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Integrated predictive maintenance strategy for manufacturing systems by combining quality

control and mission reliability analysis

Yihai He*, Changchao Gu, Zhaoxiang Chen and Xiao Han

School of Reliability and Systems Engineering, Beihang University, Beijing, China

(Received 13 February 2017; accepted 17 June 2017)

Predictive maintenance (PdM) is an effective means to eliminate potential failures, ensure stable equipment operation

and improve the mission reliability of manufacturing systems and the quality of products, which is the premise of intelli-

gent manufacturing. Therefore, an integrated PdM strategy considering product quality level and mission reliability state

is proposed regarding the intelligent manufacturing philosophy of ‘prediction and manufacturing’. First, the key process

variables are identiﬁed and integrated into the evaluation of the equipment degradation state. Second, the quality devia-

tion index is deﬁned to describe the quality of the product quantitatively according to the co-effect of manufacturing sys-

tem component reliability and product quality in the quality–reliability chain. Third, to achieve changeable production

task demands, mission reliability is deﬁned to characterise the equipment production states comprehensively. The optimal

integrated PdM strategy, which combines quality control and mission reliability analysis, is obtained by minimising the

total cost. Finally, a case study on decision-making with the integrated PdM strategy for a cylinder head manufacturing

system is presented to validate the effectiveness of the proposed method. The ﬁnal results shows that proposed method

achieves approximately 26.02 and 20.54% cost improvement over periodic preventive maintenance and conventional

condition-based maintenance respectively.

Keywords: manufacturing systems; predictive maintenance (PdM); product quality control; mission reliability analysis;

cost optimisation

1. Introduction

The effectiveness of a manufacturing system depends on the quality of its design and a proper maintenance strategy to

prevent the system from failing (Sarkar, Chandra Panja, and Sarkar 2011). Maintenance costs account for a large propor-

tion of the production cost, and this proportion increased rapidly with the development of automation and intelligent

technology (Lu and Sy 2009). A scientiﬁc maintenance strategy reduces equipment failures and prevents expensive pro-

duction shutdowns (Froger et al. 2016). Therefore, maintenance strategies have elicited increasing attention in manufac-

turing industries, and this attention is on extending the useful lifespan of equipment and improving system reliability

and availability.

Maintenance policies can be grouped into two categories according to the objective of dealing with breakdowns and

maintenance (i.e. restore and retain). Correspondingly, the maintenance mode in the operation stage can be divided into

corrective, preventive and predictive maintenance (PdM) (Ding and Kamaruddin 2015; Pan and Lee 2017).

Corrective maintenance is the earliest maintenance mode (Mechefske and Wang 2001). It is used only used to

restore the operating state of the equipment after failure occurs in practical applications; thus, this type tends to cause

serious lag and results in high economic losses. Therefore, corrective maintenance alone does not meet production

requirements.

To address the increasing complexity of manufacturing systems, extensive research has been conducted on preven-

tive maintenance. The results show that a system should be maintained to prevent equipment failure. Periodic mainte-

nance is a major preventive maintenance policy that implements preventive maintenance on equipment at integer

multiples for a ﬁxed period, such as time-based maintenance (Liao and Chen 2003; Sheu and Chang 2010; Doostparast,

Kolahan, and Doostparast 2014; Lee and Cha 2016). Taking into account the situation that the system is not or only

partly used in some period, some scholars proposed usage-based maintenance mode, which introduced monitoring tech-

nology into equipment maintenance decisions (Safaei, Banjevic, and Jardine 2010; Tinga 2010). Evidently, preventive

maintenance is an effective means to prevent or reduce equipment failure and improve equipment reliability. However,

*Corresponding author. Email: hyh@buaa.edu.cn

© 2017 Informa UK Limited, trading as Taylor & Francis Group

International Journal of Production Research, 2017

https://doi.org/10.1080/00207543.2017.1346843

in studies on time-based maintenance or usage-based maintenance, only a few prognostic technologies have been exam-

ined. In uncertain situations, it is difﬁcult to develop a maintenance schedule properly in advance, and it may cause

most equipment to be maintained with a large amount of useful life remaining and resulting in high maintenance costs

(Peng, Dong, and Zuo 2010). Therefore, several periodic preventive maintenance practices cannot satisfy the actual

operating requirements of the modern industry.

Manufacturing industries should execute maintenance activities according to the prognosis of future equipment

health rather than equipment run time because of the direct effect of component degradation on manufacturing system

availability. Therefore, PdM strategy, which is also referred to as condition-based maintenance (CBM) strategy, was pro-

posed with the growth of technology (Peng and van Houtum 2016). Shi and Zeng (2016) proposed a dynamic oppor-

tunistic CBM strategy for multi-component systems according to real-time predictions of the remaining useful life and

by considering economic factors. Gilardoni et al. (2016) proposed a PdM policy for a repairable system by considering

the information obtained from failure history. Raﬁee, Feng, and Coit (2015) presented a CBM policy that implements

imperfect repair for complex systems through a reliability analysis of system components. The direct service object of

the manufacturing system is the production task, and the purpose of system maintenance is to ensure that the production

task is completed with the minimum production cost. However, in these previous studies, the conditions are limited to

the performance status of the manufacturing system components, and the requirements of the production tasks, such as

productivity and product quality, are disregarded.

From the point of view of system engineering, maintenance activities, production planning and quality control are

closely related (Nourelfath, Nahas, and Ben-Daya 2015); maintenance is no longer considered disadvantageous but is

now viewed as a proﬁt maker (Alsyouf 2007). Many studies have been conducted on the relationship between produc-

tion planning and maintenance activities (Chiang, Zhou, and Li 2016; Wu, Zhang, and Cheng 2017). In addition, pro-

duct quality, as the decisive factor of market competition, has become an important part in production management.

Chen and Jin (2005) proposed the quality–reliability (Q–R) chain to illustrate the relationship between component relia-

bility and product quality, and this chain provides the foundation for product quality improvement oriented PdM strate-

gies of manufacturing systems. Subsequently, many scholars have made a deep research on the maintenance strategy for

various manufacturing systems considering the quality of the output, such as single-machine manufacturing systems

(Rivera-Gómez, Gharbi, and Kenné 2013), single-machine manufacturing systems consisting of multiple components

(Lu, Zhou, and Li 2015; Tambe and Kulkarni 2015), multi-station manufacturing systems (Sun et al. 2010) and multi-

stage manufacturing systems (Colledani and Tolio 2012). However, the current production mode of small batch customi-

sation increased the complexity of the operation process of manufacturing system. These studies of integrated

maintenance strategy are lack of effective measures to deﬁne the task execution state from the perspective of perfor-

mance polymorphism. Some studies has also discussed the joint optimisation model, which integrates maintenance pol-

icy, product quality and production planning (Nourelfath, Nahas, and Ben-Daya 2015; Tambe and Kulkarni 2015;

Bouslah, Gharbi, and Pellerin 2016). However, these studies addressed quality loss problems for defective items but not

for product quality level, which ignored the varying degrees of quality deviation ﬂuctuation within the tolerance range

that inﬂuence the inherent reliability of the manufactured product.

