E-Journal of Advanced Maintenance Vol.6 (2014) 1-13
Japan Society of Maintenology

Study of the Optimization of Maintenance Plan for Nuclear Power Plants
Takayuki AOKI1,*, Noriko KODAMA2, Kentaro TAKASE2 and Kenzo MIYA2
1
2

Institute of Fluid Science, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, JapanIIU Corp., 2-7-17 Ikenohata, Taito-ku, Tokyo 110-0008 Japan

ABSTRACTThis paper proposes a quantitative evaluation method for the maintenance plan for nuclear power plants,
developed by introducing the scientific approach, and also proposes a method to search for an optimum
maintenance plan to be obtained by maximizing nuclear safety and economic efficiency simultaneously, thenbalancing them. As a result of consideration, the following results were obtained.
(1) The quantitative evaluation methodology for optimizing the maintenance plan for nuclear power plants wasdeveloped.
(2) The computer simulation of maintenance planning for a couple of BWR systems by using this methodology
was carried out. It was concluded that this methodology can produce a new maintenance plan which meetsthe maintenance targets corresponding to optimum maintenance.
KEYWORDS

ARTICLE INFORMATION

Nuclear Power Plant, Maintenance Optimization, Maintenance Law,
Maintenance Equation, Maintenance Targets, Plant Safety, Plant Economic
Efficiency, Maintenance Plan, Maintenance Work-team Performance

Article history:
Received 16 January 2014
Accepted 2 May 2014

1. Introduction
Since the 1970’s, maintenance in industrial plants has become more and more important. This isbecause industrial plants began growing larger rapidly. Problems, failures and accidents in these large
plants may have very big impact on the owner, society and the environment. Only industrial plantsthat are well designed, constructed, operated and maintained can assure plant safety and economic
efficiency. Maintenance is very important and should be on the same footing with design, construction
and operation. The US nuclear power industry since 1980 is a good example. Since 1980 the US
nuclear plants have placed great emphasis on improving maintenance and, as a result, the plants are
now performing at a very high level of safety and availability.
Up to now, Japan has largely emphasized design, construction and operation rather thanmaintenance in their nuclear plants. This is because maintenance was largely field or site oriented andexperience based. There was little or no interest in developing the foundations of maintenanceactivities in a systematic way and as technical or academic discipline. This is in contrast to design,
construction, and operation where a lot of technical knowledge and experience was assembled, thencoupled with scientific techniques and methods, and organized into technical disciplines that could be
widely taught, shared and applied.
However, recently the situation is shifting. A lot of technical experience and knowledge has also
been accumulating in the maintenance area for Japanese nuclear power plants. So it is an appropriate
time to utilize that information to develop fundamental principles applicable to maintenance. We canthen lay down the foundation, couple these with scientific techniques and methods, and define astructured discipline of maintenance science or engineering.
This study, with the background described above, develops a systematic, quantitative evaluation
method of maintenance for nuclear power plants by introducing the scientific approach. The study
also reveals a method to obtain an optimum maintenance plan to be obtained by seeking to maximize
nuclear safety and economic efficiency simultaneously and balancing them. The summary of the study
is shown below.

*

Corresponding author, E-mail: aoki@wert.ifs.tohoku.ac.jp

ISSN-1883-9894/10 © 2010 – JSM and the authors. All rights reserved.

1

T. Aoki, et al. / Study of Optimization of
Maintenance Plan for Nuclear Power Plant

2. Maintenance Structure and Fundamentals
In a field that maintenance activities for an industrial plant are performed, there are a plantsystem which ageing degradation occurs as time in service passes, and a human system which restores
the ageing degradation but sometimes makes human errors. Maintenance activities are performed
between the two (Fig.1.). As a result, the plant system results in certain conditions, then is put into
service and makes a product.
Plant
SystemAging
Degradation

Human
SystemRepairRefurbishment

Maintenance Activities
Ｐ
Plan

Ａ
Ｄ
Maintenance
Corrective Cycle PDCA
Do
Action(Implement)

LargeComplex
Complex
Giant
Plant
SystemSystemＣ
Check(Evaluate)

Maintenance Implementation
Organization (Work Team)

