WANG Lei( )， ZHANG Yaohui()

Army Academy of Armored Force， Beijing 100072， China

Abstract： Overview about three key contents of condition-based maintenance decision-making of a multi-component system is analyzed based on maintenance optimization and modeling. The component deterioration model， the correlation between the degraded components and the system configuration are analyzed separately in the deterioration model of multi-component system. For the maintenance polices， the opportunistic maintenance (OM) policy and the grouping maintenance (GM) policy are analyzed and summarized in combination with the condition-based maintenance (CBM) modeling of multi-component system. It is put forward that CBM modeling of multi-component system should be further researched based on the inspection interval and the maintenance threshold of multi-component system in availability.

Key words： multi-component system； condition-based maintenance； maintenance polices

Introduction

When the engineering system is used to work under the environment， its components would be on deterioration or failure stochastically. Maintenance activities can be achieved by taking preventive maintenance and corrective maintenance to restore or improve the state of the system， as an essential part of the restoration of engineering system’s functions， they become particularly important[1]. With the improvement of the complexity of modern equipment and the development of monitoring technology and maintenance polices， condition-based maintenance (CBM) is based on the current state of the system to make maintenance polices or plans， to avoid the problems of under-maintenance and over-maintenance. CBM is known as a model and effective maintenance technique which is based on the information collected from condition monitoring process, described the deterioration of the system or component, and determined the optimal threshold for status parameters.

The existing CBM methods are made of individual components， rather than the multi-component systems. In reality， The multi-component system often consists of multiple components which have maintenance dependencies. That is， it can take the opportunity to group the maintenance of the multi-component systems simultaneously when a component is stopped for maintenance. Some of the literature is devoted to solving the problems of the multi-component system maintenance. The multi-component series system as a two-part series system was simplified and a time-based maintenance model was established. Chenetal.[3]considered the maintenance dependencies among the multi-component system， and took the preventive maintenance policy fornparallel devices whose components have similar intervals. Songetal.[4]considered the maintenance dependencies among the multi-component system， and established the interval model which combined the failure rate of components. The existing research studied the application of multi-component system maintenance polices in combination with preventive maintenance polices rather than CBM. Therefore， this paper focuses on the study of stochastic deterioration model and maintenance polices in CBM modeling of multi-component system.

1 Multi-component System Deterioration Model

In CBM model， the stochastic deterioration model is essentially to find out the function mapping relationship between the degraded parameters and the state of component. In CBM model of the multi-component system， the model is the first to find out the deterioration distribution of the system. In this section， it is consisted of three key contents which are the component deterioration model， the deteriorated components correlation， and the system configuration.

1.1 Component deterioration model

There are two kinds of deterioration modeling methods， which are based on stochastic process and life distribution. The modeling method which based on stochastic process is applied the Markov theory to describe the deterioration of the system. The modeling method which based on life distribution is mainly to establish the relationship between deterioration state and life of the multi-component system. The uncertain parameters in the second model are estimated by the data which obtained from the system monitoring technology.

In the modeling based on the stochastic process， the Markov decision model is the main method which studies the stochastic sequential decision problem. In Refs. [5-8]， it can clearly show the changing state and the transfer research， and carry out the maintenance policy on different state points. The Markov chain is used to optimizing the detection interval of system and CBM threshold when system in the steady state and the time approaches the infinity. At present， in order to avoid the problem of “dimension of the explosion” and establish the regenerative process， most of the Markov decision methods are described the state of component’s transfer process. The effect of preventive maintenance is often considered identical every time. In reality， the component’s failure rate has been continuing to increase， with the times of maintenance activities and the age of equipment service increasing. That is， the possibility of failure rate is increasing， so the preventive maintenance interval should be corresponding change， rather than be consistent.

