Product Modular Design Incorporating Preventive ...

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

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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

1 Introduction

Increased demand for functions and reliability of mechanical products, it is more complex in design and higher maintenance skills are required. Modular design is of particular concern due to reduce the burden of mechanical product in maintenance. A module is a set of some disassembly and/or non-disassembly components or parts. It is easy to repair and replace when it fails since the assembly and disassembly processes of a module are speeded up based on the reduction of the needed tools and skill in maintenance.

Traditionally, criteria for generating modules are divided into three types by the original motivations of clustering the components into modules.

(1) Function. Components are rearranged into new modules by the functional interactions between components, because components form modules (physical structures) to

* Corresponding author. E-mail: [email protected] Supported by National Natural Science Foundation of China (Grant Nos.

51205347, 51322506), Zhejiang Provincial Natural Science Foundation of China (Grant No. LR14E050003), Project of National Science and Technology Plan of China (Grant No. 2013IM030500), Fundamental Research Funds for the Central Universities of China, Innovation Foundation of the State Key Laboratory of Fluid Power Transmission and Control of China, and Zhejiang University K.P.Chao’s High Technology Development Foundation of China

© Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2016

realize the product functions. PAHL, et al[1], proposed a method that various overall functions were fulfilled by the combination of distinct building blocks or modules. They referred to modular products as components, assemblies and machines. Modules were designed as building blocks, which can be grouped together to form a variety of products. STONE, et al[2], presented a modular method for clustering the components based on functional heuristics. Modules were identified from the ‘functional structure’ according to the flow patterns shown in the product ‘functional structure diagram’. KRENG, et al[3], presented a four major phases approach to accomplish modular product design according to the maximum physical and functional relations among components and maximizing the similarity of specifically modular driving forces. They employed a non-linear programming to identify separable modules and simultaneously optimize the number of modules. THOM, et al[4], developed a modularization scheme using of the function-behavior-state model of the system to derive the entity relations. A k-means clustering algorithm was used to allow the user to try different number of clusters in a fast way, which can be adopted for design structure matrix based modularization by defining a proper entity representation, relation measure and objective function. LI, et al[5], developed a fuzzy graph based modular product design methodology to implement Design for the Environment (DfE) strategies in product modular

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formulation considering multiple product life cycle objectives guided by DfE. An optimal modular formulation was searched using the graph-based clustering algorithm to identify the best module configuration.

(2) Structure. As designers decompose a product into components and then group these components into separate modules, this requires the consideration of the structure (the geometric position and connection forms) between components when generating new modules. SALHIEH, et al[6], developed a P-median model to maximize the similarity index between the components in a module. KRENG, et al[7], proposed a QFD-based modular product design method to identify the optimal module through the interaction between the modular drivers and components. They also considered functional and physical interaction between components. GUPTA, et al[8], proposed a method to eliminate the drawbacks by providing a computerized conceptual design framework that incorporates modularity, design for assembly, and design for variety principles. TSENG, et al[9], developed a liaison graph model to the evaluation of part connections that include the component liaison intensity were evaluated by engineering structural attributes (contact type, combination type, tool type, and accessed direction).

(3) Material compatibility. Material compatibility contributes to manufacture, reuse and recycle of product in terms of high material compatibility of components in the same module. KIMURA, et al[10], proposed a modular design method based on product functionality, commonality and life cycle similarity. The new product modularization strategy was used to efficiently manage a closed loop product life cycle of a family of products and successive generation of products. QIAN, et al[11], developed a quantitative model of environmental analysis for modular design. The modularity analysis consisted of similarity and independence analysis under the restriction of junction-structure mapping. HUANG, et al[12], presented five basic rules for recycling in modular design, including life-cycle analysis, materials compatibility, recycling profit, environmental impact of recycling, and structural and physical interaction analysis. Then a fuzzy clustering algorithm was adopted to form the component clusters based on a fuzzy correlation matrix. UMEDA, et al[13], proposed a modular design methodology that determines the modular structure based on aggregating various attributes related to a product life cycle and evaluating geometric feasibility of modules. The method aggregated attributes related to a product life cycle using a technique called self-organizing maps. JOHANSSON, et al[14], introduced the concept of “material hygiene” and developed a method for grading structural properties in a recycling perspective based on the concept. SMITH, et al[15], put forward a green modularization method based on the atomic theory with green considerations. They created green modules by merging or separating structural modules with respect to environmental impacts. JI, et al[16],