In conclusion, as the direct service object of manufacturing systems, the production task cannot be disregarded in

the maintenance decision. Mission reliability can dynamically characterise the ability of equipment to meet the task

requirements (Wu and Hillston 2015), which is the comprehensive embodiment of the task execution state in manufac-

turing system. Product quality control has consistently been a focus in manufacturing operation. As a potential important

item in production task requirements, the quality state of output products should be fully considered to fully characterise

the implementation of production tasks. Mission reliability analysis and quality control enable production managers to

precisely control the manufacturing process from two key aspects of production equipment reliability and quality state

of output products, respectively. Evidently, these factors cannot be ignored in maintenance decision-making. In this

study, a PdM strategy that integrates product quality control and mission reliability analysis was proposed for a deterio-

rating multi-station manufacturing system. Comparing to previous studies in the frame of maintenance strategy for a

manufacturing system, physical multi-station and functional multi-state are fully taken into account in this paper, and

the main contributions are as follows:

(1) A mission reliability modelling method is proposed based the multi-state characteristic of equipment perfor-

mance, and the quantitative relationship between the performance in a multi-state form and the failure rate of

the equipment is established.

(2) Based on the inherent relationship between maintenance strategy, production planning and quality control, a

novel approach for decision-making of integrated PdM is proposed and the product quality is deﬁned as how

well it conforms to the speciﬁcations.

2Y. He et al.

(3) Based on the qualiﬁed rate, the evolution of task demands between the equipment is analysed, and an integrated

PdM strategy for multi-station manufacturing system is proposed.

The rest of the paper is organised as follows. Section 2presents the problem statement. Section 3expounds on the

development of the integrated PdM model. Section 4presents the cost-oriented PdM optimisation method. Section 5

introduces a case study on an automotive cylinder head manufacturing system. Section 6presents the conclusions.

2. Notations and problem description

2.1 Notations

The notations used in this paper are deﬁned as follows:

V

i

(t) Controllable process variables (i=1,2,3,4,…,h)

tRunning time of equipment

t

V

Virtual age of equipment

VðtÞVector of the controllable process variables V

i

(t)

θ

i

Scale parameter in Gamma distribution

υ

i

Positive drift rate of controllable process variables V

i

(t)

KEquipment number

kKQC number (k= 1, 2 ,3, …,n)

ρ(t) Qualiﬁed rate of equipment

q

k

(t) Expected quality deviation index of KQC kat time t

zðtÞVector of the environmental noise

Y

k

(t) Deviation of KQC k

aT

k,b

T

kVectors deﬁning the linear effects of VðtÞand zðtÞon Y

k

(t)

AkA matrix deﬁning the effects of interactions between VðtÞand zðtÞ

φ

k

Baseline constant of KQC deviation Y

k

(t)

g

k

The threshold value of KQC k

C

x

Processing capacity state which related to the failure type of equipment (x=1,2,3,…,M)

p

x

The probability that the equipment runs in processing capacity state C

x

rA binary coefﬁcient. If the rework process exists, r= 1; otherwise, r=0

dProduction task demand

R

d

Mission reliability of equipment about production task d

kðtÞFailure rate function

M, ηThe shape and scale parameters of Weibull distribution

t

l

Time duration of the lth PdM cycle (l=1,2,3,…,E+1)

a

l

Age reduction factor

b

l

Failure rate change factor

β

i

Regression coefﬁcient deﬁnes the effect of V

i

(t) on equipment failure

bA row vector consisting of regression coefﬁcients β

i

Ϛ

l

Environmental impact factor

AlUnavailability of the equipment in period t

l

τExpected value of minimal repair duration

τ′Expected value of single planned maintenance duration

c

c

Corrective maintenance cost

c

p

Planned maintenance cost

c

dq

Cost of dominant quality loss

c

hq

Cost of obsolescence loss

c

i

Cost of indirect loss

TPlanning horizon

C

T

Total cost in planning horizon T

c

r

Expected cost of a single corrective maintenance activity

c

m

Expected cost of a single planned maintenance

ϑExpected cost of economic loss caused by a single defective work in the process

ξ

k

Economic loss caused by per unit deviation of KQC k

σExpected cost of indirect loss caused by overdue

International Journal of Production Research 3

εResidual time from the last planned maintenance activity until the end of the planning horizon

R

ε

Mission reliability of equipment in residual time

R

T

Mission reliability threshold of equipment in planning horizon T

Acronyms

PdM Predictive maintenance

KQCs Key quality characteristics

CBM Condition-based maintenance

2.2 Problem description and assumptions

We considered a manufacturing system and modelled it as involving multiple machines. The production task usually

refers to the number of qualiﬁed products that a manufacturing system must process during a time horizon. The time

horizon is always pre-planned and ﬁnite. Therefore, the integrated PdM strategy studied in this paper is a maintenance

plan within a certain task cycle. Generally, the time horizon planned for a production task is shorter than the life cycle

of the equipment. Therefore, equipment replacement is disregarded in the planning horizon of a production task. The

equipment is in a state of continuous degradation during operation, which can result in increased failure rate and

reduced product quality. Whenever the equipment fails, a corrective maintenance activity is required to restore the

equipment to its state prior to failure. Planned maintenance activities are performed whenever the mission reliability of

the equipment reaches a predetermined threshold. This action reduces equipment degradation but does not restore the

equipment to an as-good-as-new condition. Accordingly, the failure rate is reduced, and product quality is improved. A

PdM model that integrates quality improvement and mission reliability analysis is proposed in this study, and the frame-

work to build the model is presented below.

As shown in Figure 1, given that the quality of manufactured products is a key factor in ensuring the completion of

the production tasks and improving the market share, the process variables that affect the KQCs of the products in the

manufacturing process were identiﬁed. The inﬂuence of these process variables on the quality of products was described

quantitatively with the process model, and the quality deviation index was modelled to characterise the quality level of

the qualiﬁed products. Then, the process variables were integrated into the modelling of the failure rate. By combining

equipment maintenance data, the equipment’s processing capacity and probability distribution state were obtained.

Thereafter, a mission reliability model was built for the equipment based on the qualiﬁed rate, production task demand

and processing capacity state. Finally, an integrated PdM was modelled by combining quality control in the case of the

mission reliability limit, and the comprehensive cost was formulated and minimised to obtain the optimal PdM strategy.

This study aims to develop an integrated PdM model for a multi-station manufacturing system by combining quality

control and mission reliability analysis. This study involves the following assumptions.

(1) Each machine is a physically independent entity, and a perfectly reliable inspection station is available for each

machine. Only qualiﬁed products can enter the next station, and defective products can only be reworked once.

(2) The KQCs are independent of one another.

Production equipment

Planned

maintenance

Imperfect

maintenance

Deterioration

Corrective

maintenance

Minimal

repair

Failure

Process

variables

Mission

reliability

The optimal

PdM strategy

Maintenance actions

Quality

deviation

Failure and

repair data

Modeling the effect of

the process variables on

product quality

Modeling the

failure rate

Analysis of equipment

processing capacity state

Integrated

Modeling and

optimization of PdM

Figure 1. Framework of building the PdM model.

4Y. He et al.

(3) PdM restores the equipment performance to between good as new and bad as old and resets the controllable

process variables to their designed nominal values.

(4) The proportion of each failure mode of the equipment is constant, and the maintenance duration of each failure

mode is independent of the equipment performance degradation level. Thus, the proportional relationship

between parameters p

x

(x=1,2,3,…,M) is constant.

