CHINESE JOURNAL OF MECHANICAL ENGINEERING ·406· Vol. 29,aNo. 2,a2016

DOI: 10.3901/CJME.2015.1217.150, available online at www.springerlink.com; www.cjmenet.com

Product Modular Design Incorporating Preventive Maintenance Issues

GAO Yicong, FENG Yixiong*, and TAN Jianrong

State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China

Received March 19, 2015; revised May 15, 2015; accepted December 17, 2015

Abstract: Traditional modular design methods lead to product maintenance problems, because the module form of a system is created according to either the function requirements or the manufacturing considerations. For solving these problems, a new modular design method is proposed with the considerations of not only the traditional function related attributes, but also the maintenance related ones. First, modularity parameters and modularity scenarios for product modularity are defined. Then the reliability and economic assessment models of product modularity strategies are formulated with the introduction of the effective working age of modules. A mathematical model used to evaluate the difference among the modules of the product so that the optimal module of the product can be established. After that, a multi-objective optimization problem based on metrics for preventive maintenance interval different degrees and preventive maintenance economics is formulated for modular optimization. Multi-objective GA is utilized to rapidly approximate the Pareto set of optimal modularity strategy trade-offs between preventive maintenance cost and preventive maintenance interval difference degree. Finally, a coordinate CNC boring machine is adopted to depict the process of product modularity. In addition, two factorial design experiments based on the modularity parameters are constructed and analyzed. These experiments investigate the impacts of these parameters on the optimal modularity strategies and the structure of module. The research proposes a new modular design method, which may help to improve the maintainability of product in modular design.

Keywords: modular design, modularity strategy, preventive maintenance, optimization design

realize the product functions. PAHL, et al[1], proposed a 1 Introduction method that various overall functions were fulfilled by the combination of distinct building blocks or modules. They Increased demand for functions and reliability of referred to modular products as components, assemblies mechanical products, it is more complex in design and and machines. Modules were designed as building blocks, higher maintenance skills are required. Modular design is which can be grouped together to form a variety of of particular concern due to reduce the burden of products. STONE, et al[2], presented a modular method for mechanical product in maintenance. A module is a set of clustering the components based on functional heuristics. some disassembly and/or non-disassembly components or Modules were identified from the ‘functional structure’ parts. It is easy to repair and replace when it fails since the according to the flow patterns shown in the product assembly and disassembly processes of a module are ‘functional structure diagram’. KRENG, et al[3], presented a speeded up based on the reduction of the needed tools and four major phases approach to accomplish modular product skill in maintenance. design according to the maximum physical and functional Traditionally, criteria for generating modules are divided relations among components and maximizing the similarity into three types by the original motivations of clustering the of specifically modular driving forces. They employed a components into modules. non-linear programming to identify separable modules and (1) Function. Components are rearranged into new simultaneously optimize the number of modules. THOM, et modules by the functional interactions between components, al[4], developed a modularization scheme using of the because components form modules (physical structures) to function-behavior-state model of the system to derive the entity relations. A k-means clustering algorithm was used to

* Corresponding author. E-mail: [email protected] allow the user to try different number of clusters in a fast Supported by National Natural Science Foundation of China (Grant Nos. way, which can be adopted for design structure matrix 51205347, 51322506), Zhejiang Provincial Natural Science Foundation of China (Grant No. LR14E050003), Project of National Science and based modularization by defining a proper entity Technology Plan of China (Grant No. 2013IM030500), Fundamental representation, relation measure and objective function. LI, Research Funds for the Central Universities of China, Innovation et al[5], developed a fuzzy graph based modular product Foundation of the State Key Laboratory of Fluid Power Transmission and Control of China, and Zhejiang University K.P.Chao’s High Technology design methodology to implement Design for the Development Foundation of China Environment (DfE) strategies in product modular © Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2016