presented a leader-follower joint optimization method based on technical system modularity and material reuse modularity. They developed taxonomy of modularity metrics in order to encompass the entire life cycle of material fulfillment. The quantification and aggregation of modularity measures are formulated by multi-attribute utilities of different dimensions of component similarity.

Relative to these above researches, the field of modular design has generally focused less on maintenance consideration. While modular design decreases the complexity of a system in maintenance. Moreover, the number of modules is much less than the number of components. It makes that the expenses in maintenance could be effectively reduced[17–19]. AVEN, et al[20], presented a general framework including various age and block replacement models for the optimization of replacement times. PIMMLER, et al[21], proposed a matrix-based modular method for improving product quality and reliability. The modular clustering was done based on the priority of interactions between the components. KUSIAK[22] formulated a cost minimization problem subject quality and testability levels constraints to identify the modules. He also analyzed the component interactions to identify the modules but it is not clear how he measures the testability and quality of the modules. TSAI, et al[23], used the fuzzy cluster identification method by considering correlation in design of components. Four years later, they presented a method of modularity based on the consideration of system maintenance policy for constructing the system modules[24]. Total maintenance costs of modules in the ‘predetermined lifecycle’ of the modules were introduced in order to extend their previous research. YANG, et al[25], proposed a modular eco-design method for life-cycle engineering based on re-design risk control. They defined functional and physical risk assessments as two constraints during the re-design optimization process. With these two constraints, the redesign risk could be controlled to an acceptable value by designers.

However, reliability objectives are treated as constraints secondary to economic objectives in modular design. The modularity design method based on the consideration of maintenance for constructing the product modules, especially the effect of reliability characteristics of components and maintenance parameters on the structure of optimal modularity strategy has not been studied yet. This paper has described a five-step modular design method with the considerations of maintenance related. According to the studies reported in past, maintenance was classified into two categories, corrective maintenance and preventive maintenance[26]. Preventive maintenance keeps a system in an available condition to avoid unpredictable fails. Therefore our modular design method focuses on preventive maintenance issues. The reliability and economic assessment models of product modularity strategies are developed. The contributions of this research

Y GAO Yicong, et al: Product Modular Design Incorporating Preventive Maintenance Issues

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as follows: (1) Preventive maintenance activities are considered in advance during modularity design. The product will perform much more effective in service stage and the production loss can be decreased by the shortening of shut-down time. (2) Two factorial design experiments based on the parameters of cost associated with preventive maintenance activities and reliability characteristics are 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 maintenance consideration;

The relationship between these five steps is shown in Fig. 1. Several definitions of the method are drawn out as follows.

Modules: A module is usually a combination of components. The components within a module often contain the similarly effective working age in use stage.

Modularity strategy: The set of all modularity decisions, consisting of the number of modules, the components’ combination of each module, and preventive maintenance activities of each module. The components within a module often contain the similarly effective working age.

Modularity parameters: Modularity parameters include preventive maintenance parameters and component reliability parameters. Preventive maintenance parameters define the economic aspect associated with preventive maintenance activities. Component reliability parameters define component reliability characteristics aspect.

Preventive maintenance activities: The approach presented here takes into account each activity involved in module preventive maintenance. These activities include disassembly process, preventive maintenance actions (maintenance action and replacement action) and assembly process. If the component is implemented replacement action, recycling action will be added.

Fig. 1. Methodology for calculating product modularity

trade-off sets based on maintenance consideration

Step 1: Define modularity parameters. Modularity parameters that must be defined include

component reliability parameters such as the scale parameter, shape parameter of component (the hazard rate function) and maintenance effect factor; preventive maintenance parameters such as cost of failure, labor price, and purchase prices. In the problem formation below, the vector s defines the set of modularity parameters for product modularity.