3. Development of the integrated PdM model

3.1 Identiﬁcation of process variables related to product quality

The parameters that signiﬁcantly inﬂuence product quality are referred to as the KQCs of the product. As the main car-

rier of product quality information in the manufacturing process, KQCs are the main starting points of quality analysis

and control. KQCs, whether controlled or not, directly determine the size of the risk of product quality (He et al. 2015).

In the manufacturing process, the process variables that affect product quality can be classiﬁed into controllable and

environmental noise variables. Controllable variables can be used to characterise the performance state of production

equipment, and environmental noise variables are usually random and cannot be controlled under normal production

conditions. Therefore, the most important premise of monitoring and controlling the quality of manufactured products is

to identify the measurable and controllable process variables that affect the perceived quality of the product.

The process variables affecting product quality can be identiﬁed by the evolution of KQCs based on the Axiomatic

design proposed by Suh (2001). Decomposition and mapping analysis are conducted by using axiomatic design theory

to determine the corresponding processing station and process parameters, as shown in Figure 2.

First, customer requirements and product failure data are analysed, and the KQCs of the product are determined.

Second, the product function module, which is related to the KQCs of the product, is determined. Third, the functional

modules are decomposed with the design object analysis method based on the function method tree (Engelhardt 2000).

Finally, the functional requirements are mapped to the corresponding structural components and process parameters.

The degradation of the performance of the manufacturing system components is usually a stochastic process with

nonnegative and independent increments, which can be characterised by the gamma process (Gorjian et al. 2010). Con-

trollable variables in the manufacturing process are expressed by V

i

(t), and the probability density distributions of V

i

(t)

are provided as

GiVitðÞvitðÞ;hi

j

ðÞ¼

hvitðÞ

iViðtÞvitðÞ1exp hiViðtÞ½

CvitðÞðÞ i¼1;2;3;...;h;(1)

where vitðÞand θ

i

are the shape and scale parameters, respectively. The designed nominal values for the controllable

variables are zero. vitðÞ¼titfor t> 0, where υ

i

is the drift rate of V

i

(t). The s-expectation and variance of V

i

(t) are

denoted as

EV

iðtÞ½¼

tit

hi

i¼1;2;3;...h;(2)

Var ViðtÞ½¼

tit

h2

i

i¼1;2;3;...;h:(3)

KQCs

FRs DPs PVs

CAs

Mapping Mapping Mapping Process

domain

Functional

domain

Physical

domain

Figure 2. Schematic of the identiﬁcation of process parameters.

International Journal of Production Research 5

3.2 Quantitative description of product quality in the manufacturing process

The enforcement of monitoring on the product KQCs can reveal the loss severity of quality variations in the manufac-

turing process. In this study, the product quality in the manufacturing process was quantiﬁed. The qualiﬁed rate (qtðÞ)

was used to represent the probability that the KQCs of the manufactured products meet the requirements. Quality devia-

tion index qkðtÞindicates the degree of conformity of the product quality characteristics (k) in the qualiﬁed product.

Y

k

(t) is the KQC deviation of products with manufacturing time t. The deviations of the input quality characteristics

can be disregarded according to assumptions 1 and 2. Therefore, based on the effect of the ordering principle in parame-

ter design, the process model can be denoted as

YkðtÞ¼ukþaT

kVðtÞþbT

kzðtÞþVðtÞTAkzðtÞ;k¼1;2;3;...;n;(4)

where φ

k

is a baseline constant; VðtÞ¼½V1ðtÞ;V2ðtÞ;;VhðtÞ is a vector of the controllable process variables V

i

(t),

and zðtÞis the vector of environmental noise; aT

kand bT

kare the vectors deﬁning the linear effects of VðtÞand zðtÞ,

respectively; and Akis a matrix deﬁning the effects of interactions between VðtÞand zðtÞ. These parameters can be

obtained either through DOE or engineering analysis based on speciﬁc physical process models.

In the ideal condition, the value of the parameter is V

i

(t) = 0. The threshold value of the quality characteristic is g

k

.The

product is not qualiﬁed when the quality test result exceeds the threshold value. Thus, qualiﬁed rate qtðÞcan be expressed as

qtðÞ¼Y

n

k¼1

PrfYkðtÞgkg:(5)

In general, threshold g

k

can be obtained through product speciﬁcations and process capability index C

p

, which is com-

monly used in quality management. The upper and lower bounds on the tolerance range for a given product quality

characteristic are USL and LSL, respectively, and the variance of KQC is MSE, that is, the threshold value of g

k

. The

process capability index is denoted as Cp¼USL LSLðÞ

6ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

MSE

p; thus, threshold g

k

can be obtained with the follow-

ing equation.

gk¼6Cp

USL LSLðÞ

2

(6)

In the ideal condition, V

k

(t) = 0 is obtained from Equation (4).

EY

ktðÞVðtÞ

j

½¼ukþbT

kEzðtÞðÞ;(7)

Var YktðÞVðtÞ

j

½¼bT

kcov zðtÞðÞbkþVðtÞTAk

cov zðtÞðÞAT

kVðtÞ

;(8)

where Y

k0

is the target value for the quality characteristic deviation.

Only qualiﬁed products can enter the next station based on assumption 1. Therefore, quality deviation index qkðtÞ

can be characterised as the closeness of a quality characteristic of the qualiﬁed product to that of the target. The control-

lable process variables are reset to the designed nominal value after each planned maintenance activity, the expected

quality deviation index at time tin each integrated PdM cycle is the same and can be deﬁned as

qktVtðÞ

j

ðÞ¼EY

ktðÞ

2VtðÞ

j

¼VtðÞ

TAkcov zðtÞðÞAT

kþakaT

k

VtðÞ

þ2bT

kcov zðtÞðÞAT

kþukaT

k

VtðÞþbT

kcov zðtÞðÞbkþu2

k

:(9)

In Equation (9), VðtÞis still random due to the uncertainty in the process of component degradation. Considering

the s-expectation on VðtÞ, Equation (9) can be rewritten as

qktðÞ¼EE Y

ktðÞ

2VtðÞ

j

hi

¼EVtðÞ

TAkcov zðtÞðÞAT

kþakaT

k

VtðÞ

þ2bT

kcov zðtÞðÞAT

kþukaT

k

VtðÞþbT

kcov zðtÞðÞbkþu2

k

"#

¼EVtðÞ

TUVtðÞþwTVtðÞþH

hi

¼EVtðÞ

T

hi

UEVtðÞ½þwTEVtðÞ½þ

X

n

i¼1

/iiVar VtðÞ½þH

;(10)

6Y. He et al.

where U¼Akcov zðtÞðÞAT

kþakaT

k,ϕ

ii

is the (i,i)th element of U,wT¼2bT

kcov zðtÞðÞAT

kþukaT

k

, and

H¼bT

kcov zðtÞðÞbkþu2

k.

Then, substituting Equations (2) and (3) into Equation (10) yields

qktðÞ¼2tTU2tt2þwT2ttþX

n

i¼1

/iitih2

itþH;(11)

where t=t1=h1;t2=h2;...th=hh;½.

3.3 Mission reliability connotation

For a manufacturing system, the unexpected shutdowns caused by equipment failures affect the processing capacity of

equipment (i.e. number of produced items per time unit). The functional goal of the manufacturing system is to meet

the production task requirements. Therefore, mission reliability can be quantitatively described as the probability of

equipment to meet the production task demand. It can be expressed by the following equation.