CHINESE JOURNAL OF MECHANICAL ENGINEERING ·407· formulation considering multiple product life cycle presented a leader-follower joint optimization method objectives guided by DfE. An optimal modular formulation based on technical system modularity and material reuse was searched using the graph-based clustering algorithm to modularity. They developed taxonomy of modularity identify the best module configuration. metrics in order to encompass the entire life cycle of (2) Structure. As designers decompose a product into material fulfillment. The quantification and aggregation of components and then group these components into separate modularity measures are formulated by multi-attribute modules, this requires the consideration of the structure utilities of different dimensions of component similarity. (the geometric position and connection forms) between Relative to these above researches, the field of modular components when generating new modules. SALHIEH, et design has generally focused less on maintenance al[6], developed a P-median model to maximize the consideration. While modular design decreases the similarity index between the components in a module. complexity of a system in maintenance. Moreover, the KRENG, et al[7], proposed a QFD-based modular product number of modules is much less than the number of design method to identify the optimal module through the components. It makes that the expenses in maintenance interaction between the modular drivers and components. could be effectively reduced[17–19]. AVEN, et al[20], They also considered functional and physical interaction presented a general framework including various age and between components. GUPTA, et al[8], proposed a method block replacement models for the optimization of to eliminate the drawbacks by providing a computerized replacement times. PIMMLER, et al[21], proposed a conceptual design framework that incorporates modularity, matrix-based modular method for improving product design for assembly, and design for variety principles. quality and reliability. The modular clustering was done TSENG, et al[9], developed a liaison graph model to the based on the priority of interactions between the evaluation of part connections that include the component components. KUSIAK[22] formulated a cost minimization liaison intensity were evaluated by engineering structural problem subject quality and testability levels constraints to attributes (contact type, combination type, tool type, and identify the modules. He also analyzed the component accessed direction). interactions to identify the modules but it is not clear how (3) Material compatibility. Material compatibility he measures the testability and quality of the modules. contributes to manufacture, reuse and recycle of product in TSAI, et al[23], used the fuzzy cluster identification method terms of high material compatibility of components in the by considering correlation in design of components. Four same module. KIMURA, et al[10], proposed a modular years later, they presented a method of modularity based on design method based on product functionality, the consideration of system maintenance policy for commonality and life cycle similarity. The new product constructing the system modules[24]. Total maintenance modularization strategy was used to efficiently manage a costs of modules in the ‘predetermined lifecycle’ of the closed loop product life cycle of a family of products and modules were introduced in order to extend their previous successive generation of products. QIAN, et al[11], research. YANG, et al[25], proposed a modular eco-design developed a quantitative model of environmental analysis method for life-cycle engineering based on re-design risk for modular design. The modularity analysis consisted of control. They defined functional and physical risk similarity and independence analysis under the restriction assessments as two constraints during the re-design of junction-structure mapping. HUANG, et al[12], presented optimization process. With these two constraints, the five basic rules for recycling in modular design, including redesign risk could be controlled to an acceptable value by life-cycle analysis, materials compatibility, recycling profit, designers. environmental impact of recycling, and structural and However, reliability objectives are treated as constraints physical interaction analysis. Then a fuzzy clustering secondary to economic objectives in modular design. The algorithm was adopted to form the component clusters modularity design method based on the consideration of based on a fuzzy correlation matrix. UMEDA, et al[13], maintenance for constructing the product modules, proposed a modular design methodology that determines especially the effect of reliability characteristics of the modular structure based on aggregating various components and maintenance parameters on the structure attributes related to a product life cycle and evaluating of optimal modularity strategy has not been studied yet. geometric feasibility of modules. The method aggregated This paper has described a five-step modular design attributes related to a product life cycle using a technique method with the considerations of maintenance related. called self-organizing maps. JOHANSSON, et al[14], According to the studies reported in past, maintenance was introduced the concept of “material hygiene” and classified into two categories, corrective maintenance and developed a method for grading structural properties in a preventive maintenance[26]. Preventive maintenance keeps a recycling perspective based on the concept. SMITH, et system in an available condition to avoid unpredictable al[15], put forward a green modularization method based on fails. Therefore our modular design method focuses on the atomic theory with green considerations. They created preventive maintenance issues. The reliability and green modules by merging or separating structural modules economic assessment models of product modularity with respect to environmental impacts. JI, et al[16], strategies are developed. The contributions of this research

·408· Y GAO Yicong, et al: Product Modular Design Incorporating Preventive Maintenance Issues as follows: (1) Preventive maintenance activities are Preventive maintenance activities: The approach considered in advance during modularity design. The presented here takes into account each activity involved in product will perform much more effective in service stage module preventive maintenance. These activities include and the production loss can be decreased by the shortening disassembly process, preventive maintenance actions of shut-down time. (2) Two factorial design experiments (maintenance action and replacement action) and assembly based on the parameters of cost associated with preventive process. If the component is implemented replacement maintenance activities and reliability characteristics are action, recycling action will be added. constructed and analyzed. These experiments investigate the effect of the modularity parameters on the structure of optimal modularity strategies in complex mechanical product. The organization of the paper is as follows. In Section 2, the method for calculating modularity trade-off solutions is illustrated. Section 3 presents a case study of optimizing modularity strategy for a CNC boring machine based on maintenance consideration. The sensitivity analysis of different modularity scenarios is shown in Section4. Finally, Section 5 concludes the research with summary and remarks.

2 Method for Calculating Modularity Trade-off Solutions

This section describes the following five-step modular design method to calculate the optimal modularity strategies for constructing the product modules based on preventive maintenance consideration. Step 1. Define modularity parameters for product modularity; Step 2. Define the product structure and the effective working age of modules; Step 3. Develop reliability and economic assessment models of product modularity strategies; Step 4. Formulate a multi-objective optimization problem based on metrics for preventive maintenance interval different degrees and preventive maintenance economics; Step 5. Calculate optimal modularity solutions based on Fig. 1. Methodology for calculating product modularity maintenance consideration; trade-off sets based on maintenance consideration The relationship between these five steps is shown in Fig. 1. Several definitions of the method are drawn out as Step 1: Define modularity parameters. follows. Modularity parameters that must be defined include Modules: A module is usually a combination of component reliability parameters such as the scale components. The components within a module often parameter, shape parameter of component (the hazard rate contain the similarly effective working age in use stage. function) and maintenance effect factor; preventive Modularity strategy: The set of all modularity maintenance parameters such as cost of failure, labor price, decisions, consisting of the number of modules, the and purchase prices. In the problem formation below, the components’ combination of each module, and preventive vector s defines the set of modularity parameters for maintenance activities of each module. The components product modularity. within a module often contain the similarly effective Step 2: Define the product structure and the effective working age. working age of modules. Modularity parameters: Modularity parameters include Defining the product structure and the effective working preventive maintenance parameters and component age of modules is the basis of the method. It can be derived reliability parameters. Preventive maintenance parameters from the following sub-steps: define the economic aspect associated with preventive Sub-step 1: Define the set of components along with maintenance activities. Component reliability parameters their reliability parameters. define component reliability characteristics aspect. It assumes that product is a series system of components