Step 2: Define the product structure and the effective working age of modules.

Defining the product structure and the effective working age of modules is the basis of the method. It can be derived from the following sub-steps:

Sub-step 1: Define the set of components along with their reliability parameters.

It assumes that product is a series system of components


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in this paper. The set of components in the product is denoted as Cset={c1, c2, , cn}. Aiming to the failures of components, most of them belong to cumulative damage. According to the studies by WANG, et al[27–28], each component is assumed to have an rate of occurrence of failure, ( )i t , where t denotes actual time, t>0. Weibull 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

( ) ,i

ii

i i

tt

-æ ö÷ç ÷= ç ÷ç ÷çè ø (1)

where i and i are the scale and the shape parameters of ci respectively.

Sub-step 2: Define an interface structure matrix of components.

A interface structure matrix of components in Cset is defined as [ ]ij n nNP np ´= , where npij is the number of interface between components ci and cj. This matrix can provide a visual depiction of relationships between each component, which can be produced by manual or computer analysis.

Sub-step 3: Define the model of effective working age. We assume that product works over the period [0, T].

The interval [0, T] is segmented into J discrete intervals. At the end of period j ( 1, ,j J= ), a preventive maintenance activity is planned. To decrease the potential risk of product or to avoid great economic loss occurrence, taking preventive maintenance activities for modules is needed. Preventive maintenance activities include disassembly process, preventive maintenance actions and assembly process. Preventive maintenance actions are classified into maintenance action and replacement action. Maintenance or replacement in period j reduces the “effective working age” of the module.

As shown in Fig. 2, to account for the instantaneous changes in working age and failure rate, let ,i jwt- denote

the effective working age of a module at the start of period j and jwt+ denote the effective working age at the end of period j. It is clear that

1( ) .j j j j jT

wt wt t t wtJ

+ - --= + - = + (2)

Fig. 2. Reliability change of product with various preventive maintenance actions

Let jwt denote the change of effective working age

of the module in period j, so on the preventive maintenance activities are taken at period j. We assume that maintenance action/replacement action occurs at the end of the period. It is clear that

1 , .j j i jwt wt wt- ++ = + (3)

Step 3: Develop evaluation model of reliability criteria

and economy criteria of modularity strategies. The evaluation model of reliability criteria and economy

criteria of modularity strategies is illustrated in Fig. 3. Modularity strategy x and modularity parameters s are the input of the evaluation model. As shown in Fig. 3, the evaluation model accounts for all processes (arrows) and actions (boxes) that occur during the execution of a given modularity strategy. The model also evaluates the revenue associated with recycling replacement module.

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


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Step 4: Formulate the multi-objective optimization

problem. The module matrix mathematically defines the

relationships between components and modules of modularity strategy MSs. The number of modules of the s-th modularity strategy MSs is Ns (1 sN n≤ ≤ , *

sN NÎ ). The set of modules of product is denoted as MDset = {MD1, MD2, , MDNs}. It finds that

1 2 ,

, 1, 2, , , where .

Ns

k

set

l s

MD MD MD MD

MD MD k l N k l

ì =ïïïíï =Æ = ¹ïïî (4)

It is defined as a sn N´ matrix:

MT= [ ]

11 12 1

21 22 2

1 2

,

s

s

s

ss

N

Nik n N

n n nN n N

mt mt mt

mt mt mtmt

mt mt mt

´

´

é ùê úê úê ú= ê úê úê úê úë û

(5)

where

1, if belongs to ,

0, otherwise.i k

ik

c MDmt

ìïï=íïïî

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

1 2( , ( ), ( ), , ( ))sNx MT PM MD PM MD PM MD= ,

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 be structurally and technically feasible. The module matrix MT [ ]

sik n N

mt´

= imposes a constraint on the components’

combination of each module of design parameter x as modularity(x) = TRUE. It can be express as:

, ; ; 0 1i set k set i k ik ikc C MD MD c b MD mt mt" Î Î = = .