In the modeling based on the life distribution， the proportional hazards model (PHM) and the proportional intensity model (PIM) are main methods. PHM is proposed by Cox， which is a multivariate nonlinear regression method. It takes into account the effect of covariates on the deterioration state of the system and characterizes the deterioration state in the form of probability[10]. Wangetal.[11]established PHM model to describe the deterioration process and combined the failure threshold and the maintenance inspection interval to minimize the total maintenance cost. The PHM model was established to describe the effect of dynamic changes on equipment status， based on the inspection interval[12]. PHM model is established to make maintenance decisions based on status monitoring information[13]. On the one hand， PHM model can take into considering the equipment’s life information and status information as covariates in the quantitative point of view. On the other hand， PHM model is hard to describe the whole process of deterioration accurately. PIM is developed on the basis of the PHM. It is applicable to describe the repairable system by imperfect maintenance[14]. make the maintenance decision， PIM is established to describe the changing state of the equipment in the minimum maintenance cost， combined with the fault data and monitoring data of the repairable system[15]. Zhaoetal.[16]took PIM to describe the status of the wind gearbox and determine the maintenance threshold. PIM is taking into account the maintenance effect of equipment to infer the covariate effect of the system life， based on a large number of historical information of maintenance and monitoring data.

1.2 Deteriorated components correlation

As most components work in common environment， to assume that components are independent is not often appropriate. There is obvious connection among the components in CBM model of the multi-component system. Cho and Parlar[17]divided the maintenance relationships among components into stochastic dependency， economic dependency， and structural dependency. In this section， stochastic dependency was discussed， which described the effect on the lifetime distribution among components. Murthy and Nguyen[18-19]summed up two related types in stochastic dependency. Nakagawa and Murthy[20]extended the two related types to the following three tyes.

(1) Type I fault related. When a component in the system fails， it will cause a certain probability of other components to be fault.

(2) Type II fault related. When a component in the system fails， it will affect the failure rate of other components， causing another component to accelerate the deterioration of component；

(3) Random damage related. Two parts of the system， when one of the components fails， it will cause random damage to another component. When the random damage accumulated to a certain extent， another component will be fault later.

In Ref. [21]， it is established the reliability model of the system in a dynamic preventive replacement policy for two-part parallel systems with type fault I and II related simultaneously. In Ref. [22]， it is established the Poisson shock deterioration model which based on the stochastic process. In the study of maintenance policy related to random correlation， the two-part system is difficult to be popularized.

1.3 System configuration

Unlike the single-component system， the multi-component system usually contains multiple components which take into account both the deterioration model of each component and the system structural factors. In this section， the system configuration will be divided intoKout ofnsystem and complex system.

1)Kout ofnsystem， that is， the system is divided into three forms： a series system， parallel system， and redundant system， by the value ofKchanging. TheKout ofnsystem is widely used in the maintenance model， in which the most extensive form is simplified the multi-component system as a series system. Parallel system and redundant system are also mentioned in the literature.

2) Complex system， that is， mixed two or more basic forms of system configuration， such as a series， parallel， redundant and other forms system. At present， the complex system is the most common form of system configuration in the industry and military areas. In order to simplify the maintenance modeling of complex system， the complex system is simplified as a system which consists of a small number of critical components and a large number of uncritical components. The fault of the uncritical component will not affect the system， but the fault of the critical components will lead the entire system to be on downtime. It is necessary to establish a deterioration model of the critical component to prevent such losses. Cheng[23]established a stochastic degradation model of critical components， in which the complex system is simplified as a multi-component system. The system is composed of critical components and common components in series.

2 Multi-component System Maintenance Policies

The development of multi-component system maintenance policies depends on the deterioration of components and thedependences among components. For systems where component fault rate is independent of each other， the optimal maintenance policy of the system only needs to consider the dependences among the components. In the multi-component system maintenance model， the most common application is economic dependency， which will not affect the deterioration model of the component. The key issue is considering how to combine the different parts of the maintenance activities into together to ensure work efficiency， meanwhile， and saving maintenance costs. While the structural dependency and stochastic dependency is caring the effect on the life distribution or deterioration of the component. The main problem is how to obtain a more accurate life distribution function or deterioration state curve when considering the mutual influence of the components.

The most popular maintenance strategies in multi-component system modeling research and application are opportunity maintenance policies and group maintenance policies which are taking into account economic dependency of component. The analysis of two kinds of maintenance policies combined with multi-component system CBM is as follows.