Rd¼Pr VC

x

ðÞBo

fg

;(12)

where VC

x

ðÞis the effective output of equipment that determined by the qualiﬁed rate and processing capacity C

x

.B

o

is

the minimal effective output of equipment in completing the overall production task demand. C

x

is the processing capac-

ity determined by the probability of each failure mode and the corresponding repair time in a certain condition. The fail-

ure modes are classiﬁed according to the length of the repair combined with the cumulative probability of the

occurrence of various failure modes. The distribution probability of processing capacity in this state can be calculated as

displayed in Table 1.

From the perspective of the material input, Equation (5) can be rewritten as follows:

Rd¼Pr CxBI

;(13)

where B

I

stands for the minimum workload of equipment in meeting the overall production task demand. It can be

calculated based on the qualiﬁed rate of the equipment.

BI¼d

qþrq1qðÞ

;(14)

where ris a binary coefﬁcient. If the rework process exists in the current equipment, then r= 1; otherwise, r=0.ρis

the average qualiﬁed rate.

3.4 Modelling of the integrated PdM

3.4.1 Decision-making of the multi-station manufacturing system

For a multi-station manufacturing system, product quality and mission reliability are subject to the common role of rele-

vant workstations. The product KQCs are assumed to be independent of one another, that is, the quality degree of the

qualiﬁed products by upstream station will not affect the production status of the current equipment. Therefore, when

given a production task, the optimal maintenance strategy of associated equipment is determined by the backward trans-

fer of the task demand, as shown in Figure 3.

The decision-making of the integrated PdM strategy for multi-station manufacturing systems is illustrated in Figure 3.

When given a production task for equipment K(d

K

), the equipment operation data of the ﬁnal station should be anal-

ysed, and the total cost of production under the different integrated PdM thresholds is analysed through simulation.

Then, the optimal PdM strategy is determined with the minimum total cost as the criterion. The minimum input load

required to meet the production task demands can be determined once the optimal integrated PdM strategy is

Table 1. Sample for the cumulative probability distribution of processing capacity under certain states.

Processing capacity C

1

C

2

C

3

C

x

…C

M

Probability p

1

p

2

p

3

p

x

…p

M

International Journal of Production Research 7

determined. Accordingly, the minimum input load is the effective output demand (BO

K1) of the previous station. By

analogy, the integrated PdM strategy for the entire manufacturing system can be established gradually.

3.4.2 PdM modelling for single equipment

The single production equipment is considered an example, as illustrated in Figure 4. This equipment is used to fulﬁla

continuous market demand. In the manufacturing process, the production equipment will inevitably lead to failure.

Equipment failure will in turn interfere with normal production activities, such that the planned production task cannot

be implemented. Therefore, the processing capacity is ﬂexible and can be set at a value between zero and the maximum

level C

M

at any time. The production equipment subject to a continuous operation-dependent degradation which leads to

an increasing failure risk and a decreasing qualiﬁed rate. For the process enterprise, maintenance activities should be

arranged reasonably by integrating operation state of the production equipment and market demand changes, so as to

both reduce the random failure of equipment and improve product quality simultaneously. Therefore, maintenance inter-

ventions are required to maintain and restore the performances of the production equipment, as depicted in Figure 4.In

response to each failure event, corrective maintenance is undertaken through minimum repair. In preventively dealing

with equipment degradation, planned imperfect maintenance is performed whenever the mission reliability reaches the

preset threshold.

Equipment K-1 Equipment K

Optimal PdM

Strategy

Material Flow Information Flow

Optimal PdM

Strategy

Mission

reliability

Product

quality

Mission

reliability

Product

quality

Quality

rate

Quality

rate

1

O

K

B−1K

d−I

K

B

1

I

K

B−

O

K

BK

d

Figure 3. Schematic of the PdM strategy for multi-station manufacturing systems.

Production equipment

Planned

maintenance

Imperfect

maintenance

Deterioration Qualified ?

Inspection

Rework ?

No

Yes

Yes

No

Defectives

Mission reliability

analysis

Work

load

Failure

number

Repair time

Probability distribution

of processing capacity

Demand

Material Flow Information Flow

Qualified rate

Corrective

maintenance

Minimal

repair

Failure

Product quality

control

Quality

deviation

I

K

B

O

K

B

Figure 4. Schematic of the integrated PdM strategy for single equipment.

8Y. He et al.

The degradation state of the related equipment can signiﬁcantly affect the failure rate, mission reliability, and product

quality. Planned maintenance activity restores the machine condition to somewhere between as good as new and as bad

as old, so age reduction factor a

l

is introduced to characterise the relative age, and failure rate change factor b

l

is pro-

posed to integrate and represent the effect of controllable process variables on the failure rate. In addition, incorporating

the external environmental factors into the model of equipment failure rate is necessary to quantitatively describe the

effect of the external environment on the evolution of equipment performance degradation. Environmental impact factor

Ϛ

l

can be obtained by feature extraction and parameter evaluation by means of all types of equipment indexes, such as

temperature and humidity (Chan and Meeker 2001). Therefore, the failure rate of the equipment after the lth planned

maintenance activity can be denoted as

klþ1ðtÞ¼1lblklðtþaltlÞ;(15)

where 0 < a

l

<1, b

l

≥1 and Ϛ

l

≥1. The evolution of the equipment failure rate in the planning horizon considering

both internal and external factors is presented in Figure 5.

Age reduction factor a

l

can be derived from historical information through estimation methods, such as maximum

likelihood and least squares. t

l

is the time duration of the lth PdM cycle. Based on the proportional hazard model (Tran

et al. 2012), failure rate change factor b

l

can be expressed by integrating the controllable process variables.

blðtÞ¼exp½bVðtÞ;(16)

where b2Rnis a row vector consisting of regression coefﬁcients deﬁning the effects of the controllable process vari-

ables on equipment failure. The expected value of b

l

is derived by considering the s-expectation on VðtÞdue to the ran-

domness of the process variables VðtÞ.

bl¼EVðtÞfexp½bVðtÞg

¼ZVðtÞ0

exp½bVðtÞG½VðtÞdVðtÞ;(17)

where G½VðtÞ is the joint probability density function of the process variables [V

1

(t), V

2

(t), V

3

(t), …,V

h

(t)]. The drift

process of the controllable process parameters is statistically independent; hence, G½VðtÞ can be expressed as the pro-

duct of the marginal probability density function G[V

1

(t)], G[V

2

(t)], G[V

3

(t)], …,G[V

h

(t)]. Thus, Equation (17) can be

rewritten as

bl¼Zþ1

0Zþ1

0Zþ1

0

exp½bVðtÞG½V1ðtÞdV1ðtÞG½VhðtÞdViðtÞ

¼Y

h

i¼1Zþ1

0

exp½biViðtÞG½ViðtÞdViðtÞ

:(18)

Then, substituting Equation (1) into Equation (18) yields

bl¼Y

h

i¼1Zþ1

0

hvitðÞ

iViðtÞvitðÞ1exp ðhibiÞViðtÞ½

CvitðÞðÞ dViðtÞ:(19)

t1t2t3

Severe environment

Good environment

Failu re rat e fun ctio n (t)

Equipment age

Environmental imp act facto

Pla nned mai ntenance

Figure 5. Hybrid evolution model for equipment failure rate.