CHINESE JOURNAL OF MECHANICAL ENGINEERING ·409· in this paper. The set of components in the product is the effective working age of a module at the start of period + denoted as Cset={c1, c2,, cn}. Aiming to the failures of j and wt j denote the effective working age at the end of components, most of them belong to cumulative damage. period j. It is clear that [27–28] According to the studies by WANG, et al , each component is assumed to have an rate of occurrence of +- -T wtjjjjj=+-=+ wt() t t-1 wt . (2) failure, i ()t , where t denotes actual time, t>0. Weibull J distribution is one of the reliability-dependent failure rate models, which is suitable in describing the cumulative failure problems, such as fatigue, wear, corrosion and thermal creep, etc. In this paper, the hazard rate function of component is given as

 -1  æöt i  ()t = i ç ÷ , (1) i ç ÷ iièøç

where i and i are the scale and the shape parameters of ci respectively. Sub-step 2: Define an interface structure matrix of Fig. 2. Reliability change of product with various components. preventive maintenance actions

A interface structure matrix of components in Cset is defined as NP= [] npij n´ n , where npij is the number of interface Let wt j denote the change of effective working age between components ci and cj. This matrix can provide a of the module in period j, so on the preventive maintenance visual depiction of relationships between each component, activities are taken at period j. We assume that maintenance which can be produced by manual or computer analysis. action/replacement action occurs at the end of the period. It Sub-step 3: Define the model of effective working age. is clear that We assume that product works over the period [0, T]. The interval [0, T] is segmented into J discrete intervals. At -+ wtj+1,=+ wtjij wt . (3) the end of period j ( j =1, , J ), a preventive maintenance activity is planned. To decrease the potential risk of product Step 3: Develop evaluation model of reliability criteria or to avoid great economic loss occurrence, taking and economy criteria of modularity strategies. preventive maintenance activities for modules is needed. The evaluation model of reliability criteria and economy Preventive maintenance activities include disassembly criteria of modularity strategies is illustrated in Fig. 3. process, preventive maintenance actions and assembly Modularity strategy x and modularity parameters s are the process. Preventive maintenance actions are classified into input of the evaluation model. As shown in Fig. 3, the maintenance action and replacement action. Maintenance evaluation model accounts for all processes (arrows) and or replacement in period j reduces the “effective working actions (boxes) that occur during the execution of a given age” of the module. modularity strategy. The model also evaluates the revenue As shown in Fig. 2, to account for the instantaneous - associated with recycling replacement module. changes in working age and failure rate, let wtij, denote

Fig. 3. Evaluation model of modularity strategy for calculating reliability and economy metrics

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Step 4: Formulate the multi-objective optimization Technical feasibility also includes the feasibility of problem. preventive maintenance activities. Therefore The module matrix mathematically defines the PM_feasibility(x, s) is a function of both x and s, denoted relationships between components and modules of as PM_feasibility(x, s)=TRUE. modularity strategy MSs. The number of modules of the In summary, the optimization problem can be stated as ≤≤ * s-th modularity strategy MSs is Ns (1 Nns , NNs Î ). follows: The set of modules of product is denoted as MDset = {MD1, MD2,, MDNs}. It finds that min difference degree(xs , ),

min preventive maintenance cost(xs , ) ïìMD= MD MD MD , ï set 12 Ns íï (4) s.t., modularity(xs , )= TRUE, ïMDMDkl=Æ ,1,2,,,where. = N kl¹ (6) îï k ls modularity_feasibility(xs , )= TRUE, PM_feasibility(xs , )= TRUE,

It is defined as a nN´ s matrix: x= (,(),(),,()). MTPMMDPMMD12 PMMDN s éùmt mt mt êú11 12 1Ns Because of the complexity of Eq. (6), a discrete êúmt mt mt êú21 22 2Ns optimization algorithm is need to solve it. Strength Pareto MT=[]mtik = êú, (5) nN´ s êú Evolutionary Algorithm 2+(SPEA2+)[29–31] is chosen êú êúmt mt mt because of its robustness to discrete problems and ëûnn12 nNs ´ nNs efficiency in handling multi-objective problems without predefined weights or bounds on objective functions. The where algorithm flow of SPEA2+ is shown in Fig. 4.

ì ï1, if cMDik belongs to , mtik = í îï0, otherwise.

The reliability and economy criteria calculated by the evaluation model (Fig. 3) represent the objective functions for the optimization problem. The objectives are both functions of the modularity strategy x and the modularity parameters s. Modularity strategy x consists of the number of module, the components’ combination of each module, and preventive maintenance schedule of each module. Then modularity strategy

x= ( MTPMMDPMMD , ( ), ( ), , PMMD ( )) , 12 Ns

where PM(MDk) is the preventive maintenance schedule of

MDk. The fundamental constraint in the problem is that all modularity and preventive maintenance actions in x must Fig. 4. Algorithm flow of SPEA2+ be structurally and technically feasible. The module matrix MT =[mtik ] imposes a constraint on the components’ nN´ s Step 5: Calculate optimal modularity solutions based on combination of each module of design parameter x as maintenance consideration. modularity(x) = TRUE. It can be express as: The set of optimal modularity strategies is shown in Fig. 5. The optimal set represents the trade-offs between "Îc C,; MD Î MD c b MD;01 mt = mt =. preventive maintenance interval difference degree and total i set k set i k ik ik preventive maintenance cost for product modularity of a

coordinate CNC boring machine. In the case study, the The constraint for technical feasibility of the modularity components within a module often contain the similarly strategy can be denoted as modularity_feasibility(x)= preventive maintenance intervals and preventive TURE. It means that maintenance actions. A module can always be separated from the coordinate CNC boring machine for implementing N N s n s the preventive maintenance actions. The details of the case å mtik =1, ååmtik = n. k=1 ik==11 study are described in the next section.