Fig.1. Maintenance phenomena in maintenance field

By regarding the relationship between the plant system and human system described above as“Maintenance Phenomena” and applying such a scientific methodology as utilized in physics to it,
fundamental things are considered below, which are necessary for maintenance optimization. These
include laws governing maintenance phenomena and its formulation, and methodologies to obtain an
optimum solution of the maintenance plan.
2.1. Maintenance Phenomena and Laws Governing Them
For all industrial plants, a high level of safety and economic efficiency are required
simultaneously, as well as it is required to meet social needs. They cannot survive without meetingthese requirements. This is a basic concept in realizing an excellent maintenance, therefore it could besaid that this is a final goal of maintenance activities.
In this study, these high level items are called as maintenance law, and are defined as follows [1].
 The first law of maintenance: Meeting of Social Needs
Maintenance shall be effective in meeting social needs.
 The second law of maintenance: Maximization of Safety
Maintenance shall demand a maximization of safety under given conditions.
 The third law of maintenance: Maximization of Economic Efficiency
Maintenance shall demand a maximization of economic efficiency (minimization ofmaintenance costs) under given conditions.
2.2. Formulization of Maintenance Law
Generally speaking, providing excessive maintenance to a component to enhance its reliability
and consequently enhance a safety of a whole plant system, then maintenance cost increases andeconomic efficiency decreases. On the contrary, by reducing maintenance activities to enhance aneconomic efficiency of a whole plant system, then the reliability and safety reduces. If thisrelationship between the safety and economic efficiency where the maintenance law governs is
reduced to determining its extreme value, it could be considered to be an equation governing
maintenance, i.e. maintenance equation [2].
The concept of risk (frequency
impact) to enable discussing safety and economic efficiency
on an equal footing, it is considered below to describe a function S relating to safety and a function
relating to economic efficiency.
Function S (hereafter called as “safety risk function”) is a function relating to the safety of thenuclear power plant system and therefore is assumed to be core damage frequency (CDF). CDF
indicates the likelihood of an accident causing reactor core damage in the nuclear power plant which2T. Aoki, et al. / Study of Optimization of
Maintenance Plan for Nuclear Power Plant

consists of n components, meaning
1, 2,3 … . When a failure rate of the i-th component isdefined as , CDF is defined as follows.
| ∈

(1)

When is defined as maintenance plan for the i-th component, a failure rate of the i-th component
can be considered to be a function of , because it is a consequence of the maintenance plan
applied to the i-th component, and is a set of the n components which the nuclear power plantconsists of.
On the other hand, Function E (hereafter called as “Economic risk function”) is a function
relating to the economic efficiency of the nuclear power plant system and, therefore, it is proper to use
a production cost for it here. It should be a maintenance related out of the total production costbecause this study focuses on maintenance only.
As the production cost is a ratio of total maintenance cost () and power generation ( ), it
is shown as below.
∑∈･･
Plannedmaintenancet∑∈

Restoration costfor component failure

･

∑∈

∙

･

Production loss from component
failure in the normal system

･

| ∈Ω

One year(8760 hours)

Plant outage time(hours/year)∑∈･

Plant down time fromcomponent failure in thenormal system

∙

∙

･

Production loss from component
failure in the safety system

Plant down time from component
failure (hours/year)∑∈･

Production loss
from component failure

∙

･

･

Plant down time from component
failure in the safety system

Where,: Total cost including a cost for the planned maintenance plan which is provided to the i-thcomponent, a cost required for the restoration in a failure of the i-th component which has afailure rate and a production loss from the i-th component failure.
: Cost for the planned maintenance plan
which is provided to the i-th component(Yen/year): Operating time per year∑∈
/ 1 ∑∈･∙ ･: Cost for the restoration of the i-th component when it fails（Yen）: Cost for power generation loss corresponding to plant down time due to the i-th component

failure: Generation Failure Frequency as an economic assessment event in the nuclear plants
which consist of the n components. The i-th component has a failure rate of .
：Coefficient of plant output reduction when component fails：Power production loss cost caused by an occurrence of the above terminal condition (\:Yen)(=Unit production loss cost (\/hour)(hours)): Total power production per year
：Rated Power output (kW/hour)3

T. Aoki, et al. / Study of Optimization of
Maintenance Plan for Nuclear Power Plant：8760 hours in a year
：Planned plant outage duration (hours/year）：Forced plant outage duration caused by component failure：Ratio of the frequency of forced plant outages caused by the incompletion of repairing safetyrelated stand-by components within the allowed outage time to the frequency of the safetyrelated stand-by component failures：Time required for restoring failed i-th component (in the case of safety-related stand-bycomponents, it is the time of forced plant outage caused by the incompletion of repairing within
the allowed outage time)Ω ：Set of safety-related stand-by components, and subset of the universal set of n components

constituting a whole plant system
Based on the above, the economic risk function E is expressed by the following equation.
⁄(2)

In this study, the functions S and E respectively are regarded as a function of maintenance planand the maintenance optimization is handled as a problem of discovering a set of maintenance plans∑
for all components in a system of interest which contains all of maintenance plan for eachis required to meet the maintenance goal or targets [3] for nuclear safety andcomponent. ∑economic efficiency.
andare defined as the
The contents discussed above can be expressed as shown in Fig. 2.
tentative targets on safety risk and economic risk respectively which are set for the calculation for
obtaining new improved maintenance plan.