The constraint for technical feasibility of the modularity strategy can be denoted as modularity_feasibility(x)=

TURE. It means that

1

1,sN

ikk

mt=

=å 1 1

.sNn

iki k

mt n= =

=åå

Technical feasibility also includes the feasibility of preventive maintenance activities. Therefore PM_feasibility(x, s) is a function of both x and s, denoted as PM_feasibility(x, s)=TRUE.

In summary, the optimization problem can be stated as follows:

1 2

min difference degree( , ),

min preventive maintenance cost( , )

s.t., modularity( , ) TRUE,

modularity_feasibility( , ) TRUE,

PM_feasibility( , ) TRUE,

( , ( ), ( ), , ( )).sN

x s

x s

x s

x s

x s

x MT PM MD PM MD PM MD

==

=

=

(6)

Because of the complexity of Eq. (6), a discrete

optimization algorithm is need to solve it. Strength Pareto Evolutionary Algorithm 2+(SPEA2+)[29–31] is chosen because of its robustness to discrete problems and efficiency in handling multi-objective problems without predefined weights or bounds on objective functions. The algorithm flow of SPEA2+ is shown in Fig. 4.

Fig. 4. Algorithm flow of SPEA2+

Step 5: Calculate optimal modularity solutions based on

maintenance consideration. The set of optimal modularity strategies is shown in Fig.

5. The optimal set represents the trade-offs between preventive maintenance interval difference degree and total preventive maintenance cost for product modularity of a coordinate CNC boring machine. In the case study, the components within a module often contain the similarly preventive maintenance intervals and preventive maintenance actions. A module can always be separated from the coordinate CNC boring machine for implementing the preventive maintenance actions. The details of the case study are described in the next section.


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Fig. 5. Optimal modularity strategy set for the coordinate CNC

boring machine based on maintenance consideration 3 Case Study: Optimal Modularity for a

Coordinate CNC Boring Machine Based on Maintenance Consideration

To understand the utility of the proposed method, the

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 (scale parameter, shape parameter and maintenance effect factor) and preventive maintenance parameters (cost of failure, labor cost and purchase price).

The main components assembly drawing of the coordinate CNC boring machine is shown in Fig. 6. Component reliability parameters of the 55 components are listed in Table 1.

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

Index Component Material Purchase price

cp,i/$

Failure cost

cfi/$ Maintenance

effect factor εi Scale

parameter ηi Shape

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

21 Feed driving motor bearing assembly

GCr15 857.1 305 0.46 62 1.95

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

24 Feed driving motor assembly

Nd-Fe-B Magnet 1142.9 275 0.67 95 1.78

25 Cooling installation Copper 17 857.1 205 0.52 68 1.90


Nd-Fe-B Magnet 1142.9 275 0.67 95 1.78


GCr15 857.1 305 0.46 62 1.95

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


GCr15 857.1 305 0.46 62 1.95


Nd-Fe-B Magnet 1142.9 320 0.62 95 1.78

33 Running status indicator light

Plastic 142.9 15 0.90 52 2.0

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

36 Spindle oil supply system

Plastic 6428.6 155 0.70 46 2.2

37 Grating ruler Electronics 11 428.6 350 0.64 48 2.10


Nd-Fe-B Magnet 1142.9 320 0.62 95 1.78


GCr15 857.1 305 0.46 62 1.95

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


Nd-Fe-B Magnet 1142.9 300 0.64 99 1.77


GCr15 857.1 290 0.53 68 1.95


Nd-Fe-B Magnet 1142.9 300 0.64 99 1.77

50 Guide rail 20Cr 3571.4 215 0.70 148 1.82 51 Feed screw 40Cr 1428.6 340 0.58 89 1.82


GCr15 857.1 290 0.53 68 1.95

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


·413· 3.2 Define the model of effective working age for the

modules The number of interface between two components is

defined in the interface structure matrix NP. Preventive maintenance schedule is a sequence of preventive maintenance actions for each module in the coordinate CNC boring machine for each period over a planning horizon. Preventive maintenance actions for modules reduce the effective working age of modules and subsequently failure rate of the coordinate CNC boring machine. Combining the effects of preventive maintenance actions to modules, the performance promotion of modules can be calculated.