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optimal set of product modularity for a typical coordinate CNC boring machine based on maintenance consideration is investigated. In this example, the trade-off between preventive maintenance interval difference degree and total preventive maintenance cost at product modularity is considered. The SPEA2+ based method described above is utilized to rapidly approximate the Pareto set of optimal modularity.

3.1 Define modularity scenario for the coordinate CNC boring machine The following modularity variables are acquired for the product modularity: component reliability parameters Fig. 5. Optimal modularity strategy set for the coordinate CNC boring machine based on maintenance consideration (scale parameter, shape parameter and maintenance effect factor) and preventive maintenance parameters (cost of failure, labor cost and purchase price). 3 Case Study: Optimal Modularity for a The main components assembly drawing of the Coordinate CNC Boring Machine Based coordinate CNC boring machine is shown in Fig. 6. on Maintenance Consideration Component reliability parameters of the 55 components are listed in Table 1. To understand the utility of the proposed method, the

Fig. 6. Main components assembly drawing of a coordinate CNC boring machine

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Table 1. Values for parameters of components in a coordinate CNC boring machine

Purchase price Failure cost Maintenance Scale Shape Index Component Material cp,i/$ cfi/$ effect factor εi parameter ηi parameter βi 1 Lathe bed Nodular cast iron 25 714.3 130 0.90 162 1.80 2 Clip conveyers Tinplate 5142.9 55 0.90 48 2.2 3 Stop dog of slide Q235 714.3 32 0.30 43 2.1 4 Torque motor Nd-Fe-B Magnet 14 000.0 300 0.87 110 1.75 5 Slide HT250 14 285.7 145 0.95 149 1.78 6 Chip trough Tinplate 285.7 55 0.98 47 2.2 7 Spindle 45# 17 142.9 220 0.65 115 1.72 8 Spindle box HT150 6428.6 135 0.92 112 1.75 9 Guide rail 20Cr 3571.4 230 0.75 148 1.82 10 Sliding plate HT250 10 000.0 135 0.94 149 1.78 11 Spindle gear box HT150 12 857.1 320 0.75 110 1.75 12 Spindle driving motor Nd-Fe-B Magnet 13 571.4 305 0.73 103 1.78 13 Gantry column HT250 22 857.1 165 0.90 160 1.80 14 Lubricating oil tank HT150 6428.6 45 0.70 80 1.82 15 Oil hydraulic pump Q235 2857.1 155 0.42 75 1.94 16 Stop dog Q235 571.4 32 0.30 43 2.1 17 Grating ruler Electronics 11 428.6 350 0.64 48 2.10 18 Guide rail 20Cr 2142.9 230 0.75 148 1.82 19 Guide rail 20Cr 2142.9 230 0.70 148 1.82 20 Feed screw 40Cr 1428.6 318 0.45 86 1.85 Feed driving motor 21 GCr15 857.1 305 0.46 62 1.95 bearing assembly 22 Top beam frame Nodular cast iron 2857.1 40 0.85 48 2.25 23 Protecting cover Tinplate 6428.6 32 0.85 50 2.3 Feed driving motor 24 Nd-Fe-B Magnet 1142.9 275 0.67 95 1.78 assembly 25 Cooling installation Copper 17 857.1 205 0.52 68 1.90 Feed driving motor 26 Nd-Fe-B Magnet 1142.9 275 0.67 95 1.78 assembly Feed driving motor 27 GCr15 857.1 305 0.46 62 1.95 bearing assembly 28 Feed screw 40Cr 1428.6 318 0.45 86 1.85 29 Guide rail 20Cr 2142.9 230 0.70 148 1.82 30 Feed screw 40Cr 1428.6 318 0.42 88 1.85 Feed driving motor 31 GCr15 857.1 305 0.46 62 1.95 bearing assembly Feed driving motor 32 Nd-Fe-B Magnet 1142.9 320 0.62 95 1.78 assembly Running status 33 Plastic 142.9 15 0.90 52 2.0 indicator light 34 Stop dog Q235 571.4 25 0.35 43 2.1 35 Servo control cabinet Electronics 13 571.4 400 0.82 48 2.05 Spindle oil supply 36 Plastic 6428.6 155 0.70 46 2.2 system 37 Grating ruler Electronics 11 428.6 350 0.64 48 2.10 Feed driving motor 38 Nd-Fe-B Magnet 1142.9 320 0.62 95 1.78 assembly Feed driving motor 39 GCr15 857.1 305 0.46 62 1.95 bearing assembly 40 Feed screw 40Cr 1428.6 318 0.42 88 1.85 41 Platen HT250 14 285.7 155 0.86 149 1.85 42 Rotary support guide 20CrMnTi 6428.6 200 0.65 128 1.95 43 Stop dog of slide Q235 714.3 35 0.30 43 2.1 44 Pulse encoder Electronics 0.0 180 0.22 51 2.25 45 Clip conveyers Tinplate 5142.9 35 0.90 48 2.2 46 Protective shield Tinplate 5714.3 30 0.85 50 2.3 Feed driving motor 47 Nd-Fe-B Magnet 1142.9 300 0.64 99 1.77 assembly Feed driving motor 48 GCr15 857.1 290 0.53 68 1.95 bearing assembly Feed driving motor 49 Nd-Fe-B Magnet 1142.9 300 0.64 99 1.77 assembly 50 Guide rail 20Cr 3571.4 215 0.70 148 1.82 51 Feed screw 40Cr 1428.6 340 0.58 89 1.82 Feed driving motor 52 GCr15 857.1 290 0.53 68 1.95 bearing assembly 53 Feed screw 40Cr 1428.6 340 0.58 89 1.82 54 Guide rail 20Cr 3571.4 215 0.70 148 1.82 55 Grating ruler Electronics 11 428.6 350 0.64 48 2.2

