
Use AHP method to calculate the weight of these k factors expressed as W ¼ {W1 ; W2 ; …; Wk }; k ¼ 1; 2; …; 13; Step 5 Derive the weighted unified attribute matrix C as described in Eq. (8) Section 4.4; Step 6 Calculate ri ; di ; Ti for each alternative Pi ; i ¼ 1; 2; …; m: Refer to Eqs. (9) –(11) Section 4.4; Step 7 Compare the maintainability of each alternative based on the Step 6, and identify the best alternative form the maintenance point of view.
j¼1
the projection of each row vector on the ideal alternative vector is
6. Case study
Ti ¼ di £ ri i ¼ 1; 2; …; m
An example of mechanisms of valve-driving system is considered for illustrating the earlier procedure. The two design alternatives of the valve-driving system are: rocker mechanisms and jib mechanisms under hydraulic pressure shown in Fig. 2. First of all it is necessary to study the system details as step 1, Section 5. After identifying the critical component from maintenance point of view, the identification of maintainability factors is carried out, which are: design simplicity, assembly/disassembly, standardization, tools and skills of maintenance personnel. In this case, some factors like design simplicity and assembly/disassembly attribute are described in system components and assembly/disassembly time obtained from the experiment. Value of other factors like standardization, tool and skills of maintenance personnel, cannot be obtained directly from experiment. These factors are therefore assigned a value with reference to MIL-HDBK-472 [19]. Here only the scoring criteria for maintenance tools is given in Table 5 for a better understanding. The value of all these five factors are shown in Table 6 [20]. Then we get the attribute matrix written as
ð11Þ
where Ti represents the consistency of each alternative and the ideal alternative, as shown in Fig. 1. Apparently the bigger the value of Ti ; the better the maintainability of the system. While the ideal alternative has a value of T p equal to 1.
5. Steps for maintainability evaluation With the above methods, the evaluation procedure can be described as follows: Step 1 Consider the given system and its various design alternatives P ¼ {P1 ; P2 ; …; Pm }: Study functions, structure details, and design features from maintenance point of view. Identify the maintainability evaluation factors V ¼ {V1 ; V2 ; …; Vk } ðk # 13Þ in the given situation. This step could be much easier by choosing from thirteen evaluation factors introduced in Section 4.2; Step 2 For each alternative Pi ; i ¼ 1; 2; …; m; assign a value aij for each factor Vj ; j ¼ 1; 2; …; k; k # 13; according to the system attribute. For those factors that can not be quantitatively represented, The values can be assigned on appropriate scale e.g. 0 –4 based on the system design features for the attribute and using MIL-HDBK-472 [19], which includes design check lists and scoring criteria for physical design factors, design dictates-facilities and design dictates-maintenance skills. The attribute takes value 4, if the system features favor maintainability to the maximum extent. Then the attribute matrix A ¼ ðaij Þm£k is developed; Step 3 Identify the type of each factor Vj ; j ¼ 1; 2; …; k; k # 13; out of altogether four different types, namely profit type, cost type, fix type and scope type. Then using Eqs. (4) and (5) to translate attribute matrix A ¼ ðaij Þm£k to matrix B ¼ ðbij Þm£k ; Step 4
" A¼
30
12
2 3
2
21
8
2 2
4
#
Fig. 2. Two kinds of mechanisms of valve-driving system.
ð12Þ
L. Chen, J. Cai / Reliability Engineering and System Safety 81 (2003) 147–154 Table 5 Scoring criteria for maintenance tools
153
Table 7 Calculation result
Description of scoring criteria
Scoring
Parameter
Mechanism (a)
Mechanism (b)
No supplementary materials are needed to perform task No more than two pieces of supplementary materials is need to perform task Three or more pieces of supplementary materials are needed
4
d r T
0.299 0.969 0.290
0.399 0.980 0.391
2
0
where the first row represents mechanism (a), the second row represents mechanism (b). This completes step 2. After data translation to a unified scale by using Eqs. (4) and (5), matrix A becomes as " # 0:45 0:77 0:5 0:75 0:5 B¼ ð13Þ 0:86 0:85 0:5 0:5 1 max min Here, we set ðamax ; amin ; aj Þlj¼2 ¼ j j Þlj¼1 ¼ ð40; 18Þ; ðaj ð52; 0Þ from the empirical data of design engineers and some skilled maintenance technicians; and ðamax ; amin j j Þlj¼3 ¼ max min max min ð4; 0Þ; ðaj ; aj Þlj¼4 ¼ ð4; 0Þ; ðaj ; aj Þlj¼5 ¼ ð4; 0Þ according to the 0 –4 scale adopted by MIL-HDBK-472 [19]. This completes step 3. Using AHP method, we can get the weight of these five factors (see calculation steps in Section 4.3), W ¼ {0:33; 0:28; 0:16; 0:13; 0:10}; which completes step 4. Then the weighted unified attribute matrix C is obtained as per the step 5 as: 2 3 0:15 0:22 0:08 0:10 0:05 6 7 7 C¼6 ð14Þ 4 0:28 0:24 0:08 0:07 0:1 5
0:33 0:28 0:16
0:13
0:10
r1 ; d1 ; T1 and r2 ; d2 ; T2 are obtained from expressions (9) – (11) as per step 6, and the result of the calculation is shown in Table 7. Where in Table 7, d; r; T mean the module of each alternative, the cosine of the angle between each alternative and the ideal alternative, and the projection of each alternative, respectively. From the result we see that mechanism (b) is better. This result is perfectly identical Table 6 The value of the maintainability factors of the two systems Maintainability factors
Mechanism (a)
Mechanism (b)
Simplicity (in terms of system components) Assembly/disassembly (in terms of assembly/disassembly time (min)) Standardization Tools Skills
30
21
12
8
2 3 2
2 2 4
with the experiment we made. Alternative (a) is composed by rocker shaft, rocker shaft spring, rocker and valve. It takes a long time to disassemble and to conduct maintenance. Instead of rocker mechanism, alternative (b) uses the jib mechanism, then its maintenance is rather easy compared with alternative (a). This procedure provides a convenient method to determine the best design alternative from maintenance point of view.
7. Conclusion DFMAIN is introduced as a way to improve maintainability through design. Maintenance, maintainability of mechanical system is defined. A number of maintainability guidelines have been presented. These guidelines are used to develop a set of maintainability factors. An evaluation method called VPM is presented in this paper as a specific application of design review to assess and comprise the system maintainability. The proposed procedure is useful for designers and practicing engineers to compare various alternatives of a system from a maintainability point of view.
Acknowledgements Sponsored by National Science Foundation of China (Granted No. 59935120).
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