Research on Maintenance Process Model Based on Advanced Petri Nets

Shengde WANG, Yu CAO, Mingfang NI, Shengliang XU Department of Technical Support Engineering

Academy of Armored Force Engineering Beijing, China

E-mail: zgyyucao@163.com

Abstract—On the basis of analyzing the rules of ranking maintenance task rank and selecting maintenance resource, the concept of time colored Petri Net with priority is put forward, and maintenance process model is founded and simulated by CPN Tools. The results of simulation show that the time colored Petri Nets with priority can simulate the real maintenance process better.

Keywords- maintenance; process modeling; Colored Petri Nets (CPN)

I. MAINTENANCE PROCESS Maintenance process includes the whole activities keeping

or recovering products to the prescribed state [1]. The process could be regarded as a work flow [2, 3]. It is a collection of activities which composed of maintenance men and various resources for maintain support in a certain relationship. An integrated maintenance process is made up of a series of ordinal maintenance activities which logic relationships could be ordinal, parallel, selective or circular etc. Besides the logic relationships, maintenance also includes principle which shows activity be triggered under what conditions, such as First-In First-Out (FIFO) and so on.

Figure 1. A brief maintenance process

Taking no account of other maintain resources, suppose one electric maintenance need 3hours and one mechanical maintenance need 4hours, In practical maintenance process, maintenance men continuously carry on electric or mechanical maintenance, maintenance hours could reduce for 0.5 hours(rule 1). When resources compete, mechanical maintenance usually carries out first(rule2).

Maintenance process simulation model illuminates what sequence maintenances carry on, which resources needed, how to get the resources, and what relationship between the

activities, then works out the data of average hours and resource utilization rate in maintenance process. The simulation model of maintenance process must consider the rules to ascertain the implement sequence of maintenance and collocation of maintenance resources.

II. EXECUTION ORDER OF MAINTENANCES AND RULES OF DISTRIBUTION MAINTENANCE RESOURCE

A. The Execution Order of Maintenances If there is a large amount of maintenances in a specific time,

the execution order of maintenances should be considered. Many kinds of heuristic methods can choose a certain order, which are First-In First-Out (FIFO), Last in First out (LIFO), Shortest Process Time (SPT), and Shortest Surplus Reply Time (SRRT) etc.

First-In First-Out (FIFO): It could distribute resources according to the prior order of applying resources or the beginning order in the maintenance process. FIFO is a simple and effective rule and is used extensively in practice.

Last In First Out (LILFO): Contrary to FIFO, the maintenance of last applying for resources gets resources at first. In a certain cases, in despite of is unfair, the rule can improve the average service level.

Shortest Process Time (SPT): Estimate the time need in advance according to the attributes of maintenance, so as to separate the activities into simplicity and time-consumption. Choose the least time-consuming activities at first could reduce the mean process time. However, if some activities consuming more time have higher PRIORITY, then the rule need to use Longest Process Time (LPT) to line up.

Fault detection

Electric maintenance

Mechanism maintenance

Testing

Shortest Surplus Reply Time (SRRT): Pay attention to the execution time that each activity needs, we can estimate the surplus time of the whole maintenance process. Distribute resources to the maintenance process with short surplus time first can reduce the quantity of courses being carrying out.

The essential of these rules is to distribute different priority to the maintenance activity or transition, and the maintenance activity with higher PRIORITY is carried out first.

B. Distribute Maintain Resources Because resources are different, it is involved in which

resources are distributed to a specific maintenance. For example, some maintenance needs a mechanic and we have

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two candidate resources named Li and Zhang. Li has the specialty of machinery, electric and computer, Zhang has the specialty of electric and machinery. Who should be assigned to carry out this maintenance?

Let the resource brings into play the specialty. A resource can usually carry out large numbers of maintenance and some maintenance may be the resource’s specialty. For example, pliers and spanner could screw down the bolt, but we usually choose the spanner to deal with it.

Make a resource carry out similar activity continuously. Anyone and machine need extra time of preheating to begin a new activity. That is, resources execute similar activity one by one, the time of preheating could be shortened. In addition, repeated activities could reduce average process time effectively.

Reserve elastic resources in advance for the future. If we have to choose from two resources which are equivalent in carrying out this activity, we’d better choose the resource that deals with a small amount of other kinds of activities relatively. In other words, when other resources can be chosen, let the more all-purpose resources be free.

The essential of these rules is to distribute different priority to various maintenance resources (tokens) in different cases. Maintenance resources having higher priority could join in the maintenance at first.

For the different priority of transitions, literature [4] put forward the definition of Petri Net with priority. For the question of tokens lining up in the places, literature [5] proposed a kind of model which is called PNiQ (Petri Nets including Queuing Net). But it studies less on the tokens have different priority in different cases. On the basis of literature [4] and literature [5], combining the research results of time colored Petri Nets [6], the concept of time colored Petri Net with priority is put forward.

III. TIME COLORED PETRI NET WITH PRIORITY In the Time colored Petri Net with priority, binding and

transition have an identification of priority. When many transitions could be enabled, only the transitions with highest priority could take place. When many tokens satisfy the conditions of binding, only the binding with highest priority could make transitions take place.

The definition and analytical methods of Time colored Petri Net are referred in literature [6].

Definition 1(Timed colored Petri Net with priority): PTCPN= (TCPN, ρ) is a timed colored Petri Net with priority.

