Proceedings of the 8th WSEAS International Conference on SYSTEM SCIENCE and SIMULATION in ENGINEERING
Condition Based Maintenance: simulation and optimization GUIDO GUIZZI, MOSE’ GALLO, PASQUALE ZOPPOLI Dipartimento di Ingegneria dei Materiali e della Produzione Università degli Studi di Napoli “Federico II” Piazzale Tecchio 80, 80125 Napoli ITALY
[email protected],
[email protected],
[email protected] http://www.impianti.unina.it Abstract: - In this paper we propose a model of a productive system subject to a condition based maintenance policy which has to be optimized by modifying the maintenance thresholds to reach the lowest level of global system cost. After a wide literature review, a simulation approach is proposed that take in count all the cost related both to production and to maintenance. At the end of the paper we propose a parametric study to determine how some critical parameters (mainly costs) can influence the achievement of the system and the maintenance policy to be adopted.
Key-Words: - condition based maintenance, maintenance policy, simulation, optimization The result is represented by 28 mathematical or simulative models about CBM. Each of them has got different characteristics that have been carefully evaluated to understand which could be the most important topics of a new model. We have identified some main characteristics of the models that are shown in Table 1, where “x” represent just a paper for which the characteristic doesn’t make sense. In the last part of the table are shown some papers with models about the optimal sizing of an interoperational buffer; in these cases there are no characteristics that have been mentioned.
1 Introduction The goal of this paper is to study a production system that has a Condition Based Maintenance (CBM) policy through the meaning of a simulation model. There are many works that have been developed in the recent years about the condition based maintenance, and we try with this contribution to build a model that has quite no limitations in the representation of the complexity of a production system and of the several variables of the maintenance management.
2 State of art
wear (w) resistence ( r )
stochastic (s) deterministic (d)
Perfect inspections (yes/no)
Partial inspections (yes/no)
Opportune maintenance (yes/no)
multithreshold (yes/no)
failures (yes / no)
series (components number/no)
Predetermined inspection period (yes/no)
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multiparameter (m) monoparametro (1)
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discrete (d) continuous ( c )
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PAPER TITLE
Mathematical (m) Simulative (s)
reference
As seen, it’s been conducted a wide review of the scientific literature about the condition based maintenance studies.
a cbm policy for stochastically deteriorating systems
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AUTHORS
Grall, Berenguer, Dieulle Castanier, Grall, Berenguer Kececioglu, Feng Bin Sun
a cbm policy with non periodic inspection for a two unit series system a general discrete time dynamic programming model for the opportunistic replacement policy and its application to ball bearing systems
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Barros, Grall, Berenguer
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Castanier, Berenguer, Grall
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Christer, Wang
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Ohnishi, Kawai, Mine
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Dieulle, Berenguer, Grall, Roussignol Liao, Elsayed, Chan Van der Duyn Shouten Vanneste
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mcCall
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Dieulle, Berenguer, Grall, Roussignol Barata, Soares, Marseguerra, Zio Van der Duyn Shouten, Vanneste
a maintenance policy optimized with imperfect or partial monitoring a sequential condition based repair replacement policy with non periodic inspections for a system subject to continuous wear a simple condition monitoring model for a direct monitoring process an optimal inspection and replacement policy for a deteriorating system
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continuous time predictive maintenance scheduling for a deteriorating system
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Maintenance of continuously monitored degrading system
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simulation modeling of repairable multi-component deteriorating systems for on condition maintenance optimization
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2 simple control policies for a multi-component maintenance system
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maintenance policies for stochastically failing equipment maintenance policy for a two components system with stochastic dependences and imperfect monitoring optimal continuous wear limit replacement under periodic inspection optimal continuous wear limit replacement with wear dependent failure optimal inspection and maintenance for stochastically deteriorating systems optimal maintenance policy for a markovian system under periodic inspection optimal maintenance policy for deteriorating systems under various maintenance strategies sequential condition maintenance scheduling deteriorating system
based for a
Condition Based Maintenance: Implementation and optimization of a two-unit serial system model with multi-threshold policy S. V. Amari, Optimal design of a conditionL. Mclaughlin based maintenance model Online maintenance policy for a Saassouh, deteriorating system with random Dieulle, Grall change of mode Economic and economic-statistical design of a chi-square chart for Wu, Makis CBM W. Wang, W. An asset residua life prediction model based on expert judgments Zhang a maintenance model with failures Montoroand inspection following Markovia Carloza Delia, Pérez- arrival processes and two repair modes Ocon Rafael Optimal maintenance policies in Kahle incomplete repair models A condition-based orderL. Wang, J. replacement policy for a singleChu, W. Mao unit system I. Zequeira, Optimal buffer inventory and preventive E. Valdes, opportunistic maintenance under random Berenguer Guizzi, Santillo, Zoppoli
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M.K. Salameh, R.E. Ghattas
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A.Chelbi, Rezg
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E.G. Kyriakidis, T.D. Dimitrakos
N.