International Journal of Production Research 9

θ

i

–β

i

must be positive for i=1,2,…,h; otherwise, the value of parameter b

l

will be inﬁnity under any given t

(Lu, Zhou, and Li 2015). Then, Equation (19) can be rewritten as

bl¼Y

h

i¼1Zþ1

0ðhibiÞvitðÞ

ViðtÞvitðÞ1

CvitðÞðÞexp ðhibiÞViðtÞ½

dViðtÞ

¼Y

h

i¼1Zþ1

0½ðhibiÞViðtÞvitðÞ1

CvitðÞðÞexp ðhibiÞViðtÞ½

d½ðhibiÞViðtÞ

¼Y

h

i¼1

hi

hibi

tit

:(20)

Considering that Weibull distribution is widely adopted to ﬁt the failure rate function of complex mechanical-electric

facilities (Awad 2016), assume that the initial failure rate function can be presented as k1ðtÞ¼ m

=

g

t

=

g

m1. Then,

Equation (15) can be denoted as follows:

klþ1ðtÞ¼1lYh

i¼1

hi

hibi

titm

g

ðtþtVþP

l

f¼1

aftfÞ

g

2

6

6

6

4

3

7

7

7

5

m1

;(21)

where mand ηare the shape and scale parameters, respectively. t

V

is the virtual age of the equipment. If the production

equipment begins operating in a good-as-new state, we have t

V

= 0 These parameters can be ﬁtted based on data from

either the reliability test or historical production.

Assuming that the cumulative probability distribution of the equipment processing capacity within the l+ 1th PdM

cycle is as shown in Table 1, unavailability can also be expressed as follows:

Alþ1¼X

x¼1;2M

pxCMCx

ðÞ

=

CM:(22)

According to the traditional deﬁnition of equipment availability, equipment unavailability can be expressed as the

ratio of the total accidental shutdown time to the total task time. Therefore, in the l+ 1th PdM cycle, equipment

unavailability can be denoted as follows:

Alþ1¼sRtlþ1

0klþ1tðÞdtþs0

tlþ1þs0;(23)

where Rtlþ1

0klþ1tðÞdtrepresents the expected number of failures in the l+ 1th PdM cycle; τ′is the expected value of the

planned maintenance duration. If there is no planned maintenance activity in a cycle, τ′= 0, such as the residual time

from the last planned maintenance activity until the end of planning horizon T.τis the expected value of the minimal

repair duration. It can be ﬁtted by the sum of the products of the proportion of each failure mode δ

e

and the correspond-

ing repair time tr

eas follows:

s¼X

U

e¼1

detr

e:(24)

where Uis the number of failure modes for an equipment.

The qualiﬁed rate produces slight ﬂuctuations because of the change in equipment performance. Consider the pro-

portion of qualiﬁed items produced at time tin the lth PdM cycle, qltðÞ, is a continuous decreasing function of the per-

formance degradation state of the equipment represented by the number of failures per unit time. The constant ρ

0

is

used as the manufacturing qualiﬁed rate in the initial condition, and the expectation of the qualiﬁed rate in the lth PdM

cycle can be denoted as follows:

Eql

ðÞ¼q0c1

tlZtl

0

kldt:(25)

The primary maintenance objective in actual production is ensuring the functional objectives with a cost constraint.

In the intelligent manufacturing idea of ‘prediction and manufacturing,’dynamic modelling and analysis of manufactur-

ing process can be conducted before the production task is performed based on the above analysis. Thereafter, the

10 Y. He et al.

models of related costs for the integrated PdM strategy are established (see Figure 4). Finally, the optimal integrated

PdM strategy can be determined with mission reliability as the variable and total cost as the optimisation objective.

4. Optimisation of the integrated PdM

4.1 Evaluation of related costs for the integrated PdM

Maintenance strategy, production planning and quality are strongly linked. Therefore, when establishing the related cost

model for maintenance activities, despite the corrective maintenance and planned maintenance costs, several other

related costs should be considered. According to the modelling mechanism of the integrated PdM model, related costs

should also include the cost of hidden quality loss resulting from the quality deviation of qualiﬁed products, the cost of

dominant quality loss resulting from unqualiﬁed products and the cost of indirect loss determined by mission reliability,

such as late penalty or reduced orders caused by diminished corporate reputation and other factors. In this section, cor-

rective maintenance cost (c

c

), planned maintenance cost (c

p

), cost of dominant quality loss (c

dq

), cost of obsolescence

loss (c

hq

) and cost of indirect loss (c

i

) are discussed. These costs are formalised in a quantiﬁable manner to determine

how these cost-changing trends play fundamental roles in the selection of PdM strategies and optimal determination of

a speciﬁc integrated PdM strategy.

(1) Corrective maintenance cost

In the manufacturing process, the equipment will inevitably experience random failure. Corrective maintenance is an

equipment performance repair activity that is performed once the equipment fails. A linear relationship exists between

the corrective maintenance cost of equipment and the quantity of random failure in planning horizon T. The equipment

has various failure modes, and these failure modes correspond to different corrective maintenance methods and costs.

Similar to the calculation method of the expected time required for a single corrective maintenance activity, the expecta-

tion of the cost of a single corrective maintenance activity (c

r

) can be obtained. Then, the model of the corrective main-

tenance cost generated in planning horizon Tcan be expressed as

cc¼crX

E

l¼1Ztl

0

kldtþZe

0

kEþ1dt

!

;(26)

e¼TX

E

l¼1

tlEs0;(27)

where E+ 1 stands for the number of PdM cycles in planning horizon Tand Eis the number of planned maintenance

activities in planning horizon T.εcharacterises the residual time from the last planned maintenance activity until the

end of planning horizon T, that is, the duration of the E+ 1th PdM cycle.

(2) Planned maintenance cost

Planned maintenance activity is used to restore the equipment’s performance in the PdM mode. Mission reliability

state is used as a threshold for planned maintenance activities in this study. A planned maintenance activity is performed

whenever mission reliability reaches the preset threshold. The planned maintenance cost is determined by the number of

planned maintenance activities in planning horizon Tunder the assumption that the cost of each planned maintenance

activity is constant, and the number is related to the change trend of mission reliability. c

m

is used to represent the cost

of a single planned maintenance, and the cost of the planned maintenance in planning horizon Tcan be calculated as

follows:

cp¼X

E

l¼1

Nlcm:(28)

where N

l

=1.

(3) Dominant quality loss

Dominant quality loss is caused by an obsolete material with poor quality in the manufacturing process. In this

study, the output quality of each key station is detected by 100%, and the unqualiﬁed WIP is reworked or scrapped

according to the process characteristics. Obviously, the cost of dominant quality loss is affected by the equipment manu-

facturing qualiﬁcation rate. In the process of mission reliability evaluation with processing load as one of the main

International Journal of Production Research 11

parameters, the qualiﬁed rate of the equipment is not improved because the rework process is performed on the original

equipment, and rework also increases the processing load of the equipment. Therefore, the cost of dominant quality loss

in planning horizon Tcan be expressed as

cdq ¼#X

E

l¼1

tlþs0

ðÞ

d

Eql

ðÞ

d

þed

EqEþ1

d

! !

;(29)

where ϑis the cost of economic loss caused by a single defective work in the process.