3.2.1 Maintenance action In this case, MDk is maintained in period j, which places

it into a state somewhere between “good-as-new” and “bad-as-old”. The maintenance action reduces the effective working age of all components in MDk by a stated percentage of their actual age, that is

, , ,k j j k jwt wt +=- (7)

where j is the maintenance effect factor at period j.

The factor j is similar to that proposed by JAYAALAN, et al[32]. This factor describes the effect of maintenance on the aging of a component or product. When

0,j = component turns to a state of “good-as-new” by the effect of maintenance; when 1,j = maintenance has no effect and component remains in a state of “bad-as-old”. The maintenance action effectively reduces the age of MDk for the start of the next period. It finds that:

, 1 , , ,

, 1

100

(1 )

(1 ) ( )

(1 ) ( ).

k j k j j k j j k j

j k j j j

j h

j r j h j hrh

wt wt wt wt

wt t t

t t

- + + ++

-

- - - -==

= - = - =

é ù- + - =ê úë û

- -å

(8)

Then rate of occurrence of failure for MDk is ,( )k k jwt +

at the end of period j and drops to ,( )k k jwt - at the start of period 1j+ .

3.2.2 Replacement action In this case, we assume that MDk is to be replaced at the

end of period j, immediately placing it in a state of “good-as-new”. Its age is effectively returned to time zero. It finds that:

, 1 ,0 0.k j k jwt wt- ++ = = (9)

Therefore rate of occurrence of failure for MDk

instantaneously drops from ,( )k k jwt + to (0)k .

3.3 Multiple evaluation criteria model for modularity strategy

The following paragraphs outline mathematical models

utilized in the evaluation criteria for modularity strategy of the coordinate CNC boring machine.

3.3.1 Quantification of preventive maintenance interval difference degree

Modularity strategy, a particular characteristic modularity, is the development of product modules with minimal preventive maintenance dependencies upon other components in the product with regard to preventive maintenance. In addition, group components which undergo similarly preventive maintenance interval into the same module where possible. The preventive maintenance interval difference degree of MDk can be expressed as

2

1

1[( ) ],

n

k i k ikik

S E E mtD =

= -å (10)

where iE is the preventive maintenance interval of ci,

kE is the mean preventive maintenance interval of MDk. and Dk is the component number of MDk. kE can be defined as

1

1.

n

k i ikik

E E xD =

= å (11)

The preventive maintenance interval difference degree of

product is derived as

1

11 .

max( )

sNk

Dks k

SF

N S=

æ ö÷ç ÷= -ç ÷ç ÷çè øå (12)

3.3.2 Quantification of total preventive maintenance cost To calculate the total preventive maintenance cost in an

expected life, the cost of every module in maintenance action/replacement action, disassembly process and assembly process need to be investigated. HUANG, et al[33], also indicated that taking joint replacement to some components is always cheaper than replacing these components individually. It assumes that taking maintenance to a module can be regarded as carrying out joint maintenance to the related components.

(1) Maintenance action. The component carries a high rate of occurrence of failure through a period, and then the component is at risk of experiencing high cost of failures. Conversely, a low rate of occurrence of failure in period j should yield a low cost of failure. To account for this, USHER, et al[34], 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 of failures attributable Fi,j to ci in period j as:

,

,

,

,

, ,

1, ,

( )d

d ( ) ( ) .

i j

i j

i ji i i i i

i j

wt

i j i i j i iwt

wt

i i i i i i j i jwt

CF cf F cf t t

cf t t cf wt wt

+

-

+

-- - - + -

= = =

é ù= -ê úë û

ò

ò

(13)


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If maintenance is performed on MDk, the maintenance cost is calculated by

, , ,1 1

,1 1 1 1

2

2 ( ) ,

M M

M k F k D k Fi ik Di iki i

M J M M

i j ik ij ik jk iki j i j

C C C C mt C mt

CF mt CD mt mt mt

= =

= = = =

= + = + =

+ -

å å

åå åå

(14)

where CDij is the cost of disassembly and assembly operation of interface between two components