production capacity availability Optimal just-in-time buffer inventory for regular preventive maintenance Analysis of a production/inventory system with randomly failing production unit subjected to a minimum required availability level Optimal preventive maintenance of a production system with an intermediate buffer
Table 1: Papers about condition based maintenance and their characteristics
The first two thresholds tell the system to make maintenance immediately to prevent the failure and the system stop. The last thresholds tell the system to evaluate the possibility to reduce the period between inspections. With this kind of model we can evaluate the interactions between different machines due to the series. In particular, the opportune threshold, that is always lower than the preventive one, give the possibility to make a maintenance intervention on a machine even if it hasn’t reached yet the preventive threshold but there is a global stop of the system to make maintenance on other machines. In this case we should have an economic convenience to work on that machine, resetting its lifecycle, because we opportunely use the stop of the whole system to work on several machines. The economic convenience in this case is related to the high cost of each system stop (setup cost, production loss etc.), due to the fact that the machine are in series and so we have to stop all of them to repair one of them.
3 The model 3.1
The physical model
The choice of a simulation approach give the chance to represent the production system and the CBM policy with a very respondent to reality model. In fact, we could notice that the complexity of this kind of system can be represented by a mathematical model with a set of equations, only when it’s simplified by a certain number of constraints, that could not be representative of the real system. In our model, the wear has been identified as an obsolescence parameter instead of a resistence parameter, while the wear process is designed as a continuous process and not discrete. According to quite all the studies, we have modeled the wear process as a gamma process. The failure probability is modeled through a weibull distribution, that is not leaded by the time, as usual, but by the wear parameter, according to the real phenomenon. In most of the papers we examined, one component is considered in failure only when its wear parameter goes over a certain threshold, usually identified by L. While this idea is in line with the CBM conception, it seems to be something very far from the true experience. We know that failures, even if they are more likely to occur when wear parameter is high, can anyway be revealed also at any time and at any wear level. That’s why we used a weibull distribution that can also give failures on components at any time of their lifecycle. In our model there is a series of several machines working, with the possibility to put an interoperational buffer between them. For each machine we have three maintenance thresholds which lead the decision system: 1. preventive maintenance threshold 2. opportune maintenance threshold 3. alarm threshold
ISSN: 1790-2769
3.2 The simulation model Using a simulation approach, we have to limit the model to a certain number of components of the series. Anyway we can use the software Arena to model any number of components series. The model has two different logics: • production logic s • maintenance logics The production logics is the way we model the production system that is responsible for the machines wearing process, So it will determine the wear increments and the failure likelihood. The maintenance logic is the way we use to model the maintenance process, characterized by inspection phases to determine the status of machines and by the different maintenance processes.
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After the inspection, the model can decide if a maintenance intervention is needed or if it’s necessary to anticipate the next inspection. The decision is taken by the comparison between the machine wear, taken from inspection, and the thresholds that have been fixed to determine the maintenance policy. Moreover, the inspection process has been modeled as imperfect, so that the wear parameter is known with a certain degree of error due to a gauss distribution that affects the measure, according to the possibility that there is always an error in each measuring process.
For any event of production or maintenance process, the model calculate the related cost (example: production of each piece, inspection, maintenance intervention, buffer etc.). Moreover, the model is able to calculate the free machine cost. A cost related to the time is associated to the global cost, whenever a machine is not working; being stopped because of a system stop, because there is a maintenance intervention on it or even if there is a stop of another machine in the series that doesn’t give pieces to work with. The production process has been modeled in Arena in modules; every machine is represented buy a submodel that can be repeated as many times as the real system. The wear parameter is increased through an “Assign” module (fig. 1) at predetermined time intervals, that have been fixed at one minute to simulate the continuous nature of this parameter and to allow the failure of the machine during the manufacturing of a piece.
Fig. 3: Interfaccia dei moduli di processo ispezione e manutenzione
4 The model optimization Once defined the model, it has been used to understand the achievement of a particular production system and also to determine the optimal thresholds to be fixed to reach the lower global cost, taking in count both the cost of production and the cost of maintenance. There have been launched a lot of optimization with the OptQuest module of Arena, to search the best maintenance policy, depending on different system configurations. First of all, we used the inspection cost as a parametric variable to understand which would be the thresholds, and so the maintenance policies, depending on the cost of inspection. The result is represented by the graph in fig. 4, in which we used an a-dimensional parameter ρisp, given by the ratio between the cost of a single inspection on a machine and the cost of a preventive maintenance. The graph shows the convenience to reduce the number of inspections (by increasing the alarm threshold) related to the increasing of the cost of any inspection, and this is very easy to understand. This lead to a lower threshold of preventive maintenance to prevent the failures anyway. So that when you reduce your inspections you have to pay
Fig.1: Assign module for wear increasing The failure is determined by a “decide” module and it sends a message to the maintenance model to activate an intervention (fig. 2). So it’s not needed to have an inspections to know if there is a failure, as in many models that have been studied before.