Fig.2 Relationship between plant safety and plant economic efficiency in maintenance field4

T. Aoki, et al. / Study of Optimization of
Maintenance Plan for Nuclear Power Plant

2.3. Approaches on Maintenance Plan and Maintenance Work-team Performance(1) Evaluation of an effect due to the appropriateness of maintenance plan [4]The maintenance plan, i.e. inspection plan or corrective action plan, for components, is very
important. It should be take into account the essential features of component portions that degrade,and their degradation modes. It also needs to specify appropriate maintenance plan for the component
and the appropriate timing when the tasks should be implemented. If the maintenance plan is not
carried out in time, then it is difficult to maintain functions of the component and of the plant systemthat consists of the components, even if maintenance activities based on the appropriate maintenanceplan are appropriate. Therefore, quality of the maintenance plan could give an impact on component
failure rates in the second and the third period in the bathtub curve shown in Fig. 3, rather than failure
rate in the first period known as "initial failure period" by human error, etc. This means that thequality of maintenance plan could change component failure rates in the second and the third period
in the curve.
Thus, in a simulation analysis on maintenance planning, it is necessary to make it possible toincorporate the quality of maintenance plan on the failure rate of components by taking account of theabove.
(2) Evaluation of the effect of performance [4] by maintenance work-team
Maintenance work team performances (accuracy and efficiency) can be considered to be
determined by the three factors of human system, that is, (i) maintenance procedure, (ii) maintenancework-team and (iii) tools including equipment and materials for maintenance. They could give aneffect on component conditions after maintenance work. Therefore, the accuracy of maintenancework-team is evaluated as a factor which gives an effect on component failure rate as describedabove.
If a maintenance work team has higher effectiveness of maintenance work performances, then thatcan be considered to produce lower human error frequency in the first period in the bathtub curve
shown in Fig. 3. If the team has lesser effectiveness, then that can be considered to produce higher
human error frequency.

Fig.3 Relationship between appropriateness of maintenance applied to component and its failure rate

3. Simulation Analysis for Inspection Planning
3.1 Overview of Analysis
The simulation analysis was done by focusing on an inspection plan which is one of themaintenance plans. The primary goal is to obtain an optimum inspection plan for a simplified set ofthe overall BWR systems, i.e. RFW (Reactor Feed Water System) and HPCS (High Pressure Core
Spray system) shown in Fig.4. An overview of the analysis is shown in Fig.5.
3.2 Analytical Model

5

T. Aoki, et al. / Study of Optimization of
Maintenance Plan for Nuclear Power Plant(1) Governing equation used in the Analysis
The functions S and E discussed in the section 2.2 were used for evaluating the safety andeconomic efficiency of the plant systems described above.
Feed Water Heater Room

Feed Water Heater Room

RFW System

Fig.4 Plant systems for the simulation analysis

Fig.5 Production process of optimum maintenance plan(2) Probabilistic analysis model used in this analysis
As for the function S, CDF was calculated by using the example calculation [5] in the condition of
1,100 MWe BWR-5 full-power operation released on the internet. Specifically, the CDF was obtainedby substituting the HPCS failure frequency calculated in this study into one in the example
calculation. In addition, the calculation was done only for large break LOCA, medium break LOCA
and small break LOCA which are major contributors to the CDF.
As for the function E, the calculation was done by taking account of failures of the components
constituting the RFW system and HPCS system.
The failure rate of the RFW was calculated by using the probabilistic risk assessment method. For
this calculation, the power decreased events shown in Table 1 was taken into account and the6

T. Aoki, et al. / Study of Optimization of
Maintenance Plan for Nuclear Power Plant

analytical model including fault tree analysis model shown in Fig.6 was constructed to calculate
failure frequencies of the each event.
The failure rate of the HPCS was also calculated by using the probabilistic risk assessment
method. The failures of HPCS as the safety related stand-by system do not lead to a forced plant
outage if they can be repaired within AOT. But if they cannot, they lead to forced plant shutdown. The
frequency of such forced plant shutdowns was assumed to be 10% of the failure frequency of thesafety related stand-by systems in this study, taking account of the past experiences.