Time of disassembly and assembly operations is the most important factor of preventive maintenance cost. We assume that assembly is the reverse disassembly process. The cost necessary for disassembly operation is defined by the following expression:

wt ( ),ij ijij ij n tCD c np t n = (15)

where cwt is the labor cost per unit time,

ijnt is the normalized disassembly time that corresponds to the typology of ci and cj (the correspondence depends on the typology index of the component) and

ijtn is the normalized execution time that corresponds to the operations necessary for the removal of ci and cj (the correspondence depends on the index of operation typology).

Different disassembly operations are performed on the components so defined. Indicating with 5 types of disassembly operations, the distinction between the operations is simple, because once the diversification of joints is incorporated into the analysis of the components, the operations are reduced to translation movements[35]. In this case the times of execution are normalized with respect to the simplest horizontal linear translation, and are summarized in Table 2.

Table 2. Index of component typology and characterization

Index Description Mean time

ijnt /s

Normalized

time ijtn /s

1 Component (to be removed) 1.25 1 2 Screw (to be removed) 0.6 (×turn) 0.48 (× turn)3 Snap fit (to be opened) 1.5 1.2 4 Clip (to be removed) 1 0.8 5 Connection (to be broken) 2 1.6

(2) Replacement action. If MDk is replaced, in period j, the replacement cost is

calculated by

, , , , ,1

,1 1 1

2 ( ) ,

M

R k P k r k D k p i iki

M M M

i i m i ik ij ik jk iki i j

C C C C c mt

w c mt CD mt mt mt

=

= = =

= - + = -

+ -

å

å åå

(16)

where cp,i is the purchase price of ci, iw is the weight of ci,

i is the recyclable coefficient and cm,i is the revenues from the reuse/recycle of the material per unit weight of ci.

The preventive maintenance cost parameter values used in the case study are listed in Table 3.

Table 3. Values for preventive maintenance cost parameters

Parameter Value

Labor cost cwt/($ • h–1) 20.0 Recycled plastic price ($ • kg–1) 0.15 Recycled aluminum price ($ • kg–1) 2.35 Recycled steel price ($ • kg–1) 0.45 Recycled electronics price ($ • kg–1) 0.38 Recycled rubber price ($ • kg–1) 2.45 Recycled copper price ($ • kg–1) 2.45 Recycled Nd-Fe-B Magnet ($ • kg–1) 17.15 Recyclable coefficient 0.85

From the two kinds of cost, the total cost function can be

written as follows:

, ,1 1

.s sN N

C M k R ki i

F C C= =

= +å å (17)

3.4 Formulate multi-objective modularity strategy

optimization problem The two objective functions of the formulation in Eq. (6)

are defined as follows:

1

, ,1 1

minimize difference degree:

1 min ( , ) 1 ,

max( )

minimize preventive maintenance cost:

min ( , ) ,

s.t., modularity( , ) TRUE,

modularity_feasibility( , )

s

s s

Nk

Dks k

N N

C M k R ki i

SF x s

N S

F x s C C

x s

x s

=

= =

æ ö÷ç ÷= -ç ÷ç ÷çè ø

= +

=

=

å

å å

1 2

TRUE,

PM_feasibility( , ) TRUE,

( , ( ), ( ), , ( )).sN

x s

x MT PM MD PM MD PM MD=

=

(18) The properties of the genetic algorithm chromosome are

listed in Table 4.

Table 4. Definition of a genetic algorithm chromosome representing parameter

Chromosome position

Chromosome position name

Crossover method

Possible values

Segment 1 Number of

module Arithmetic 1–55

Segment 2

Physical relationships

between components and

modules

Single point

1–55

Segment 3 Preventive

maintenance schedule

Uniform

0=do nothing 1=maintenance2=replacement


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3.5 Calculate optimal product modularity trade-off

sets based on maintenance consideration. The 100 members of starting population of SPEA2+ are

seeded at random, and the algorithm is run through 500 generations. As shown in Fig. 5, each optimal modularity strategy is represented as a point on the Pareto curve. MS-D is the minimum preventive maintenance interval difference degree modularity strategy, and MS-C is the minimum total preventive maintenance cost modularity strategy. MS-C involves high recycled price components in a module with replacement action and high purchase price components in a module for the maintenance action implementing.