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3.2 Define the model of effective working age for the utilized in the evaluation criteria for modularity strategy of modules the coordinate CNC boring machine. The number of interface between two components is 3.3.1 Quantification of preventive maintenance interval defined in the interface structure matrix NP. Preventive difference degree maintenance schedule is a sequence of preventive Modularity strategy, a particular characteristic maintenance actions for each module in the coordinate modularity, is the development of product modules with CNC boring machine for each period over a planning minimal preventive maintenance dependencies upon other horizon. Preventive maintenance actions for modules components in the product with regard to preventive reduce the effective working age of modules and maintenance. In addition, group components which subsequently failure rate of the coordinate CNC boring undergo similarly preventive maintenance interval into the machine. Combining the effects of preventive maintenance same module where possible. The preventive maintenance actions to modules, the performance promotion of modules interval difference degree of MD can be expressed as can be calculated. k

3.2.1 Maintenance action 1 n SEEm=-[( )2 t ], (10) In this case, MD is maintained in period j, which places kikikå k D ik =1 it into a state somewhere between “good-as-new” and “bad-as-old”. The maintenance action reduces the effective where Ei is the preventive maintenance interval of ci, working age of all components in MDk by a stated Ek is the mean preventive maintenance interval of MDk. percentage of their actual age, that is and Dk is the component number of MDk. Ek can be defined as + wtkj,,=- j wt kj, (7) 1 n EEx= . (11) where is the maintenance effect factor at period j. kiikå  j D ik =1 The factor  j is similar to that proposed by [32] JAYAALAN, et al . This factor describes the effect of The preventive maintenance interval difference degree of maintenance on the aging of a component or product. When product is derived as

 j = 0, component turns to a state of “good-as-new” by Ns the effect of maintenance; when  j =1, maintenance has 1 æöS F =-ç1.k ÷ (12) no effect and component remains in a state of “bad-as-old”. D åç ÷ NSskk=1 èøç max( ) The maintenance action effectively reduces the age of MDk for the start of the next period. It finds that: 3.3.2 Quantification of total preventive maintenance cost To calculate the total preventive maintenance cost in an -+ + + wtkj,1+ =- wt kj ,  j wt kj, =-(1j ) wt kj, = expected life, the cost of every module in maintenance éù action/replacement action, disassembly process and (1-+-= jkjjj ) êúwt,1 ( t t - ) ëû assembly process need to be investigated. HUANG, et al[33], j h also indicated that taking joint replacement to some å  (1-- jr---- ) (tt jh jh1 ). (8) h=0 r=0 components is always cheaper than replacing these components individually. It assumes that taking + Then rate of occurrence of failure for MDk is kkj()wt , maintenance to a module can be regarded as carrying out - at the end of period j and drops to kkj()wt , at the start of joint maintenance to the related components. period j +1 . (1) Maintenance action. The component carries a high 3.2.2 Replacement action rate of occurrence of failure through a period, and then the component is at risk of experiencing high cost of failures. In this case, we assume that MDk is to be replaced at the end of period j, immediately placing it in a state of Conversely, a low rate of occurrence of failure in period j “good-as-new”. Its age is effectively returned to time zero. should yield a low cost of failure. To account for this, [34] It finds that: USHER, et al , proposed the computation of the expected number of failures in each period for each component. The -+ cost of each failure is cfi, which in turn is computed the cost wtkj,1+ ==00. wtkj , (9) of failures attributable F to c in period j as: i,j i

Therefore rate of occurrence of failure for MDk wt+ + ij, instantaneously drops from kkj()wt , to k (0) . CFij,,== cf i F ij cf i i()d t t = òwt- ij, + wtij, 3.3 Multiple evaluation criteria model for modularity cf--ii t1d()(). t=- cf  - iéù wt+-  i wt  i iiiiiijijò - ëûêú,, strategy wtij, (13) The following paragraphs outline mathematical models