Table 1 Relation between function failure of reactor feed water system and plant power loss
Power Generation
Loss
100%

75%
50%

25%

0%

Failures of the Feed Water Pumps
TD- FWP A

TD-FWP B

MD-FWP A

MD-FWP B

×
－
－
×
×
○
×
×
○
○
×
×
×
○
○
○
○

×
－
－
×
×
×
○
×
×
×
○
○
○
×
○
○
○

×
－
－
○
×
×
×
○
○
×
○
×
○
○
○
×
×

×
－
－
×
○
×
×
○
×
○
×
○
○
○
×
○
×

Failures of the Feed
Water Heaters

Failures of the Feed
Water System Checkvalves

－
×
－
－
－
－
－
－
－
－
－
－
－
－
－
－
－

－
－
×
－
－
－
－
－
－
－
－
－
－
－
－
－
－

×: Failure○: Running－: N/A

Fig.6 Fault tree for used in the simulation analyses (Example)(3) Analytical models of inspection plan and maintenance work-team performance① Improvement of inspection plan
When trying to improve an inspection plan consisting of three factors, i.e. an object to beinspected, inspection tasks for it and timing of the implementation, the followings are taken into
account.
a) Initial failure (The first period in the bathtub curve in Fig.3.)
The initial failure rate can be considered not to be affected by the quality of inspection plan but
could be by maintenance work-team performance, i.e. accuracy of maintenance work. So theinspection is assumed to have no impact from inspection plan in this simulation.
b) Random failure (The second period in the bathtub curve)7

T. Aoki, et al. / Study of Optimization of
Maintenance Plan for Nuclear Power Plant

The random failure rate can be considered to be affected by the quality of inspection plan. So thesimulation analysis is conducted by considering the followings.
 Case 1-1: Overhaul Interval Extension
The period between overhaul of components is extended by a factor of two. The component failure rate in the second period of bathtub curve is assumed to increase proportional to the extended
period. (Ⓐ in Fig.7)
 Case 1-2: Overhaul Interval Extension with Reduced Component Failure Rate Compared to Case
1-1.)
As with the case 1-1, the overhaul interval of component is extended some years, but the failure
rate is assumed to be a half of the case 1-1. (Ⓑ in Fig.7)
 Case 2: Introduction of Simplified Disassembly Inspection
The overhaul interval of component is extended some years, and the simplified disassembly inspection, which means to conduct only maintenance plan of uncoupling and centering for rotating
components, is conducted at the midpoint during the overhaul interval. (ⓒ in Fig.7) This is applied
to only rotating components. As the components are not completely disassembled in this case andtherefore, do not need many, complex or laborious works, it is proper to assume a low probabilityof causing human errors in field work or to expect no initial failures induced by human error.
 Case 3: Condition Based Maintenance (Periodic Monitoring)
The overhaul interval of component is extended some years and the periodic monitoring ofcomponent conditions is frequently conducted between overhauls in a condition-based maintenance mode. (Ⓓ in Fig.7) This is applied to only rotating components like pump or motor, MOV,
and check valve. The other components are assumed to have a regular overhaul as in the past.

Fig.7 Relation between maintenance plan and analytical models of component failure rate

② Maintenance work-team performanceis consisted of the initial failure rate
As shown in Fig.8, the component failure rateand is expressed as follows.
random failure rate
∆

∆

∆

≒

∆

Changing the above equation, the following equation can be obtained.

8∆

and theT. Aoki, et al. / Study of Optimization of
Maintenance Plan for Nuclear Power Plant
∆

∙

(3)

∆

Where,: Average failure rate of the component over the overhaul interval∆ : Initial failure period, ∆ ：Random failure period: Average of the initial failure rateover the initial failure period ∆: Average of the initial failure rateover the initial failure period ∆∆ ：Overhaul interval of the component
As the maintenance work-team performance, i.e. accuracy of field work can be considered to affectmainly an initial failure rate, the following equation is assumed to be true by incorporating an
influence factor ε into the above equation (3). If the maintenance work-team has higher effectivenessthan before, it is assumed to be ε 1. On the contrary, if the maintenance work-team has lesser
effectiveness, it is assumed to be ε 1.

Fig.8 Component failure rate composed of initial and random failure

∙

∆
∆

∙ε

(4)

According to the operating experiences in Japanese nuclear plants, the human error frequency isreported to be about 15% [6], the initial failure rate and random failure rate are 15%, 85%
respectively.
3.3 Method of Analysis(1) Procedure of the simulation analysis
The simulation analysis is conducted as follows.
① The contents of the existing inspection plan for a certain target system are assumed. To improve
the plan, the maintenance plans for some components in the system are selected for maintenanceoptimization, are gathered together as a new inspection plan, and both the old and new plans are9