• TCPN=(∑,P,T,A,N,C,G,E,I,R,r0) is a timed colored Petri Net;

• Priority relationship ρ is a transition or a partial sequence relationship on a binding. (t1,t2)∈ρ represents that transition t1 has a high priority than transition t2. (b1,b2)∈ρ represents that the priority of binding b1 is higher than binding b2. When many priority rules exist, (ρ1, ρ2, …, ρk) could be used to show the sequence of these priority rules.

Definition 2( ρ Transition Rules): The transition rules of a timed colored Petri Net with priority PTCPN=(TCPN,ρ) is adding two restrictions in the transition rules of time colored Petri Net TCPN.

• ρ∈′∈∈′¬ ),(:}),(|{ ttYbttt

• ρ∈′∈∈′¬ ),(:}),(|{ bbYbtbb

The explanations of these two rules is when there are not enable transitions having higher priority than t in a step Y, then t takes place, and only the binding b with highest priority can make t happen in a step Y.

P0

P11 P12

P2 P3

P4 P5

P6

R0

t1

t5 t4

P

t6

t3 t2

P P

P P

P

R PxR PxR

x

x

x

x

x

x

x

x

(x,r) r

x

r

r

@+4

(x,r)

r

x

(x,r) (x,r)@+3

Rule2

Rule1

colset P=int; colset R=int; colset PxR=product P*R; var x:P; var r:R;

Figure 2. Time colored Petri Network with PRI

IV. USING TIME COLORED PETRI NET TO BUILD UP MODEL OF MAINTENANCE PROCESS

Fig. 2 is the timed colored Petri Net Model with priority of the brief maintenance process in Fig.1. Transition t1, t2, t3, t4, t5 and t6 respectively symbolizes fault diagnosis, electric maintenance start, mechanical maintenance start, electric maintenance finish, mechanical maintenance finish and testing. The place R0 represents the maintenance men are free. Rule 1 represents that the time of maintenance men continuously carrying out the same maintenance could reduces by 0.5 hours. Rule 2 represents that the priority of t3 is higher than t2. The broken line pointing from Rule 1 to Rule 2 shows that Rule 2 has a higher priority than Rule 1.

Compared with ordinary time colored Petri Net, time colored Petri Net with priority increased the rule of restraining and the actual maintenance process could be reflected exactly.

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V. SIMULATION MODEL OF MAINTENANCE PROCESS Fig. 3 is the CPN Tools simulation model of the brief

maintenance process in Fig.1. Because CPN Tools do not support the Petri Net with priority directly, the distribution of resources in Fig.3 adds place RE, place RJ, transition rule and corresponding arcs so as to realize the expression of priority.

• The type of maintenance man is ‘record’, which includes 3 kinds of information such as the serial number of resources, the times of carrying out electric maintenance and the times of carrying out mechanical maintenance. The type of resource pool R is list mainly for inputting all resource entities of the whole resource pool into the transition rule for one time to provide foundation for the execution of rules.

• Transition rule is used for carrying out rule 1 and rule 2, RE represents resource buffer pool which carries out the electric maintenance, and RJ represents resource buffer pool which carries out the mechanical maintenance.

• Guard function of transition rule ‘rs<> [] and also ps1^^ps2<> []’ shows that the transition rule takes place when the number of resources in resource pool should not be 0 and sum of the token of electric maintenance and mechanical maintenance to get should not be 0.That is, only when maintenance resources and execution-waiting maintenance exist synchronously, transition rule has the right to takes place. The function of code segments of transition rule is to confirm which maintenance the resource entities participate in, according to the attributes of resource entities in resource pool, the token number electric maintenance and mechanical maintenance accomplished, rule 1 and rule2. The tokens times of carrying out electric and mechanical maintenance activities increase by 1 accordingly when participate in a maintenance activity.

• The function of code segment t4 and t5 code is to confirm whether execution time reduces by 0.5 hours according to the times of carrying out electric maintenance and mechanical maintenance respectively.

Figure 3. CPN tools simulation model of a brief maintenance process

VI. ANALYSIS OF SIMULATION RESULTS Suppose that there are 5 pieces of equipment for

maintenance and 2 maintenance men. If the simulation model

can't express priority, namely the model can't reflect rule 1 and rule 2, the total mean maintenance time is 19.5 hours using CPN Tools According to the method of this text, setting up the simulation model including priority, the total mean maintenance time is 17 hours and 16 hours are needed for actual maintenance process [8]. The errors of the simulation model using priority or not are 6.3% and 21.8% respectively. It shows that CPN Tools simulation model which can express the restrictions of priority consists with actual maintenance process much more.

TABLE I. THE MEANING OF PLACES AND TRANSITIONS IN FIG. 3

Place Meanings Transition Meanings P0 Beginning state t1 Fault diagnosis P11 Electric maintenance

being ready t2 Electric maintenance

start P12 Mechanical maintenance

being ready t3 Mechanical

maintenance start P2 Electric maintenance are

carrying out t4 Electric maintenance

end P3 Mechanical maintenance

are carrying out t5 Mechanical

maintenance end P4 Electric maintenance

finish t6 Testing

P5 Mechanical maintenance finish

rule Realizing transition of rules

P6 Maintenance process end R Resource pool RE Buffer pool of electric

maintenance men

RJ Buffer pool of mechanical maintenance men

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[5] M. Becker, and H. Szczerbicka, “PNiQ-A concept for performability evaluation,” System Performance Evaluation: Methodologies and Applications, pp.263-274.

[6] K. Jensen, Coloured petri nets: basic concepts, analysis methods, and practical use. New York: Springer, 1996.

[7] “Computer Tool for Coloured Petri Nets,” http://wiki.daimi.au.dk/cpntools/, 2006.

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