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If maintenance is performed on MDk, the maintenance  i is the recyclable coefficient and cm,i is the revenues cost is calculated by from the reuse/recycle of the material per unit weight of ci. The preventive maintenance cost parameter values used MM in the case study are listed in Table 3. CCCMk,,,=+= Fk Dkåå CmtCmt Fi ik +2 Di ik = ii==11 MJ MM Table 3. Values for preventive maintenance cost parameters ååCFi, j mt ik+-2(), åå CD ij mt ik mt jk mt ik Parameter Value ij==11 ij == 11 –1 Labor cost cwt/($ • h ) 20.0 (14) Recycled plastic price ($ • kg–1) 0.15 Recycled aluminum price ($ • kg–1) 2.35 where CDij is the cost of disassembly and assembly Recycled steel price ($ • kg–1) 0.45 operation of interface between two components Recycled electronics price ($ • kg–1) 0.38 Time of disassembly and assembly operations is the most Recycled rubber price ($ • kg–1) 2.45 –1 important factor of preventive maintenance cost. We Recycled copper price ($ • kg ) 2.45 Recycled Nd-Fe-B Magnet ($ • kg–1) 17.15 assume that assembly is the reverse disassembly process. Recyclable coefficient  0.85 The cost necessary for disassembly operation is defined by the following expression: From the two kinds of cost, the total cost function can be

CD= c np(), t n (15) written as follows: ij wt ij nij t ij NNss where cwt is the labor cost per unit time, t is the FCCMkRk=+åå,, C. (17) nij normalized disassembly time that corresponds to the ii==11 typology of c and c (the correspondence depends on the i j 3.4 Formulate multi-objective modularity strategy typology index of the component) and n is the tij optimization problem normalized execution time that corresponds to the The two objective functions of the formulation in Eq. (6) operations necessary for the removal of c and c (the i j are defined as follows: correspondence depends on the index of operation typology). minimize difference degree: Different disassembly operations are performed on the 1 Ns æöS components so defined. Indicating with 5 types of minFxs ( , )=-ç 1k ÷ , D åç ÷ disassembly operations, the distinction between the NSskk=1 èømax( ) operations is simple, because once the diversification of minimize preventive maintenance cost: joints is incorporated into the analysis of the components, NNss [35] the operations are reduced to translation movements . In minFxsCMkRk ( , )=+åå C,, C , this case the times of execution are normalized with respect ii==11 s.t., modularity(xs , )= TRUE, to the simplest horizontal linear translation, and are summarized in Table 2. modularity_feasibility(xs , ) = TRUE, PM_feasibility(xs , )= TRUE, Table 2. Index of component typology and characterization x= (,(),(),,()). MTPMMDPMMD PMMD 12 Ns Mean time Normalized (18) Index Description t /s time n /s nij tij 1 Component (to be removed) 1.25 1 The properties of the genetic algorithm chromosome are 2 Screw (to be removed) 0.6 (×turn) 0.48 (× turn) listed in Table 4. 3 Snap fit (to be opened) 1.5 1.2 4 Clip (to be removed) 1 0.8 Table 4. Definition of a genetic algorithm chromosome 5 Connection (to be broken) 2 1.6 representing parameter

Chromosome Chromosome Crossover (2) Replacement action. Possible values position position name method If MD is replaced, in period j, the replacement cost is k Number of Segment 1 Arithmetic 1–55 calculated by module

Physical M relationships CCCCRk,,,,=-+= Pk rk Dk cmt pi , ik - Single å Segment 2 between 1–55 i=1 point MMM components and modules åååwi i c m, i mt ik+-2(), CD ij mt ik mt jk mt ik (16) ii===111j Preventive 0=do nothing Segment 3 maintenance Uniform 1=maintenance schedule 2=replacement where cp,i is the purchase price of ci, wi is the weight of ci,

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machine are grouped into 10 modules, which are illustrated 3.5 Calculate optimal product modularity trade-off in Fig. 7. The module structure and module property of sets based on maintenance consideration. MS-T for the coordinate CNC boring machine is shown in The 100 members of starting population of SPEA2+ are Table 5. Table 6 describes the preventive maintenance seeded at random, and the algorithm is run through 500 structure of MS-T. MS-T can be used to compare different generations. As shown in Fig. 5, each optimal modularity product designs and modularity situations for their strategy is represented as a point on the Pareto curve. maximum “economical” product modularity based on MS-D is the minimum preventive maintenance interval maintenance consideration. The minimum, maximum, and difference degree modularity strategy, and MS-C is the average effective working age of each module in MS-T are minimum total preventive maintenance cost modularity shown in Table 7. It shows that the minimum effective strategy. MS-C involves high recycled price components in working age of each module is equal to zero at the a module with replacement action and high purchase price beginning. The effective working age for the modules components in a module for the maintenance action ranges from roughly 0 to 10 520 h with an average age of implementing. about 2880 h. It is helpful to maintenance mangers to track MS-T is defined as the optimal tradeoff modularity the effective working age of the components. When a strategy between the minimum difference degree and the module reaches a set effective working age, additional minimum preventive maintenance cost in Fig. 5. The monitoring, tests or inspections are needed to assist in the considered components of the coordinate CNC boring detection of imminent failure.