T. Aoki, et al. / Study of Optimization of
Maintenance Plan for Nuclear Power Plant

analyzed.
② By making use of the relation between tasks for inspection and component failure rate shown in
Fig.7, the safety risk function S and the economic risk function E are calculated for both the oldand new maintenance approaches. Then the difference between the existing and new inspection
plan is evaluated.
③ By making use of the relation between maintenance work-team performance and component failure rate discussed above or varying ε in the equation (4) as a parameter, the safety risk function S
and the economic risk function E are calculated. Then the difference between before and after thechange of ε is evaluated, and the impact of the new plan can be assessed.
(2) Analytical conditions① Assumptions
In consideration of the past performance etc., the followings are assumed in the calculation of thesafety risk function S and the economic risk function E.
 Plant: 1,100MWe BWR-5
 Plant Life: 40 years
 Operating Cycle: 13 months (396 days）
 Plant Outage Duration: 3 months (91 days) Unit production loss cost: \200M/day② Initial conditions etc.
The followings are assumed.
a) Inspection plan
The existing inspection planfor the components in the plant systems is shown at the prechange column in Table 2. The new inspection plan consisting of the candidate tasks for somecomponents in the plant systems is shown at the post-change column in Table 2.
of component in the pre change, cost for repair etc.
b) Failure rate
The data contained in the reference “Investigation on failure rate for PRA [7]” is used in thissimulation analysis. The cost for repair and the duration required for repair are assumed as follows.
 Small failures: \100M, Two weeks
 Medium failures: \500M, One Month Major failures: These cases are excluded in this simulation analysis because they vary over a wide
range with each case.
3.4 Obtained Results and Consideration
The results of the simulation analysis with the change of inspection plan and maintenance workteam performance are shown in Table 3 and table 4 respectively.
(1) Results of the cases of changing inspection plan
The objective of Case 1-1 (Overhaul Interval Extension) is to confirm how much the change ofinspection plan to expand the overhaul intervals for higher economic efficiency impacts on the safetyfunction S (CDF) and the economic function E (Production cost). The result of the analysis showsthat E decreases while failure rates of the components increase. This means that the reduction of E due
to the expansion of overhaul intervals is bigger than the increase of E due to the increase ofcomponent failure rates. The problem here is that for the results of the analysis to be valid, more effort
is required. The effort is needed to develop probabilistic analysis models for the economic risk
evaluation and to create the data base of various component failure rates etc. suitable for the economicrisk evaluation. This is because the PRA methodology was developed for plant safety evaluation andthe component failure rate data for it were also created for plant safety evaluation. Therefore, they
may not have been developed for the purpose of economic risk evaluation as discussed in this paper.
Thus, it may be necessary to review the methodology proposed in this paper and to revise a part of themethodology if necessary.
When component failures, troubles or incidents occur in nuclear power plant in Japan, larger costand longer period for repair are needed in comparison with other advanced countries because

10

T. Aoki, et al. / Study of Optimization of
Maintenance Plan for Nuclear Power Plant

thorough investigation and determination of their causes and perfect countermeasures are required.
For this reason, it is predicted that there is a big difference in the result of economic risk evaluation
between Japanese and other advanced countries’ nuclear power plants.
On the other hand, the result shows that S increases while failure rates of the components increase.
In this way, if the overhaul intervals of the components are extended without anticipation of keeping
their failure rates equal or less than before, sometimes the safety risk becomes higher while theeconomic risk becomes less. If the increase of the safety risk is acceptable comparing with the safetytarget preset before changing the inspection plan.
The objective of Case 1-2 is to confirm how much the change of the inspection plan -- extending
the overhaul intervals of some components for higher economic efficiency -- gives an impact on thesafety function S (CDF) and the economic function E (Production cost). This option is effective only
when a planner has the firm conviction that the extension of overhaul intervals produces no major
increase in the component failure rates. The result of the analysis shows that S remains the same as
before and E significantly decreases. This is quite natural because the component failure rates wereassumed to remain the same as before in Case 1-1. This option may be very effective in such plants as
the Japanese nuclear plants where periodic overhaul of the components in relatively short intervals
has been historically done.
Table 2 Analytical conditions before and after the change of maintenance plan
Reactor Feed Water System
Before the Change
Maintenance Objects

AreaaroundFW
Heaters
AroundFW
Check
ValvesFW Heater

18

Main Pipe

390

Small Bore Pipe
Check Valve

137
4

Main Pipe

36

Small Bore Pipe

10
2

TD-FW Pump(including the
Turbine for Pump
Drive)
AreaaroundTD-FW
Pumps

Main Pipe

6

Small Bore Pipe
Auxiliary Oil Pump

23
1

Motor-driven Pump(including the
motor)

Areaaround
MD-FW
Pumps

Unit
Num
ber

Control System for
the Pump
FCV
Control System for
the FCV

2

Maintenance plan

TBM（Tube ECT）
TBM（Wall Thickness
Measurement etc.）
TBM（NDI）
TBM（Overhaul）

TBM（Wall Thickness
Measurement etc.）
TBM（NDI）
TBM（Overhaul）

TBM（Wall Thickness
Measurement etc.）
TBM（NDI）
TBM（Overhaul）

TBM（Overhaul）

After the Change

Cost(\/Component)