(4) Hidden quality loss

The cost of hidden quality loss is affected by the technical level and equipment performance and is caused by the

quality deviation of a qualiﬁed product. In the manufacturing stage, ﬂuctuations exist in the quality of qualiﬁed prod-

ucts; these ﬂuctuations are eventually reﬂected through customer use, resulting in product reliability problems. To quan-

titatively express these ﬂuctuations, the quality deviation index of the product is deﬁned in Section 3.2, and its

quantitative model is also provided. Constant parameter ξ

k

(ξ

k

> 0) is determined based on ﬁnancial considerations. The

cost of hidden quality loss is

chq ¼X

n

k¼1X

Eþ1

l¼1

nkZtl

0

qktðÞdt

¼X

n

k¼1X

Eþ1

l¼1

nkZtl

0

2tTU2tt2þwT2ttþX

n

i¼1

/iiVartih2

itþH

!

dt

:(30)

(5) Indirect loss

Accidental equipment shutdown leads to a reduction in equipment processing capacity, which in turn affects the mis-

sion reliability of the equipment. Mission reliability pertains to the probability that the production task would be com-

pleted within the speciﬁed time and condition. Production tasks that cannot be completed on time negatively affect

customer satisfaction, which indirectly results in economic losses, such as late penalty or reduced orders caused by

diminished corporate reputation and other factors. The expected cost of indirect loss (σ) is determined according to

ﬁnancial considerations, the value of which can be derived from expert evaluation. Therefore, the cost of indirect loss c

i

can be expressed as

ci¼rPE

l¼1ðtlþs0Þ

T1RT

ðÞþ

e

T1Re

ðÞ

!

:(31)

The cumulative total cost for a given production task throughout planning horizon Tis deﬁned as follows:

CT¼ccþcpþcdq þchq þci:(32)

The optimal integrated PdM strategy for this production task stage can be obtained by minimising the cumulative

total cost.

4.2 Optimisation of the cumulative total cost

Given the scientiﬁcity and comprehensiveness of mission reliability in describing the production state of equipment,

optimisation of the integrated PdM strategy is analysed with mission reliability as the optimisation variable and mini-

mum cumulative total cost as the optimisation objective. An iterative numerical optimisation procedure for single equip-

ment is developed, as shown in Figure 6.

The optimal mission reliability threshold can be obtained by minimising C

T

according to the integrated PdM strategy

optimisation procedure illustrated in Figure 6, and the associated speciﬁc methods applied to each step are illustrated

below.

Step 1. Basic operation data, such as failure, maintenance and economic data, should be collected before performing

the integrated PdM strategy optimisation. The purpose is to estimate several constant parameters in the models.

Step 2. An initial value (Rmin

T) is set as mission reliability threshold R

T

for an equipment.

12 Y. He et al.

Step 3. The common difference between adjacent processing capability values is set based on the analysis of step 1.

Then, the cumulative probability distribution of processing capacity Cx;px

½is determined based on the given pro-

duction task demand and mission reliability threshold R

T

.

Step 4. Unavailability is calculated with Equation (22). Then, the expected qualiﬁed rate is obtained with Equation

(25).

Step 5. The integrated PdM schedule is determined. The corresponding planned maintenance time points (t

l

) are cal-

culated based on Equation (21) and the unavailability in each integrated PdM cycle. Then, the expected number of

failures in each integrated PdM cycle is obtained with Equation (23).

Step 6. The residual time is calculated based on Equation (27), and the failure rate function is obtained with Equa-

tion (21). Correspondingly, the related parameters in residual time, such as unavailability, expected number of fail-

ures, expected qualiﬁed rate and cumulative probability distribution of processing capacity Cx;p0

x

, are obtained.

Step 7. The cost of hidden quality loss in each integrated PdM cycle is calculated with Equations (11) and (30).

Step 8. Corrective and planned maintenance costs are calculated with Equations (26) and (28)), respectively, in the

planning horizon.

Step 9. According to the expected qualiﬁed rate of each integrated PdM cycle, the cost of dominant quality loss in

the planning horizon is calculated.

Step 10. Mission reliability in residual time is calculated, and the cost of indirect loss is obtained with Equation

(31).

Step 11. The total cost under the mission reliability threshold R

T

limit is calculated.

Step 12. R

T

=R

T

+ΔR

T

is used with ΔR

T

as the step size.

Given an initial

threshold

Determine the

unavailability

Determine the

expected qualified rate

Calcu late the time poin t

(tl) and cumulative

failure number

Determine the related

parameters during

residual time

Calcu late the mission

reliability in residual

time (E+1th cycle)

Calculate the total cost

Optimal mission reliability

threshold (Min CT)

Determine the

Determine the relevant

parameters in PdM

cycle (l=1,2, ,E+1)

Collect the basic

operation data

Determine the

unavailability

Determine

Determine the

expected qualified rate

Quantify the

quality deviation

index of products

Calculate ci

Calculate

cdq

Calculate

cc, cp,chq

1

T

R>TT T

RR R=+Δ

No

Yes

[]

,

xx

Cp

T

R

[]

,

xx

Cp

′

Figure 6. Optimisation procedure of the integrated PdM strategy.

International Journal of Production Research 13

Step 13. Checking is performed to determine whether the optimisation procedure should be terminated. If R

T

>1,

the optimisation procedure is terminated and Step 14 is performed. Otherwise, the process returns to Step 3.

Step 14. The optimal mission reliability threshold, where the mission reliability threshold corresponds to the minimal

comprehensive cost, is determined.

5. Case study

5.1 Background

In this study, the engine cylinder head manufacturing system is regarded as an example to validate the integrated PdM

strategy in consideration of product quality. The cylinder head is the key part of the engine; it is installed on the

cylinder body and seals the cylinder from the upper part. Therefore, the cylinder head is always in contact with high-

temperature, high-pressure gas and bears large mechanical and thermal loads. The machining dimension deviation of the

cylinder head is a bottleneck problem in engine manufacturing. The processing precision of the cylinder head directly

affects the working performance of the engine. Therefore, hidden quality loss cannot be ignored in the manufacturing of

the cylinder head, and quality control of the manufacturing process of the cylinder head is one of the most important

procedures in the quality control of engines. In addition, high accuracy requirements and complex manufacturing pro-

cesses make reasonable maintenance of the cylinder head manufacturing system an important basis to ensure production

task completion. However, the periodic preventive maintenance strategy, which is often used by enterprises, is not good

in dealing with the relationship among maintenance, production and quality and does not conform to the intelligent

manufacturing concept of ‘prediction and manufacturing’. Therefore, facing the ﬁerce competition in the market, estab-

lishing an integrated PdM strategy based on production state prediction and in consideration of the quality of manufac-

turing products is one of the most effective means of improving the competitiveness of products.

In this case, the machining process of the cylinder head involves 19 processes (Table 2). The operation setting of

the cylinder head machining is shown in Figure 7. The KQCs are identiﬁed with the help of manufacturing and quality

experts from the engine provider. The equipment (with ID number 16), which is used in ﬁnishing the intake-side guide

hole, is selected to illustrate the validity and enhancement of the integrated PdM strategy proposed in this study. The

corresponding KQCs are presented in Figure 7.

5.2 Numerical example

The reamer is the key component related to the KQCs in equipment 16. The controllable variables are beat radial and

radius direction of the reamer, which are denoted by V

1

(t) and V

2

(t), respectively. The vibrations of the reamer can affect

the diameter and proper alignment of the guide hole and are regarded as a noise variable denoted by z

1

.

Table 2. Machining process of the cylinder head.