Fig. 7. Modular solution of the coordinate CNC boring machine

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Table 5. Module structure and module property of MS-T for the coordinate CNC boring machine

Modularity strategy MS-T Number of module 10

Module structure

Module index Component Intervals Module I 3, 23, 43, 46 5-6-6-3-4-6 Module II 5, 47, 48, 49, 51, 52, 53 6-5-6-3-4-6 Module III 14, 15, 25, 36 5-1-5-6-7-6 Module IV 10, 16, 30, 31, 32, 34, 38, 39, 40 5-1-5-6-3-4-6 Property of module Module V 4, 41, 42 6-5-6-7-6 Module VI 20, 21, 24, 26, 27, 28 5-1-5-6-3-4-6 Module VII 2, 6, 22, 45 6-5-6-7-6 Module VIII 1, 9, 13, 18, 19, 29, 50, 54 6-11-7-6 Module IVV 7, 8, 11, 12 5-6-6-3-4 Module VV 17, 33, 35, 37, 44, 55 6-5-9-4-6

Table 6. Preventive maintenance structure of MS-T

Preventive maintenance index Module index 1 2 3 4 5 6 7 Module I R R R M R R – Module II R R R M R R – Module III M R M R R R – Module IV M M R R M M R Module V M M R M M – – Module VI M M R R M R R Module VII R R R R R – – Module VIII M R M M – – – Module IVV M M R M M – – Module VV R R R M R – –

Table 7. Effective working age of modules in optimal modularity strategy MS-T

Module Minimum effective working age wtmin/h Maximum effective working age wtmax/h Average effective working age wtavg/h Module I 0.0 4320.00 2391.20 Module II 0.0 4320.00 2400.80 Module III 0.0 5940.00 2755.00 Module IV 0.0 6300.00 2875.00 Module V 0.0 7929.22 4397.02 Module VI 0.0 4320.00 2415.25 Module VII 0.0 5040.00 2540.00 Module VIII 0.0 9302.40 4147.62 Module IVV 0.0 10 520.06 4533.73 Module VV 0.0 6480.00 2818.40

Point P in Fig. 5 is the direct production modularity modularity the coordinate CNC boring machine imposes strategy of the coordinate CNC boring machine. Direct less preventive maintenance interval difference degree and production modularity strategy involves a production more preventive maintenance cost. module that is formed by an assembly of many components. The direct function modularity strategy is defined as point 4 Sensitivity Analysis of Modularity F in Fig. 5. It is a function module that is constructed either Parameters by a signal function or by more than one function. It can be observed that point D and F are far from the Pareto curve. The optimization model developed in Step 4 involves That means optimal modularity strategies always have two different types of modularity parameters: preventive lower potential for total preventive maintenance cost than maintenance parameters and component reliability direct function modularity (technology development aspect) parameters. Each component also has three different types or direct production modularity (production capacity of cost, failure cost, labor cost (maintenance cost), and aspect). Directly production modularity or directly function purchase price (replacement cost). Component reliability

CHINESE JOURNAL OF MECHANICAL ENGINEERING ·417· parameters include i and i , the scale and the shape 8 different trials. The first experiment assumes that the parameters of component, and i , the maintenance effect scale parameter, shape parameter and maintenance effect factor for each component. A sensitivity analysis for two factor of all components are the same, but each component different types of modularity parameters is provided in the has two levels, low and high, for failure cost, labor cost, following paragraphs. and purchase prices; see Table 8. The second experiment In order to find the effect of the modularity parameters assumes that the preventive maintenance parameters of all on the structure of the optimal solution two 23 factorial components are the same, but each component has two design experiments are designed. Based on this levels for the reliability parameters; as shown in Table 9. consideration, each experiment has three factors, each with MATLAB (R2008 a2) software is utilized to solve the two levels. With one replicate in each experiment, there are model to reach the exact optimal solution.

Table 8. Values for modularity parameters of experiment 1

Maintenance effect factor Scale parameter Shape parameter Failure cost Labor cost Purchase price Component –1 εi ηi βi cfi/$ cwt/($ • h ) cp,i/$ 1 0.85 43 2.0 200 50 100 2 0.85 43 2.0 200 50 400 3 0.85 43 2.0 200 200 100 4 0.85 43 2.0 200 200 400 5 0.85 43 2.0 500 50 100 6 0.85 43 2.0 500 50 400 7 0.85 43 2.0 500 200 100 8 0.85 43 2.0 500 200 400

Table 9. Values for modularity parameters of experiment 2

Maintenance effect factor Scale parameter Shape parameter Failure cost Labor cost Purchase price Component –1 εi ηi βi cfi/$ cwt/($ • h ) cp,i/$ 1 0.30 40 1.5 125 125 125 2 0.30 40 2.5 125 125 125 3 0.30 165 1.5 125 125 125 4 0.30 165 2.5 125 125 125 5 0.70 40 1.5 125 125 125 6 0.70 40 2.5 125 125 125 7 0.70 165 1.5 125 125 125 8 0.70 165 2.5 125 125 125

4.1 Sensitivity analysis for component reliability the same. According to the proposed modularity strategy, parameters the preventive maintenance times of system progressed and Tables 10–13 present the optimal module structure and its effective working age under the set preventive preventive maintenance structure of MS-D (minimum maintenance intervals are shown in Tables 10–13. preventive maintenance interval difference degree Observing the effective working age distribution and the modularity strategy) and MS-C (minimum total preventive preventive maintenance actions, it finds that the failure cost maintenance cost modularity strategy) for experiment 1. does not noticeably affect the module structure and the Although first four components with less failure cost and frequency (intervals) of preventive maintenance activities the last four components with more failure cost, it can be in the optimal modularity strategy. seen that optimal module structure of MS-C and MS-D are

Table 10. Module structure and module property of MS-D for experiment 1

Modularity strategy MS-D Number of module 4

Module structure

Module index Component Interval Module I 1,5,7 5-3-5-5-2-6-4 Property of module Module II 2,6 4-3-2-2-4-2-3-2-3-6 Module III 3,4 8-5-5-4-4-4-2 Module IV 8 12-9-7

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Table 11. Preventive maintenance structure of MS-D for experiment 1

