Abstract
This paper provides an inspection maintenance model for a production system which is subjected to deterioration and random failures. A Markov model for preventive maintenance of such a continuously operating device whose condition deteriorates with time in service has been proposed by Sim and Endrenyi (1993). This model incorporates deterioration and so-called Poisson failures, minimal repair, periodic minimal maintenances, and major maintenance after a given number of minimal maintenance. In this study, the Sim and Endrenyi model is represented by Generalized Stochastic Petri Net (GSPN). This model then has been developed into a condition based maintenance model aimed to develop a more comprehensive model for maintenance of Automated Manufacturing Systems such as Flexible Manufacturing Systems or Cells. In this model instead of periodic maintenance, after inspection based on the condition of the system the repairman can choose one of the following three choices: 1) performing a minimal maintenance, 2) performing a major maintenance, 3) doing no maintenance action. Taking into account the performability, rather than reliability of the system, the throughput of the manufacturing system is chosen as performance measure. By solving and analyzing GSPNs model, the obtained results indicate that the system performs better under inspection policy. A number of different policies, then are examined that illustrate how performance of the system could further be improved by making better decision between minimal, major and no maintenance action, considering the condition of the system after inspection. Further numerical analyses has been carried out to investigate the effect of varying parameters such as mean duration of minimal maintenance, major maintenance and major repair.
Preview
Unable to display preview. Download preview PDF.
Abbreviations
- n:
-
state of device
- n:
-
0: state following a Poisson failure
- n:
-
1: operating state
- n:
-
2: minimal maintenance state
- k:
-
number of stages of deterioration before deterioration failure
- s:
-
at maintenance event s after s-1 minimalmaintenance the maintenance must be a major maintenance
- P(i,j,n):
-
steady-state probability that the device is in state (i,j,n); i=deterioration-stage index, j=minimal maintenance number
- Pd :
-
steady-state probability that the device is being overhauled after a deteriorating failure
- PM, Pm, P0 :
-
steady-state probability that the device is out of service due to major maintenance,minimal maintenance, minimal repair respectively
- 1/λ d :
-
mean time between “as good as new” and deterioration failure if no maintenance is initiated
- 1/λ 0 :
-
mean time to Poisson failure
- 1/λ m :
-
mean time to the next maintenance event
- 1/μ d :
-
mean duration of overhauling the device following a deterioration failure
- 1/μ m :
-
mean duration of minimal maintenance
- 1/μ M :
-
mean duration of major maintenance
- 1/μ 0 :
-
mean duration of repair after Poisson failure
- U:
-
steady-state unavailability of the device
References
Ajmone Marsan, M., Balbo, J., and Conte, G., 1984, A class of generalized stochastic Petri nets for the performance analysis of multiprocessor systems, ACM Transactions on Computer Systems, 2, 93–122.
Ajmone Marsan, M., Balbo, J., G., Chiola, G., and Conte, G., 1987, Generalized Stochastic Petri Nets revisited: Random Switches and Priorities, Proceedings of the International Workshop on Petri Nets and Performance models, Madison, Wisconsin, 44–53.
Ajmone Marsan, M., Donatelli, S., and Neri, F., 1990, GSPN model of Markovian multiserver multiqueues systems, Performance Evaluation, 11, 227–240.
Balbo, J., G., Chiola, G., Franceschinis, G., and Molinar Roet, G., 1987, Generalized Stochastic Petri Nets for the performance evaluation of FMS, Proceedings of International Conference on Robotic and Automation, Raleigh, NC, 1013–1018.
Balbo, J., Balbo, G., Chiola, G., Bruell, S. C., and Chen, P. 1992, An example of modeling and evaluation of a concurrent program using colored stochastic Petri Nets: Lamport's fast mutual exclusion algorithm, IEEE Transactions on Parallel Distributed Systems, 3, 221–240.
Chiola, G., 1991, GreatSPN 1.5 software architecture, proceedings of 5th International on modeling Techniques and Tools for Computer Performance Evaluation, Torino, Italy.
Chiola, G., Ajmone Marsan, M., Balbo, J., and Conte, G., 1993, Generalized Stochastic Petri Nets: A Definition at the Net Level and Its Implications, IEEE Transactions on Software Engineering, 19, 89–107.
Geraerds, W. M. J., (1990), Maintenance development and Future, IFRIM Report, 2–23
Sim, S. H. and Endrenyi, J., 1993, A Failure-Repair model with Minimal & Major Maintenance, IEEE Transactions on Reliability, 42(1), 134–140.
Mc Call, 1965, J. J., Maintenance Policies for Stochastically Failing Equipment: A Survey, Management Science, 11, 493–521.
Morito, S., Takano, T., Mizukawa, H., and Mizoguchi, K., 1991, Design and Analysis of a Flexible Manufacturing System with Simulation—Effects of Flexibility on FMS Performance, Proceedings of the 1991 Winter Simulation Conference, Nelson, B. L., David Kelton, W., Clark, G. M., (Eds), 249–301.
Nowlan, F. S., and Heap, H. F., 1978, Reliability Centered Maintenance, National Technical Information Services, US Department of Commerce, res. no: A566-579.
Peterson, J. L., 1981, Petri Net Theory and The modeling of Systems, Englewood Cliffs, NJ: Prentice-Hall
Pierskalla, W. P. and Voelker, J. A., 1976, A survey of Maintenance models: The control Surveillance of Deteriorating Systems, Naval Research Logistics Quarterly, 23, 353–388
Valdez-Flores, C., and Feldman, R. M., 1989, A survey of Preventive Maintenance models for Stochastically Deteriorating Single-Unit Systems, Naval Research Logistics Quarterly, 36, 419–446.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Molla-Hosseini, M., Kerr, R.M., Randall, R.B., Platfoot, R.B. (1995). An inspection model with minimal and major maintenance for a Flexible Manufacturing Cell using Generalized Stochastic Petri Nets. In: De Michelis, G., Diaz, M. (eds) Application and Theory of Petri Nets 1995. ICATPN 1995. Lecture Notes in Computer Science, vol 935. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60029-9_48
Download citation
DOI: https://doi.org/10.1007/3-540-60029-9_48
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60029-9
Online ISBN: 978-3-540-49408-9
eBook Packages: Springer Book Archive