Equipment ID

number Processing procedure

Equipment ID

number Processing procedure

1 Rough-machining the top surface 11 Finishing the tappet column

2 Processing the bottom surface 12 Cleaning

3 Drilling the spark plug hole 13 Assembling the cam shaft cover

4 Machining the valve base 14 Finishing the spark plug hole

5 Pre-cleaning 15 Finishing the exhaust valve base and

guide hole

6 Leakage test 16 Finishing the intake valve base and guide

hole

7 Press ﬁtting the seat ring and catheter 17 Polishing the camshaft hole burr

8 Finish-machining the top surface 18 Final cleaning

9 Polishing the burr in the front and back end

faces

19 Final leakage test

10 Polishing the burr in the intake and exhaust

sides

14 Y. He et al.

Basic data are collected from the production management department. The values of the relevant parameters are

obtained with the maximum likelihood method, as displayed in Table 3. The values for the parameters of the process

model are derived with the response surface method (see, e.g. Allen 2010) and shown in Equations (33) and (34).

Y1ðtÞ¼0:774V1ðtÞþ0:363Z10:481V1ðtÞz1(33)

Y2ðtÞ¼0:982V2ðtÞþ0:523Z1þ0:372V1ðtÞz1(34)

This production equipment is not in a good-as-new state at the beginning of operation, so the equipment has a virtual

age. The interval between adjacent processing capacities is set to Δ= 20. Then, the cumulative probability distribution

of the processing capacity is determined based on failure and maintenance data, as shown in Table 4.

The production task demand for the equipment 16 is d= 150/day based on the parameter values shown in Table 3.

The initial value of the mission reliability threshold is 0.1, and the search range for R

T

is RT2ð0:100;1:000Þwith

R

T

= 0.001 as the searching step length. A numerical search is conducted in MATLAB. Figure 8shows the variation

trend of the ﬁve cost types under different mission reliability thresholds.

The corrective maintenance cost and the cost of hidden quality loss, dominant quality loss and indirect loss exhibit a

downward trend with the increase in the threshold of mission reliability; meanwhile, the planned maintenance cost

Intake -side guide hole

Proper Alignment 0.15

Diameter

0.012

0

5

+

1 2 3 4 5 6 7

8

9

10

11

12

13141516171819

Figure 7. Operation setting of cylinder head machining.

Table 3. Parameter values of the case.

Parameters Values Parameters Values Parameters Values

θ

1

2.05 τ′(day) 0.4 ρ

0

0.99

θ

2

4.28 t

V

(day) 14.24 γ0.03

υ

1

0.0153 ξ

1

($) 10.2 T (day) 150

υ

2

0.0225 ξ

2

($) 23.8 m3

a

l

0.0712 ϑ($) 1.2 η50

Ϛ

l

1c

m

($) 100 β

1

0.436

cov ðz1Þ0.001 c

r

($) 20 β

2

0.910

τ(day) 0.424 σ($) 3000

Table 4. The cumulative probability distribution of processing capacity in the case.

C

x

0 20 40 60 80 100 120 140 160 180 200

p

x

pp p3p5p7p7p10p12p17p1–64p

International Journal of Production Research 15

(c) cdq against RT

(e) ciagainst RT

(a) ccagainst RT

(d) chq against RT

(b) cpagainst RT

00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Mission reliability threshold

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

100

200

300

400

500

600

700

800

Mission reliability threshold

t

s

o

Ccp

t

s

o

Ccc

0 0.2 0.4 0.6 0.8 1

0

200

400

600

800

1000

1200

1400

1600

1800

Mission reliability threshold

ts

o

Cchq

00.2 0.4 0.6 0.8 1

0

500

1000

1500

2000

2500

3000

Mission reliability threshold

t

s

o

Cci

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

200

300

400

500

600

700

800

Mission reliability threshold

tsoC cdq

Figure 8. c

c

,c

p

,c

dq

,c

hq

and c

i

against R

T.

00.1 0.2 0.3 0.4 0.5 0.6 0. 7 0. 8 0.9 1

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Mis s io n reliab ility thres h o ld

(

t

socla

to

TCT )

0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1

800

1000

1200

1400

1600

1800

2000

2200

2400

Mis s io n reliab ilit

y

threshold

(tsoclatoT CT )

Figure 9. C

T

against R

T.

16 Y. He et al.

shows an increasing trend. The trend chart of the total cost against the different mission reliability thresholds is obtained

by combining these ﬁve types of costs; the results are shown in Figure 9.

In Figure 9, the left ﬁgure shows the variations of the total cost (C

T

) against the mission reliability threshold (R

T

)

throughout the search range. The total cost shows a downward trend in general with the increase in the mission reliabil-

ity threshold, and an optimal mission reliability threshold between 0.8 and 1.0 is observed. The right ﬁgure shows the

variations of the total cost in the search range R

T

∈(0.8, 1.0). The total cost generally decreases for R

T

∈(0.8, 0.969]

and increases rapidly for R

T

∈(0.969, 1). The optimal mission reliability threshold is R

T

= 0.969. The optimal integrated

PdM schedule is determined and shown in Table 5.

In Table 5, seven planned maintenance activities are required to be performed in the planning horizon, and the

planned maintenance interval shows a decreasing trend with the increase in the planned maintenance activities because

the planned maintenance activities do not restore the equipment to its ‘good-as-new’condition, but instead slow down

the degradation rate of equipment performance.

With regard to the different equipment and production tasks, the parameter values in Table 3are different, so the

inﬂuence of the different parameter values on the optimal PdM strategy is analysed in this numerical example, as pre-

sented in Tables 6–10.

Table 6shows that the PdM cycle shortens with the increase in the expected cost of a single corrective maintenance

activity; meanwhile, the number of planned maintenance activities increases. This result is due to the necessity of using

frequently planned maintenance activities to reduce equipment failures and the economic loss caused by the shortage of

maintenance.

Table 7shows that when the expected cost of a single planned maintenance activity increases, the time interval of

each PdM cycles increases, and the number of planned maintenance activities decreases. This result implies that when

the planned maintenance costs are high, the planned maintenance activities should be performed less frequently to pre-

vent the wastes caused by excessive maintenance.

Table 8shows that with an increase in both ξ

1

and ξ

2

, the number of planned maintenance activities increases. This trend

implies that with an increase in both ξ

1

and ξ

2

, the product quality defect caused by the deviation of the manufacturing

Table 5. Optimal integrated PdM strategy.

Planned maintenance interval (t

l

)

Residual time C

T

123

42.87 38.82 35.08 32.03 948.12

Table 6. Optimal integrated PdM strategy for different c

r.

c

r

Planned maintenance interval (t

l

)

Residual time Mission reliability threshold1234

20 42.87 38.82 35.08 32.03 0.969

50 37.26 33.64 30.31 27.26 19.93 0.975

Table 7. Optimal integrated PdM strategy for different c

m.

c

m

Planned maintenance interval (t

l

)

Residual time Mission reliability threshold1234

50 37.26 33.64 30.31 27.26 19.93 0.975

100 42.87 38.82 35.08 32.03 0.969

International Journal of Production Research 17

process cannot be ignored. This result implies that more frequent planned maintenance activities are required to reduce

manufacturing process deviation and product quality degradation.

Table 9shows that the higher the importance of a production task is, the higher the mission reliability required to

ensure on-time completion of the task. Accordingly, more planned maintenance is required to ensure the performance of

the equipment.