2.1 Opportunistic maintenance (OM) policies

To maximize the availability， minimize the cost of a multi-component system， OM policy takes full advantage of planned or component maintenance downtime and other opportunities for the components in non-failure status. Zhaoetal.[24]proposed a new definition of “opportunity”， which can take maintenance activities for other components simultaneously when a component in system monitoring or taking maintenance activities. Meanwhile they defined the concept of the status indicator to describe the state of the component， established CBM threshold function and OM threshold function. Then it determines whether the component needs to be repaired， how to repair it and makes the maintenance policy according to the relationship between the status indicator and the two threshold functions. Based on the gamma distribution of the components， Javidetal.[25] established the simulation model with the continuous monitoring technologies， with taking use of dynamic grouping opportunistic maintenance policy combined with CBM applied to multi-component system maintenance. Xuetal.[26]defined the expression of the relevance set for power equipment in a series system， based on the OM combined with CBM. Based on the exponential distribution of the components， Zhuetal.[27]proposed a multi-component system OM model with two failure modes in the context of the system， to evaluate the average long run cost per time unit， by imperfect prediction signal. Based on a stochastic gamma process， Mahmoodetal.[28]used a deterioration model for offshore wind turbine system， and proposed an opportunistic condition-based maintenance， using a Monte-Carlo simulation technique to evaluate the average long-run maintenance cost per unit time.

The advantages of combined OM with CBM are sharing fixed maintenance costs and maintenance time， reducing system maintenance costs and improving system availability through the combination of maintenance activities. The shortages of combined OM with CBM are lacking the plan of maintenance according to the changing status of component.

2.2 Grouping maintenance (GM) policy

To form a system maintenance plan， GM policy takes full advantage of components the maintenance task and interval to establish a model. Su and Chen[29]established multi-component system CBM deterioration model， based on the stochastic process， combining the minimum maintenance， preventive maintenance and corrective maintenance at the inspection point with equidistant time intervals. Based on the economic dependency of components， Bouvardetal.[30]presented a dynamic grouping maintenance policy for multi-component system deterioration models， according to the rolling horizon， to improve the maintenance planning. With positive economic dependency of components， Phucetal.[31]presented a new algorithm called maintenance opportunities combined the dynamic grouping maintenance policy for multi-component system， to reduce maintenance costs. With positive and negative economic dependency of components， Haietal.[32]proposed a dynamic grouping maintenance policy based on rolling horizon and genetic algorithm， to take into account system structure and reduce the maintenance cost. Phucetal.[33]simplified the multi-component system to a series system， to find a maintenance planning in dynamic grouping policy with genetic algorithm and MULTIFIT algorithm. With structural dependency and economic dependency of components， Verbertetal.[34]proposed a dynamic grouping maintenance policy based on timely maintenance planning combined CBM in multi-component systems， established a degradation model for component， discussing the maintenance planning at the system level.

The advantages of combined GM with CBM can adjust the way of combination to achieve dynamic maintenance timely， according to the environment. Meanwhile the maintenance policy can be fully prepared. The shortages of combined GM with CBM are that there will be a repeat preparation at the inspection point， if the planned time is greater than the detection interval， it will lead to a reassessment of the preparation.

3 Summary and Prospects

In summary， most of the researches on multi-component system CBM modeling focused on cost-saving goals. There is a limit to the availability of military equipment.

(1) Research on optimization modeling of multi-component system CBM with opportunity context

Most multi-component system CBM models are simplified the maintenance policy of system. It is commonly to combine the maintenance policy of component rather than multi-component system. It is necessary to study maintenance policy of multi-component system with opportunity context. When the one component is in monitoring or taking maintenance activities, others can take CBM activities simultaneously.

(2) Research on optimization modeling of multi-component system CBM inspection interval

Most CBM models are based on the equidistant inspection interval， and the state is transformed into the amount of time to analysis the remaining life of the components. It could focus on the research which considered the maintenance effect and combined the optimization of the inspection interval at the system level.

(3) Research on the availability of Multi-component system CBM threshold modeling

To minimize cost and improve the general demand for profits， the research of multi-component system CBM modeling is focus on modeling of cost target. In military areas， it is often focused on the availability of the system than the cost which is only as a constraint. In view of the availability of the system， the research on optimization modeling of multi-component system CBM threshold is more effectiveness in the military system， to reduce the number of downtime and improve the availability of system are to be further studied.