Research Papers

Markov-Based Maintenance Planning Considering Repair Time and Periodic Inspection

[+] Author and Article Information
Seungchul Lee

Department of Mechanical Engineering,
University of Michigan,
1035 H. H. Dow, 2350 Hayward Street, Ann Arbor, MI 48109
e-mail: seunglee@umich.edu

Lin Li

Department of Mechanical and Industrial Engineering,
University of Illinois at Chicago,
3057 ERF, 842 W. Taylor Street, Chicago, IL 60607
e-mail: linli@uic.edu

Jun Ni

Department of Mechanical Engineering,
University of Michigan,
1023 H. H. Dow, 2350 Hayward Street, Ann Arbor, MI 48109
e-mail: junni@umich.edu

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the Journal of Manufacturing Science and Engineering. Manuscript received November 25, 2009; final manuscript received March 19, 2013; published online May 27, 2013. Assoc. Editor: Steven J. Skerlos.

J. Manuf. Sci. Eng 135(3), 031013 (May 27, 2013) (12 pages) Paper No: MANU-09-1339; doi: 10.1115/1.4024152 History: Received November 25, 2009; Revised March 19, 2013

The equipment degradation and various maintenance decision processes with unreliable machines have been studied extensively. The traditional degradation modeling using Markov process only focuses on single machine system and ignores maintenance or repair duration. This paper is devoted to analytical and numerical study of production lines within the Markov process framework considering repair time and periodic inspection. Nonexponential holding time distributions in Markov chain are approximated by inserting multiple intermediate states based on a phase-type distribution. Overall system availability is calculated by recursively solving the balance equations of the Markov process. The results show that the optimal inspection intervals for two repairable-machine systems can be achieved by means of the proposed method. By having an adequate model representing both deterioration and maintenance processes, it is also possible to obtain different optimal maintenance policies to maximize the availability or productivity for different configurations of components.

Copyright © 2013 by ASME
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Fig. 1

A state transition diagram and its transition rate matrix

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Fig. 2

Simulation results for single unit deterioration process

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Fig. 3

Markov chain for Erlang process

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Fig. 4

Simulation result from Erlang process with 200 intermediate states

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Fig. 5

Illustration of maintenance policy

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Fig. 6

Markov process for the abovementioned maintenance policy

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Fig. 7

State probabilities for the abovementioned maintenance policy

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Fig. 8

Sample path for the abovementioned maintenance policy

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Fig. 9

Availability with different inspection intervals

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Fig. 10

Maintenance policy comparison

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Fig. 11

Two Markov models and their simulation results

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Fig. 12

Markov degradation model for a two-unit system without maintenance

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Fig. 13

Parallel (a) and serial (b) configurations

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Fig. 14

Maintenance policy in parallel configuration

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Fig. 15

Maintenance Markov model for a two-unit parallel system

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Fig. 16

Maintenance in serial configuration

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Fig. 17

Maintenance Markov model for a two-unit serial system

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Fig. 18

Optimal intervals for PM with different connections

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Fig. 19

Optima PM interval to maximize productivity of system

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Fig. 20

Five-state Markov chain with the corresponding transition probability matrix P

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Fig. 21

State probabilities and reliability distribution

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Fig. 22

Historical inspection intervals from the real Fab data




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