1

Same as on the left

3M

Same as on the left

3M

No change(8)1M
20M

Same as on the left
Same as on the left
CBM (Valve Disc
Monitoring)

1M
20M

No change(8)Interval（6→9,12）
Monitoring Frequency（Every two month)

3M

Same as on the left

3M

No change(8)

1M
130M

Same as on the left
Same as on the left
TBM (Simplified
Disassembly Inspection)
CBM (Vibration
Analysis, Oil Analysis)

1M
130 M

No change(8)Interval（4→6.8）

15 M

Interval（4→6,.8）

0. M

Monitoring Frequency【Every two month】

3M

Same as on the left

3M

No change(8)1M
10MSame as on the left
Same as on the left
TBM (Simplified
Disassembly Inspection)

1M
10 M

No change(8)Interval（8→12,16）

3MInterval（8→12,16）

CBM (Vibration
Analysis, Oil Analysis)

0. M

Monitoring
Frequency(Every twomonth)

Same as on the left

70 M

Interval（8→12,16）

22 M

Interval（8→12,16）

0. M

Monitoring Frequency(Every two month)

50 M

No change(4)

70M

50M

Same as on the left

TBM（Overhaul）

10M

Same as on the left

10 M

No change(4)

3

TBM

17M

TBM

17 M

No change(4)TBM(Pipe Wall
Measurement)
TBM（NDI）
TBM（Overhaul）

3M

Same as on the left

3M

No change(8)1M
10MSame as on the left
Same as on the left
TBM (Simplified
Disassembly Inspection)
CBM (Vibration
Analysis, Oil Analysis)

1M
10 M

No change(8)Interval（8→12,16）

3MInterval（8→12,16）

0. M

Monitoring Frequency(Every two month)

6
23
1

Auxiliary oil pumpOutsidePCVControl System for
the Valve
Emergency DG

InsidePCV

20M

2

Small Bore Pipe

Control System for
the Pump
Reactor Injection
Valve

Cost
(\/Component)

20M

TBM (Simplified
Disassembly Inspection)
CBM (Vibration
Analysis, Oil Analysis)

Main Pipe

High Pressure Core Injection System
Motor-driven Pump

Maintenance plan
(Candidate)Contents of the Change of the Maintenance Plan
Case 2
Case 1
Extension of the Interval(Introduction ofCase 3(Extension of(Before →After)
Simplified(Introduction of
the overhaul
Unit: Month
Disassembly
CBM)
Interval)
Inspection)
Interval（8→12,16）○

1

TBM (Overhaul)

50 M

Same as on the left
TBM (Simplified
Disassembly Inspection)
CBM (Vibration
Analysis, Oil Analysis)

50 M

Interval（8→12,16）

15 M

Interval（8→12,16）

0. M

Monitoring Frequency(Every two month)

1

TBM

50 M

Same as on the left

50 M

No change(4)1

TBM（Overhaul）

10 M

Same as on the left

10 M

Interval（8→12,16）

CBM (Valve Disc
Monitoring)

0. M

Monitoring Frequency(Every two month)

1

TBM

50 M

Same as on the left

50 M

No change(4)2

TBM（Overhaul）

125 M

Same as on the left
CBM (Engine Signature
Analysis)

200 M

Interval（8→12,16）
Monitoring Frequency(Every one month)

25 M

Same as on the left

50 M

3M
10 M

Same as on the left
Same as on the left

3M
10 M

No change(8)No change(8)30 MSame as on the left

30 M

Interval（8→12,16）

3M

Same as on the left

3M

No change(8)1MSame as on the left

1M

No change(8)Control System for
the EDG
Main Pipe
Small Bore Pipe
Condensate Storage
Tank

60
13

Main Pipe

5

Small Bore Pipe

1

2

1

TBM

TBM（Overhaul）
TBM(Pipe Wall
Measurement)
TBM（NDI）

11

0. M

○
○

○
○
○

○
○
○
○
○
○

○
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T. Aoki, et al. / Study of Optimization of
Maintenance Plan for Nuclear Power Plant

The objective of Case 2 (Introduction of Simplified Disassembly Inspection) is to confirm how
much the change of the inspection plan -- extending the overhaul intervals of some components andadding simplified maintenance (for example, simple maintenance works including just only
uncoupling and centering for rotating components) at the midpoint of the extended interval between
two overhauls -- gives an impact on S and E. This case is derived from the good practices in the US
nuclear plants that the simplified maintenance (uncoupling and centering) has been successfully
applied to such rotating components as pumps or motors because they have had relatively many
failures due to misalignment, mismatch, center shifting etc. The result of the analysis shows that S
does not increase and E decreases. This option promises a certain level of economic effect without
any increase of plant safety risk. It may also provide less human error rate because of less field workby maintenance team. But it should be noted that this option is effective only when it needs less fieldwork or cost, and a planner has the firm conviction that it produces no major increase in thecomponent failure rates.
Table 3 Effect of the change of maintenance plan on plant safety and economic efficiency
Case