MS-T is defined as the optimal tradeoff modularity strategy between the minimum difference degree and the minimum preventive maintenance cost in Fig. 5. The considered components of the coordinate CNC boring

machine are grouped into 10 modules, which are illustrated in Fig. 7. The module structure and module property of MS-T for the coordinate CNC boring machine is shown in Table 5. Table 6 describes the preventive maintenance structure of MS-T. MS-T can be used to compare different product designs and modularity situations for their maximum “economical” product modularity based on maintenance consideration. The minimum, maximum, and average effective working age of each module in MS-T are shown in Table 7. It shows that the minimum effective working age of each module is equal to zero at the beginning. The effective working age for the modules ranges from roughly 0 to 10 520 h with an average age of about 2880 h. It is helpful to maintenance mangers to track the effective working age of the components. When a module reaches a set effective working age, additional monitoring, tests or inspections are needed to assist in the 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

Property of module

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 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

Module index Preventive maintenance 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

strategy of the coordinate CNC boring machine. Direct production modularity strategy involves a production module that is formed by an assembly of many components. The direct function modularity strategy is defined as point F in Fig. 5. It is a function module that is constructed either 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. That means optimal modularity strategies always have lower potential for total preventive maintenance cost than direct function modularity (technology development aspect) or direct production modularity (production capacity aspect). Directly production modularity or directly function

modularity the coordinate CNC boring machine imposes less preventive maintenance interval difference degree and more preventive maintenance cost.

4 Sensitivity Analysis of Modularity

Parameters

The optimization model developed in Step 4 involves two different types of modularity parameters: preventive maintenance parameters and component reliability parameters. Each component also has three different types of cost, failure cost, labor cost (maintenance cost), and purchase price (replacement cost). Component reliability


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parameters include i and ,i the scale and the shape parameters of component, and ,i the maintenance effect factor for each component. A sensitivity analysis for two different types of modularity parameters is provided in the following paragraphs.

In order to find the effect of the modularity parameters on the structure of the optimal solution two 23 factorial design experiments are designed. Based on this consideration, each experiment has three factors, each with two levels. With one replicate in each experiment, there are

8 different trials. The first experiment assumes that the scale parameter, shape parameter and maintenance effect factor of all components are the same, but each component has two levels, low and high, for failure cost, labor cost, and purchase prices; see Table 8. The second experiment assumes that the preventive maintenance parameters of all components are the same, but each component has two levels for the reliability parameters; as shown in Table 9. MATLAB (R2008 a2) software is utilized to solve the model to reach the exact optimal solution.

Table 8. Values for modularity parameters of experiment 1

Component Maintenance effect factor

εi

Scale parameter

ηi

Shape parameter

βi

Failure cost

cfi/$

Labor cost

cwt/($ • h–1)

Purchase price

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

Component Maintenance effect factor

εi Scale parameter

ηi Shape parameter

βi Failure cost

cfi/$ Labor cost cwt/($ • h–1)

Purchase pricecp,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

parameters Tables 10–13 present the optimal module structure and

preventive maintenance structure of MS-D (minimum preventive maintenance interval difference degree modularity strategy) and MS-C (minimum total preventive maintenance cost modularity strategy) for experiment 1. Although first four components with less failure cost and the last four components with more failure cost, it can be seen that optimal module structure of MS-C and MS-D are

the same. According to the proposed modularity strategy, the preventive maintenance times of system progressed and its effective working age under the set preventive maintenance intervals are shown in Tables 10–13. Observing the effective working age distribution and the preventive maintenance actions, it finds that the failure cost does not noticeably affect the module structure and the frequency (intervals) of preventive maintenance activities in the optimal modularity strategy.