Preventive maintenance index Module index 1 2 3 4 5 6 7 8 9 10 Module I R R R M R M R – – – Module II M M M M M M M M M M Module III R R R R R R R – – – Module IV R R R – – – – – – –

Table 12. Module structure and module property of MS-C for experiment 1

Modularity strategy MS-C Number of module 4

Module structure

Module index Component Interval Module I 1, 5, 7 6-4-5-5-3-3-4 Property of module Module II 2, 6 6-1-4-5-5-3-3-4-1 Module III 3, 4 7-8-5-3-3-5 Module IV 8 7-3-13-7

Table 13. Preventive maintenance structure of MS-C for experiment 1

Preventive maintenance index Module index 1 2 3 4 5 6 7 8 9 10 Module I R R R R R R R – – – Module II M M M M M M M M M M Module III R R R R R R – – – – Module IV R R R R – – – – – –

Module II (components 2 and 6) is only maintained, effect factor reduces the effective working age of because the labor cost for maintenance of components 2 component more than component that has a higher and 6 are much less than their purchase prices for maintenance effect factor. Components 1, 3, 5 and 7 are replacement, but they have different failure costs, as shown more likely to be maintained. Therefore, their preventive in Table 8. It is also seen that module I (components 1, 5 maintenance intervals are shorter than the others. However, and 7), III (components 3 and 4) and IV (components 8) are as in Tables 14 and 16, it can be observed that the optimal only replaced, except one maintenance action for module I module structure of MS-D and MS-C are the same. It in Tables 11 and 13. In the above module, labor cost for means that maintenance effect factor does not affect the maintenance of components is greater or equal to their optimal module structure, when failure cost, labor cost, and purchase prices for replacement. It seems that the purchase prices of all components are the same and scale preventive maintenance schedule contains replacement and shape parameters are different. actions instead of maintenance actions. However, module As shown in Tables 15 and 17, by comparing the IV is replaced less frequently than other modules because reliability parameters for components in module I and of high labor cost and purchase prices of components 8. module II, components of each module have the same scale By reviewing the labor cost and purchase prices parameter but components in module II have larger value of presented in Table 8 and the optimal module structure in the shape parameter. It makes more replacement actions for Table 10 and 12, it can be concluded that if all components have the same reliability parameters, the module structure module II. Considering module I and module III, all of and the frequency (intervals) of preventive maintenance them have the same shape parameter, but components in activities in the optimal modularity strategy is affected by module I have a smaller scale parameter than components just ratio of the labor cost and purchase prices. In addition, in module III. Therefore, more frequent replacement the failure cost does not play a significant role in the actions are performed in module III. It can be seen that the optimal modularity strategy. shape parameter has an effect on the schedule of preventive maintenance actions and much more than scale parameter 4.2 Sensitivity analysis for preventive maintenance does. Finally, by comparing the frequency (intervals) of parameters preventive maintenance actions of module I and module IV Tables 14–17 present the optimal module structure and in Tables 15 and 17, it can be found that module IV with preventive maintenance structure of MS-D and MS-C for great scale and shape parameters is replaced more experiment 2. As shown in Eq. (7), the smaller maintenance frequently than module I with small parameters values.

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Table 14. Module structure and module property of MS-D for experiment 2

Modularity Strategy MS-D Number of module 4

Module structure

Module index Component Interval Module I 1, 5 20 Property of Module Module II 2, 6 4-3-6-2-5-5-5 Module III 3, 7 7-7-6-5-6 Module IV 4, 8 4-3-6-2-5-5-4-2

Table 15. Preventive maintenance structure of MS-D for experiment 2

Preventive maintenance index Module index 1 2 3 4 5 6 7 8 Module I R – – – – – – – Module II R R R R M R R – Module III R R R R R – – – Module IV R R R R R R M M

Table 16. Module structure and module property of MS-C for experiment 2

Modularity Strategy MS-C Number of module 4

Module structure

Module index Component Interval Module I 1, 5 15-11 Property of Module Module II 2, 6 8-4-5-7-7 Module III 3, 7 8-9-9 Module IV 4, 8 3-5-4-3-4-4-3-5

Table 17. Preventive maintenance structure of MS-C for experiment 2

Preventive maintenance index Module index 1 2 3 4 5 6 7 8 Module I R R – – – – – – Module II R R R R R – – – Module III R R R – – – – – Module IV R R R R R R R R

price along with scale and shape parameters affect the 5 Conclusions structure of the optimal modularity strategy but failure cost and improvement factor do not appear to play as an (1) This paper has described a five-step modular design important role. method with the considerations of maintenance related. The (3) In most cases, the considered product is supposed to reliability and economic assessment models of product wear-out continuously. A continuation of this work intends modularity strategies are established with the introduction to investigate more realistic situations, where the of the effective working age of components. As regards probabilistic properties of the failure intensity models preventive maintenance to the module, the maintenance obtained by more elaborated models. The properties of the times of product should be decreased so that the total parameters estimators have to be theoretically studied. maintenance cost would be cut down. (2) Two factorial design experiments based on the References modularity parameters are used to investigate the effect of [1] PAHL G, BEITZ W, FELDHUSEN J, et al. Engineering design: a modularity parameters on structure of the optimal systematic approach[M]. Springer, 2007. modularity strategy.. It finds that labor cost and purchase [2] STONE R B, WOOD K L, CRAWFORD R H. A heuristic method

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