Fig. 2: Failure determination The maintenance process is characterized by periodic inspections to determine the status of each machine wear, that has been determined by production.
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Proceedings of the 8th WSEAS International Conference on SYSTEM SCIENCE and SIMULATION in ENGINEERING
your ignorance about the wear, increasing the number of preventive maintenance intervention to avoid the failures.
Fig. 6: Trend of the thresholds depending on ρmlib The graphs analysis shows the achievement of the model to determine the best maintenance policy, that is the one that leads to the lowest level of global cost, by setting the right level of thresholds.
Fig. 4: Trend of the thresholds depending on ρisp In fig. 5 the graph shows the achievement of the model depending on the failure cost. As we could expect, all the thresholds decrease when the failure cost is higher. The higher is the impact of a failure, the higher is the number of inspections and of preventive maintenance to make.
References: [1] Dekker R., Wildeman R., van der Duyn Schouten F. – A review of multi-component maintenance models with economic dependences – Mathematical method of operations research (1997) [2] Dekker R. – Applications of maintenance optimization models: a review and analysis Reliability engineering and system safety (1996) [3] Yam R.C.M., Tse P.W., Li L., Tu P. – Intelligent predictive decision support system for Condition Based Maintenance – Advance Manufacturing Technology (2001) [4] A Report of the IEEE/PES Task Force on Impact of Maintenance Strategy on Reliability of the Reliability, Risk and Probability Applications Subcommittee – The present status of maintenance strategies and the impact of maintenance on reliability – IEEE transaction on power systems (2001) [5] Pandey M.D., van Noortwijk J.M., Kallen M.J. – Gamma processes for time-dependent reliability of structures – Preprint submitted to Elsevier science [6] Tsilevich N., Vershik A., Yor M. – Distinguished properties of gamma processes and related topics – preprint (2000) [7] Sundberg A. – Management aspects on CBM, the new opportunity for maritime industry – 9th international conference on marine engineering systems [8] M. Bengtsson, E. Olsson, P. Funk M. Jackson – Technical design of condition based maintenance system – Maintenance and Reliability Conference, Proceedings of the 8th Congress, May 2nd – 5th, 2004, University of
Fig. 5: Trend of the thresholds depending on ρgua Finally, in fig. 6, we have the trend of thresholds depending on free machine cost. At the beginning, the free machine cost is zero, all the thresholds are quite the same. It means that the model suggest us to don’t use the condition based maintenance at all. In fact, if there is no cost related to the not working machine, there is also not so much convenience to make many inspections and many preventive maintenance. The higher is the free machine cost, the higher will be the impact of a series system stop, so that we will need more inspections (lower alarm threshold) and more opportune maintenance (lower opportune threshold).
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Tennessee – Maintenance and Reliability Center, Knoxville, USA. [9] Jarrell D., Sisk D., Bond L. – Prognostics and CBM, a scientific crystal ball – Nuclear Technology (2004) [10] M. Bengtsson, Olsson E., Funk P., Jackson M. - Condition Based Maintenance System Technology, Where is Development Heading? Euromaintenance 2004, Proceedings of the 17th European Maintenance Congress, 11th – 13th of May, 2004, AMS (Spanish Maintenance Society), Barcelona [11] Brochure informative della Vibrosystem sui sistemi CBM – Part 1: a CBM approach – (2004) [12] Cattaneo M. – La manutenzione in Italia nelle PMI – indagine dell’ Associazione Italiana Manutenzione (2004) [13] Mitchell, J. S. - Five to ten year vision for CBM, ATP Fall Meeting – Condition Based Maintenance Workshop, Atlanta, USA [14] H. Haymann – Dispense sull’ affidabilità, section 3: reliability – University of Portsmouth UK [15] Jiang R., Murthy D.N.P. - Mixture of weibull distributions – parametric characterization of failure rate function - applied stochastic models and data analysis, volume 14 (1998) [16] Speaks S. – Reliability and MTBF overview – Dispense dal corso interro tenuto alla Vicor System. [17] Scarf P.A. – On the application of mathematical models in maintenance – European Journal of operational research (1997) [18] Wenocur M.L. – A reliability model based on the Gamma Process and its analytic theory – Advances in applied probability, vol. 21, n°4 (1989) [19] Grall A., Berenguer C., Dieulle L. – A condition-based maintenance policy for stochastically deteriorating systems – Reliability engineering and system safety (2002) [20] Castanier B., Grall A., Berenguer C. – A condition-based maintenance policy with nonperiodic inspections for a two unit series system – Reliability engineering and system safety (2005) [21] Kececioglu D., Feng-Bin Sun – A general discrete time dynamic programming model for the pportunistic replacement policy and its application to ball bearing systems – Reliability engineering and system safety (1995)