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

Modularity strategy MS-D

Number of module 4

Module structure

Property of module

Module index Component Interval

Module I 1,5,7 5-3-5-5-2-6-4 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


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

Property of module


Module I 1, 5, 7 6-4-5-5-3-3-4 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


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,

because the labor cost for maintenance of components 2 and 6 are much less than their purchase prices for replacement, but they have different failure costs, as shown in Table 8. It is also seen that module I (components 1, 5 and 7), III (components 3 and 4) and IV (components 8) are only replaced, except one maintenance action for module I in Tables 11 and 13. In the above module, labor cost for maintenance of components is greater or equal to their purchase prices for replacement. It seems that the preventive maintenance schedule contains replacement actions instead of maintenance actions. However, module IV is replaced less frequently than other modules because of high labor cost and purchase prices of components 8.

By reviewing the labor cost and purchase prices presented in Table 8 and the optimal module structure in Table 10 and 12, it can be concluded that if all components have the same reliability parameters, the module structure and the frequency (intervals) of preventive maintenance activities in the optimal modularity strategy is affected by just ratio of the labor cost and purchase prices. In addition, the failure cost does not play a significant role in the optimal modularity strategy. 4.2 Sensitivity analysis for preventive maintenance

parameters Tables 14–17 present the optimal module structure and

preventive maintenance structure of MS-D and MS-C for experiment 2. As shown in Eq. (7), the smaller maintenance

effect factor reduces the effective working age of component more than component that has a higher maintenance effect factor. Components 1, 3, 5 and 7 are more likely to be maintained. Therefore, their preventive maintenance intervals are shorter than the others. However, as in Tables 14 and 16, it can be observed that the optimal module structure of MS-D and MS-C are the same. It means that maintenance effect factor does not affect the optimal module structure, when failure cost, labor cost, and purchase prices of all components are the same and scale and shape parameters are different.

As shown in Tables 15 and 17, by comparing the reliability parameters for components in module I and module II, components of each module have the same scale parameter but components in module II have larger value of the shape parameter. It makes more replacement actions for module II. Considering module I and module III, all of them have the same shape parameter, but components in module I have a smaller scale parameter than components in module III. Therefore, more frequent replacement actions are performed in module III. It can be seen that the shape parameter has an effect on the schedule of preventive maintenance actions and much more than scale parameter does. Finally, by comparing the frequency (intervals) of preventive maintenance actions of module I and module IV in Tables 15 and 17, it can be found that module IV with great scale and shape parameters is replaced more 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

Property of Module


Module I 1, 5 20

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


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

Property of Module


Module I 1, 5 15-11

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


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

5 Conclusions (1) This paper has described a five-step modular design

method with the considerations of maintenance related. The reliability and economic assessment models of product modularity strategies are established with the introduction of the effective working age of components. As regards preventive maintenance to the module, the maintenance times of product should be decreased so that the total maintenance cost would be cut down.

(2) Two factorial design experiments based on the modularity parameters are used to investigate the effect of modularity parameters on structure of the optimal modularity strategy.. It finds that labor cost and purchase

price along with scale and shape parameters affect the structure of the optimal modularity strategy but failure cost and improvement factor do not appear to play as an important role.

(3) In most cases, the considered product is supposed to wear-out continuously. A continuation of this work intends to investigate more realistic situations, where the probabilistic properties of the failure intensity models obtained by more elaborated models. The properties of the parameters estimators have to be theoretically studied.

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Biographical notes GAO Yicong, born in 1982, is currently an assistant research fellow at State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, China. He received his PhD degree from Zhejiang University, China, in 2011. His research interests include mechanical design methodology, product green design and advanced manufacturing technology. E-mail: [email protected]

FENG Yixiong, born in 1975, is currently an associate professor at Zhejiang University, China. He received his PhD degree from Zhejiang University, China, in 2004. His research interests include mechanical design methodology and advanced manufacturing technology. E-mail: [email protected]

TAN Jianrong, born in 1954, is currently a professor at Zhejiang University, China. His research interests include mechanical design methodology, CAD/CAE and advanced manufacturing technology. E-mail: [email protected]

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