Table 10 shows that when the wear rates t1;t2

½increase, the time interval of each PdM cycles increases in the plan-

ning horizon because planned maintenance activities should be performed frequently to prevent the equipment from

degrading and to ensure normal production activities.

5.3 Comparative study

A comparative study of the proposed method, periodic preventive maintenance mode, and conventional CBM mode is

performed to verify the effectiveness and advancement of the proposed method based on the case of equipment 16.

Periodic preventive maintenance mode has the characteristics of constant planned maintenance interval. As the name

suggests, the planned maintenance activities will be carried out whenever the running time of the equipment reached its

threshold in this mode. In order to facilitate comparison, the periodic preventive maintenance mode integrates mission

reliability analysis and product quality control. Therefore, the total cost is still the sum of corrective maintenance cost,

planned maintenance cost and the cost of hidden quality loss, dominant quality loss and indirect loss. Based on the

assumptions in Section 2.2, modelling and analysis of the periodic preventive maintenance are conducted. In detail, in

the context of the case study, the time threshold is used as the optimisation target to analyse the total cost change trend.

MATLAB is used to analyse the change trend of the total cost under different time thresholds, and the results are shown

in Figure 10.

The above ﬁgure shows the variations of the total cost (C

T

) against the time threshold throughout the search range t

l

∈(0,150) with time step 0.01. When the planned maintenance interval is too short, a large number of planned

Table 8. Optimal integrated PdM strategy for different ξ

1

and ξ

2.

n1;n2

½

Planned maintenance interval (t

l

)

Residual time Mission reliability threshold1234

[10.2, 23.8] 42.87 38.82 35.08 32.03 0.969

[20.4, 57.6] 37.26 33.64 30.31 27.26 19.93 0.975

Table 9. Optimal integrated PdM strategy for different σ.

c

r

Planned maintenance interval (t

l

)

Residual time Mission reliability threshold1234

3000 42.87 38.82 35.08 32.03 0.969

5000 37.26 33.64 30.31 27.26 19.93 0.975

Table 10. Optimal integrated PdM strategy for different υ

1

and υ

2.

t1;t2

½

Planned maintenance interval (t

l

)

Residual time Mission reliability threshold123

[0.00765, 0.01125] 45.96 41.15 36.76 24.93 0.970

[0.0153, 0.0225] 42.87 38.82 35.08 32.03 0.969

18 Y. He et al.

maintenance activities should result in high economic losses. Therefore, with the increase of the time threshold, the total

cost of the project shows a downward trend; however, when the planned maintenance interval is too long, a large num-

ber of equipment failures would result in high economic losses from corrective maintenance cost and the cost of hidden

quality loss, dominant quality loss and indirect loss, thus the total cost will show a rising trend. The optimal planned

maintenance interval is t

l

= 29.61. The optimal maintenance schedules under the integrated PdM model and periodic pre-

ventive maintenance mode are obtained and shown in Table 11. The comparative result shows that the approach pro-

posed in this study demonstrates a cost saving of 26.02% on average than the periodic preventive maintenance mode.

In conventional CBM mode, the equipment failure rate or basic reliability is usually used to characterise the perfor-

mance state of the equipment, and as a basis for guiding planned maintenance activities. As the name implies, the

planned maintenance activities will be performed whenever the performance state of the equipment reached the predeter-

mined threshold in this mode. In this study, the conventional CBM mode that adopts the basic reliability limit policy is

considered; the total cost is still the sum of the ﬁve costs. A numerical search is conducted in MATLAB, and the results

are shown in Figure 11.

In Figure 11, the variation of the total cost against the basic reliability of equipment is depicted. The overall change

trend is ﬁrst decreased and then increased, and the optimal basic reliability threshold is 0.135. The planned maintenance

schedules under this condition are shown in Table 12.

The total cost in conventional CBM mode is 1193.16. Compared with it, 20.54% should be saved by the proposed

method in this paper. The result implies that with the degradation of the equipment, the capacity of the equipment is

often over-estimated in the conventional CBM mode, resulting in delayed maintenance.

Therefore, the method proposed in this study demonstrates better economic performance than the periodic preventive

maintenance mode and conventional CBM mode.

0 50 100 150

0

2000

4000

6000

8000

10000

12000

14000

Time threshold

Total cost ( CT )

Figure 10. Total cost (C

T

) against the time threshold.

Table 11. Comparison of the proposed method and periodic preventive maintenance mode.

Maintenance modes

Planned maintenance interval (t

l

)

C

T

Cost saving rate1234

Proposed method 42.87 38.82 35.08 948.12 26.02%

Periodic maintenance mode 29.61 29.61 29.61 29.61 1281.60 －

Note: Cost saving rate: the ratio of cost saving to C

T

under the periodic maintenance mode.

International Journal of Production Research 19

6. Conclusions

In this study, in reference to the strong relationship among maintenance strategy, production planning and quality, a

novel idea for an integrated PdM strategy that combines product quality control and mission reliability constraints was

presented in the context of the intelligent manufacturing idea of ‘prediction and manufacturing.’The key controllable

process variables were identiﬁed and integrated into the evaluation of the equipment failure rate. Based on the co-effect

of manufacturing system component reliability and product quality in the QR chain, the quality deviation index was

deﬁned to quantitatively describe the output product quality and was used as a key indicator for quality control in the

manufacturing process. Mission reliability was deﬁned to comprehensively characterise the level of equipment health to

meet the production task demands and was used to characterise the production state. Planned maintenance activities

were performed whenever the mission reliability reached its threshold. The optimal PdM schedule was obtained by min-

imising the total cost, including the corrective maintenance cost, planned maintenance cost, dominant quality loss, hid-

den quality loss and indirect loss over the planning horizon. The integrated PdM strategy formulation for multi-station

manufacturing systems was presented based on task correlation. Finally, a case study was conducted on the integrated

PdM decision-making for a cylinder head manufacturing system to illustrate the effectiveness of the proposed method.

The ﬁnal result showed that the integrated PdM strategy demonstrates better economic performance than the periodic

preventive maintenance mode and the conventional CBM mode in general.

Three issues are provided below for future research on the integrated PdM strategy for manufacturing systems.

(1) Planned maintenance activities with different restoration degrees can be adopted for the modelling of PdM.

(2) Integrating other types of costs during optimisation, such as personnel costs, can be performed.

(3) Integrated production scheduling of manufacturing systems can be adopted in consideration of product quality

improvement, production planning and maintenance strategy formulation.

00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

1000

1500

2000

2500

3000

3500

4000

4500

5000

Basic reliabilit

y

threshold

Total cost ( CT )

Figure 11. Total cost against the basic reliability threshold.

Table 12. Comparison of the proposed method and conventional CBM mode.

Maintenance modes

Planned maintenance interval (t

l

)

C

T

Cost saving rate123

Proposed method 42.87 38.82 35.08 948.12 20.54%

Conventional CBM 43.58 41.11 38.84 1193.16 －

Note: Cost saving rate: the ratio of cost saving to C

T

under the conventional CBM.

20 Y. He et al.

Acknowledgments

The authors would like to thank Prof. Xie Min for his comments and help in preparing the early draft of the paper.

Disclosure statement

No potential conﬂict of interest was reported by the authors.

Funding

This study was supported by the National Natural Science Foundation of China [grant number 61473017] and a general project [num-

ber 6140002050116HK01001] funded by the National Defence Pre-Research Foundation of China.

ORCID

Yihai He http://orcid.org/0000-0002-9110-2672

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