Base Case(A)\/Year490,024,686

Planned Maintenance Cost\/Year448,600,000

Unplanned Maintenance Cost\/Year23,139,899

Cost due to Generation Loss ( Failure of RFW)\/Year

13,029,172

Cost due to Generation Loss (Failure of HPCS)\/YearCase 1-1(Overhaul interval: twice
the base case)371,892,377
298,743,081
316,575,000
228,550,000
31,681,399
40,799,170
16,410,376
20,066,989
7,225,602
9,326,922
5,988,649,900
5,987,620,300
227
227
0.109
0.134
0.04820.06220.0621 (24% Decrease)0.0499 (39% Decrease)

Evaluation Items
1

2

Total Maintenance Cost

(2）

Total Power Generation (B)5,255,615

Kwh/Year

5,989,581,800

Annual Ope. Hour－Plant Outage Hours

Day/Year

227

Generation Loss (Failure of RFW)

Day/Year

0.0869Generation Loss (Failure of HPCS)

Day/Year0.0350

Unit Cost for Maintenance (A/B)\/Kwh
3(Economic Risk )(1) Upper row：Calculation results in case of 1.5 times the overhaul interval in the base case.
Lower row：Calculation results in case of 2 times the overhaul interval in the base case.
(2) This includes a maintenance cost of all the components considered in this calculation.
Case

Base Case

Evaluation Items

1

Core Damage Frequency(1)
CDF( /Reactor Year）（Safety Risk ）0.0818

Case of 1.5 times the overhaulinterval in the base case
2.07

Case of 2 times the overhaul intervalin the base case

10

Case 1-2(Failure rate: a half ofCase 1-1)
357,999,686
269,974,686
316,575,000
228,550,000
23,139,899
23,139,899
13,029,172
13,029,172
5,255,615
5,255,615
5,989,581,800
5,989,581,800
227
2270.08690.08690.03500.03500.0598 (27% Decrease)0.0451 (45% Decrease)

Case 2(Introduction of Simplified
Disassembly Inspection)
453,166,224
433,433,976
416,425,000
393,350,000
18,562,288
21,831,700
12,954,697
13,005,625
5,224,240
5,246,650
5,989,600,300
5,989,587,100
227
2270.08640.08670.03480.03500.0757 ( 7% Decrease)0.0724 (11% Decrease)

Case 3(Introduction of CBM)
408,652,158
381,464,272
391,600,000
365,100,000
3,927,386
3,380,835
12,549,573
12,539,476
575,199443,961
5,990,554,900
5,990,511,100
227
2270.08370.08360.00380.00300.0682 (17% Decrease)0.0637 (22% Decrease)

Case 1-1

Case 1-2

Case 2

Case 32.65 10(28％ Increase)

2.07 10( 0%)

2.06 10(0.5% Decrease)

6.98 10(66% Decrease)

3.26 10(57％ Increase)

2.07 10( 0%)

2.07 10( 0%)6.60 10(68% Decrease)(1) The calculation was done by focusing on Small, Intermediate and Large LOCA out of all CDF events.

Table 4 Effect of the change of maintenance work-team performance on plant safety and economic efficiency
Case
Evaluation Items
ε 0.1
(1）
Total Maintenance Cost (A)\/Year
484,410,423
Planned Maintenance Cost\/Year448,600,000
Unplanned Maintenance Cost\/Year20,013,325
Cost due to Generation Loss ( Failure of\/Year11,250,991
RFW)
Cost due to Generation Loss (Failure of\/Year4,546,107
HPCS)
2Total Power Generation (B)Kwh/Year
5,990,200,000
Annual Ope. Hour－Plant Outage Hours
Day/Year
227
Generation Loss (Failure of RFW)
Day/Year0.0750Generation Loss (Failure of HPCS)
Day/Year0.0303
3
Unit Cost for Maintenance (A/B)
0.0809\/Kwh(Economic Risk )(1.1%)(1) This includes a maintenance cost of all the components considered in this calculation.