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[22] Barros A., Grall A., Berenguer C.– A maintenance Policy Optimized with imperfect monitoring and/or partial monitoring – Annual reliability and maintainability symposium (2003) [23] Castanier B., Berenguer C., Grall A. – A sequential condition-based repair/replacement policy with non-periodic inspections for a system subject to continous wear – Applied stochastic models in business and industry [24] Christer A.H., Wang W. – A simple condition monitoring model for a direct monitoring process – European journal of operational research (1995) [25] Ohnishi M., Kawai H., Mine H. – An optimal inspection and replacement policy for a deterioratng system – Journal of applied probability (1986) [26] Dieulle L., Berenguer C., Grall A., Roussignol M. – Continous time predictive maintenance scheduling for a deteriorating system – Annual reliability and maintanability symposium (2001) [27] Liao H., Elsayed E.A., Chan L.Y. – Maintenance of continuously monitored degrading system – Preprint submitted to Elsevier Science (2004) [28] Van der Duyn Schouten F.A., Vanneste S.G.– Maintenance optimization of a production system with buffer capacity – European journal of operational research ( 1995) [29] McCall J.J. – Maintenance policies for stochastically failing equipment: a survey – Management science (1965) [30] Barros A., Berenguer C., Grall A. – Maintenance policy for a two components system with stochastic dependences and imperfect monitoring – Preprint submitted to Elsevier science (2005) [31] Park K.S. – Optimal continuous wear limit replacement under periodic inspection – IEEE transaction on reliability (1988) [32] Park K.S. – Optimal wear limit replacement with wear dependet failures – IEEE transaction on reliability (1988) [33] Newby M., Dagg R. - Optimal inspection and maintenance for stochastically deteriorating systems – Preprint of Norwegian Institute of Technology [34] Chiang J.H., Yuan J. - Optimal maintenance policy for a markovian system under periodic inspection – Reliability engineering and system safety (2001) [35] Teresa Lam C., Yeh R.H. – Optimal maintenance policies for deteriorating systems
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under various maintenance strategies – IEEE transaction on reliability (1994) [36] Dieulle L., Berenguer C., Grall A., Roussignol M. – Sequential condition based maintenance scheduling for a deteriorating system – European Journal of operational research (2003) [37] Barata J., Guedes Soares C., Marseguerra M., Zio E. - Simulation modelling of repairable multi component deteriorating systems for ‘on condition’ maintenance optimisation – Reliability engineering and system safety (2002) [38] van der Duyn Schouten F.A., Vanneste S.G. – Two simple control policies for a multicomponent Maintenance system – Operations research (1993) [39] Guizzi G., Santillo C.L., Zoppoli P. - Condition Based Maintenance: Implementation and optimization of a two-unit serial system model with multi-threshold policy – 8th international conference on “The modern information technology in the innovation processes of the industrial enterprise” settembre 2006 Budapest, Ungheria. [40] Suprasad V. Amari, Leland McLaughlin – Optimal design of a Condition-Based Maintenance Model – Relax Software Corporation (2004) [41] Saassouh B., Dieulle L., Grall A. – Online maintenance policy for a deteriorating system with random change of mode - Reliability engineering and system safety (2006) [42] Wu J., Makis V. - Economic and economicstatistical design of a chi-square chart for CBM - European Journal of operational research (2007) [43] Wang W., Zhang W. – An asset residual life prediction model based on expert judgments European Journal of operational research (2007) [44] Montoro-Carloza Delia, Pérez-Ocon Rafael – A maintenance model with failures and inspection following Markovia arrival processes and two repair modes – European Journal of operational research (2007) [45] Kahle W. - Optimal maintenance policies in incomplete repair models - Reliability engineering and system safety (2006) [46] Wang L., Chu J., Mao W. - A condition-based order-replacement policy for a single-unit system – Applied mathematical modelling (2007) [47] Zequeira I., Valdes E., Berenguer - Optimal buffer inventory and opportunistic preventive
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maintenance under random production capacity availability - International Journal of Production Economics (2008) [48] Salameh M.K., Ghattas R.E. - Optimal just-intime buffer inventory for regular preventive maintenance - International Journal of Production Economics (2001) [49] Chelbi A., Rezg N. - Analysis of a production/inventory system with randomly failing production unit subjected to a minimum required availability level - International Journal of Production Economics (2006) [50] Kyriakidis E.G., Dimitrakos T.D. - Optimal preventive maintenance of a production system with an intermediate buffer - European Journal of Operational Research (2006)
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