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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 intelligent 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 deviation index is defined to describe the quality of the product quantitatively according to the co-effect of manufacturing system 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.
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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 identied and integrated into the evaluation of the equipment degradation state. Second, the quality devia-
tion index is dened to describe the quality of the product quantitatively according to the co-effect of manufacturing sys-
tem component reliability and product quality in the qualityreliability chain. Third, to achieve changeable production
task demands, mission reliability is dened 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 nal 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 scientic 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 xed 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 difcult 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. Raee, 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 prot 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 qualityreliability (QR) 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 dene 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 uctuation within the tolerance range
that inuence 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 dened as how
well it conforms to the specications.
2Y. He et al.
(3) Based on the qualied 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 dened 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) Qualied 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 dening the linear effects of VðtÞand zðtÞon Y
k
(t)
AkA matrix dening 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 coefcient. 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 coefcient denes the effect of V
i
(t) on equipment failure
bA row vector consisting of regression coefcients β
i
Ϛ
l
Environmental impact factor
AlUnavailability of the equipment in period t
l
τExpected value of minimal repair duration
τExpected 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 qualied products that a manufacturing system must process during a time horizon. The time
horizon is always pre-planned and nite. 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 identied. The inuence 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 qualied products. Then, the process variables were integrated into the modelling of the failure rate. By combining
equipment maintenance data, the equipments processing capacity and probability distribution state were obtained.
Thereafter, a mission reliability model was built for the equipment based on the qualied 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 qualied 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 Identication of process variables related to product quality
The parameters that signicantly inuence 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 classied 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 identied 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
iðtÞ½¼
tit
hi
i¼1;2;3;...h;(2)
Var ViðtÞ½¼
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 identication 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 quantied. The qualied 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 qualied 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 dening the linear effects of VðtÞand zðtÞ,
respectively; and Akis a matrix dening the effects of interactions between VðtÞand zðtÞ. These parameters can be
obtained either through DOE or engineering analysis based on specic 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 qualied when the quality test result exceeds the threshold value. Thus, qualied rate qtðÞcan be expressed as
qtðÞ¼Y
n
k¼1
PrfYkðtÞgkg:(5)
In general, threshold g
k
can be obtained through product specications 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
6ffiffiffiffiffiffiffiffiffi
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
½¼ukþbT
kEzðtÞðÞ;(7)
Var YktðÞVðtÞ
j
½¼bT
kcov zðtÞðÞbkþVðtÞTAk

cov zðtÞðÞAT
kVðtÞ

;(8)
where Y
k0
is the target value for the quality characteristic deviation.
Only qualied 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 qualied 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 dened 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
UEVtðÞ½þwTEVtðÞ½þ
X
n
i¼1
/iiVar VtðÞ½þH
;(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 qualied 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 classied 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 qualied rate of the equipment.
BI¼d
qþrq1qðÞ
;(14)
where ris a binary coefcient. If the rework process exists in the current equipment, then r= 1; otherwise, r=0.ρis
the average qualied 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
qualied 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 nal 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 fulla
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 exible 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 qualied 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
B1K
dI
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 signicantly 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 coefcients dening 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.
bl¼EVðtÞfexp½bVðtÞg
¼ZVðtÞ0
exp½bVðtÞG½VðtÞdVðtÞ;(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
0Zþ1
0
exp½bVðtÞG½V1ðtÞdV1ðtÞG½VhðtÞdViðtÞ
¼Y
h
i¼1Zþ1
0
exp½biViðtÞG½ViðtÞdViðtÞ
:(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 innity 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
0½ðhibiÞViðtÞvitðÞ1
CvitðÞðÞexp ðhibiÞViðtÞ½
d½ðhibiÞViðtÞ
¼Y
h
i¼1
hi
hibi

tit
:(20)
Considering that Weibull distribution is widely adopted to t 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 tted 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;2M
pxCMCx
ðÞ
=
CM:(22)
According to the traditional denition 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; τis 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 tted 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 qualied rate produces slight uctuations because of the change in equipment performance. Consider the pro-
portion of qualied 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 qualied rate in the initial condition, and the expectation of the qualied 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 qualied products, the cost of
dominant quality loss resulting from unqualied 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 quantiable manner to determine
how these cost-changing trends play fundamental roles in the selection of PdM strategies and optimal determination of
a specic 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 equipments 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 unqualied WIP is reworked or scrapped
according to the process characteristics. Obviously, the cost of dominant quality loss is affected by the equipment manu-
facturing qualication rate. In the process of mission reliability evaluation with processing load as one of the main
International Journal of Production Research 11
parameters, the qualied 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 qualied product. In the manufacturing stage, uctuations exist in the quality of qualied prod-
ucts; these uctuations are eventually reected through customer use, resulting in product reliability problems. To quan-
titatively express these uctuations, the quality deviation index of the product is dened in Section 3.2, and its
quantitative model is also provided. Constant parameter ξ
k
(ξ
k
> 0) is determined based on nancial 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 specied 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
nancial 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 dened 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 scienticity 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 specic 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
½is 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 qualied 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 qualied 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 qualied 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 erce 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 identied with the help of manufacturing and quality
experts from the engine provider. The equipment (with ID number 16), which is used in nishing 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 tting 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 RT0:100;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 ve 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 p3p5p7p7p10p12p17p164p
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 ve types of costs; the results are shown in Figure 9.
In Figure 9, the left gure 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 gure 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-newcondition, 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
inuence of the different parameter values on the optimal PdM strategy is analysed in this numerical example, as pre-
sented in Tables 610.
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
½increase, 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 gure 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 ve 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 rst 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 identied 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
dened to quantitatively describe the output product quality and was used as a key indicator for quality control in the
manufacturing process. Mission reliability was dened 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 nal 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 conict 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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22 Y. He et al.
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Due to the development of sensor technologies nowadays, condition-based maintenance (CBM) programs can be established and optimized based on the data collected through condition monitoring. The CBM activities can significantly increase the uptime of a machine. However, they should be conducted in a coordinated way with the production plan to reduce the interruptions. On the other hand, the production lot size should also be optimized by taking the CBM activities into account. Relatively fewer works have been done to investigate the impact of the CBM policy on production lot-sizing and to propose joint optimization models of both the economic manufacturing quantity (EMQ) and CBM policy. In this paper, we evaluate the average long-run cost rate of a degrading manufacturing system using renewal theory. The optimal EMQ and CBM policy can be obtained by minimizing the average long-run cost rate that includes setup cost, inventory holding cost, lost sales cost, predictive maintenance cost and corrective maintenance cost. Unlike previous works on this topic, we allow the use of continuous time and continuous state degradation processes, which broadens the application area of this model. Numerical examples are provided to illustrate the utilization of our model.
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This paper presents a dynamic opportunistic condition-based maintenance strategy for multi-component systems. The strategy is based on real-time predictions of the remaining useful life under the simultaneous consideration of economic and stochastic dependence. First, the effect of a component’s degradation level on the remaining useful life of other components is considered. The remaining useful life of components that have a stochastic dependence on one another is predicted using stochastic filtering theory. Given the condition monitoring history data, we model the effect of a component’s degradation level on the remaining useful life of other components. And a penalty cost evaluates the additional cost of shifting the maintenance time. This allows us to determine the optimal trade-off between reducing the remaining useful life of some components and decreasing the set-up cost of maintenance. An optimization model is then established by choosing the dynamic opportunistic maintenance zone and optimal group structure that minimizes the long-term average maintenance cost of the system. A numerical example including three multi-component systems is presented. The results show that our proposed method maximizes production efficiency on the premise of ensuring system reliability, and reduces the system operation and maintenance costs.