ε1

Maintenance Work-team Performance Improvement Factor
0.5
ε 0.8
ε 1.0
486,904,806
489,400,541
490,024,686
448,600,000
448,600,000
448,600,000
21,402,810
22,792,460
23,139,899

ε1.5
493,146,678
448,600,000
24,877,246

12,831,300

13,029,172

13,425,139

4,861,444

5,176,781

5,255,615

5,413,283

5,649,786

5,989,824,700
227
0.08030.03240.0813(0.6% Decrease)

5,989,632,000
227
0.08550.03450.0816(0.2% Decrease)

5,989,581,800
227
0.08690.03505,989,484,100
227
0.08950.03610.0820(0.2% Increase)

5,989,336,300
227
0.09350.03770.0823(0.6% Increase)

0.081814,019,646

Maintenance Work-team Performance Improvement Factor
ε

0.1

ε

0.5

ε

0.8

ε

1.0

ε

1.2

ε

1.5

Core Damage Frequency CDF（ ）（ /炉年）

1.81 10

1.92

10

2.01

10

2.07

10

2.13

10

2.21

10

（安全リスク ）(12.6% Decrease)

1

1

1.2
491,273,229
448,600,000
23,834,807

12,040,552

Case
Evaluation Items

ε(7.2% Decrease)(2.9% Decrease)（Base Case）(2.9% Increase)(6.8% Increase)(1) The calculation was done by focusing on Small, Intermediate and Large LOCA out of all CDF events.

The objective of Case 3 (Condition Based Maintenance) is to confirm how much the change of theinspection plan -- extending the overhaul intervals of some components and adding frequent condition
monitoring to check the integrity of the components over the extended interval between overhauls-gives an impact on S and E. The result of the analysis shows that both S and E decrease significantly.
This option should be incorporated into the existing inspection plan for maintenance optimization. But

12

T. Aoki, et al. / Study of Optimization of
Maintenance Plan for Nuclear Power Plant

it is effective only when some condition monitoring technologies exist which are applicable to detect
failure symptom due to degradation and a planner has the firm conviction that it is a reliable
technology. Fortunately, several kinds of condition monitoring technologies, for example, vibration
analysis, lubricant analysis, MOV analysis, diesel engine analysis etc., have been applied tocomponents in US and European nuclear power plants for a long time and they are considered to be
proven. So it is expected that those technologies are applied to Japanese nuclear power plants andmany other new condition monitoring technologies will be developed.
(2) Results of the cases of changing maintenance work-team performance
The objective of this analysis is to confirm how much the change of maintenance work-teamperformance (Accuracy of field work) gives an impact on S and E. The result of the analysis showsthat the maintenance work-team performance has an insignificant effect on E, but has a significant
effect on S because an improvement of maintenance work-team performance could reduce the safety
risk S significantly.
εε

0.1 (The initial failure rate is assumed to nearly equal zero.): 12.5% down
1.5 (The initial failure rate is assumed to be much greater than in previous years.): 6.8% up

If the rationalization of maintenance progresses in the future, then the future random failure rates
of components would be less than in previous years, and the improvement of maintenance work-teamperformance to reduce initial failure rates would become increasingly important. Therefore, it will
become more important to make a quantitative correlation quantitatively between maintenance workteam performance and component failure rates. Additionally, the improvement of maintenance workteam performance can be achieved by improving the three factors of the human system inmaintenance (maintenance work procedure, maintenance work-team and tools) through education andtraining, benchmark activities, workshops etc.
4. Conclusion
Recently a lot of technical experience and knowledge has been accumulating in the maintenancearea for Japanese nuclear power plants. So it is an appropriate time to utilize that information todevelop fundamental principles applicable to maintenance. With this background, this study
developed a methodology of making a new inspection plan and new on-site work-team plan, whichmeet the maintenance targets considered to be optimum at that time. The method introduces the use of
the scientific and quantitative approach, and also revealed that it was possible to assess new plans
through computer simulation.

References[1] Japan Society of Maintenology, “Investigation on the methods inspecting maintenance activities based on
the maintenance program for the nuclear power plants”, pp.199-201 (February 2008)[2] Kenzo Miya, “Construction of Maintenology (1) -Framework for construction and methodology -”, Japan
Society of Maintenology, Vol.7，No.1 (2008)[3] Takayuki Aoki, “Study on a quantitative evaluation method of maintenance importance for giant complex
plant system”, Japan Society of Maintenology, Vol.9, No.3, pp.25-30 (2010)[4] Takayuki Aoki, “Study on quantitative evaluation method of equipment maintenance level and plant safetylevel for giant complex plant system”, Japan Society of Maintenology, Vol.9, No.3, pp.31-36 (2010)[5] Japan Nuclear Energy Safety Organization, “Standardization of PSA methodology in JNES = Level 1 PSA
method for internal events during power operation = (Separate volume 2) Report on Level 1 PSA standard
for internal events during power operation = BWR-5 plant = ”, JNES/SAE07 -040, 07解部報-0040 (April
2007)[6] Satoshi Haba, “What is “Limiting Conditions for Operation”? About the current LCO events”, Atomic
Energy Society of Japan, Vol. 51, No. 6, pp.479-483 (2009)[7] “Investigation on failure rate data for PSA”, Nuclear Safety Research Association (March 1997)

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