Available online at www.sciencedirect.com
ScienceDirect Procedia CIRP 57 (2016) 674 – 679
49th CIRP Conference on Manufacturing Systems (CIRP-CMS 2016)
Maintenance decision support for manufacturing systems based on the minimization of the life cycle cost Alice Reinaa*, Ádám Kocsisb, Angelo Merloc, István Némethb, and Francesco Aggogerid b
a Mach4Lab,Corso Roma 4, Cologno Monzese (MI), 20093, Italy Department of Manufacturing Science and Engineering, Budapest Univeristy of Technology and Economics, MĦegyetem rkp. 3,Budapest, 1111, Hungary c CeSI, Centro Studi Industriali, via Tintoretto 10, Cologno Monzese (MI), 20093, Italy d Department of Mechanical and Industrial Engineering, Univeristy of Brescia, vi Branze 38, Brescia 25123, Italy
* Corresponding author. Tel.: +39-02-25118007; fax: +39-02-27306205. E-mail address:
[email protected]
Abstract The reduction of the overall Life Cycle Costs (LCC) is a key issue in manufacturing sector. Among the various contributions to LCC an important part is due to Reliability and Maintainability (R&M) issues and therefore a substantial reduction in LCC can be achieved by a conscious decisions and planning. Besides the failure and repair characteristics, the R&M related costs vary according to the maintenance strategy and policy selected for each components that form the manufacturing system. The aim of this paper is to describe a mathematical model that takes into account the R&M related fraction of the LCC in order to compare scenarios in which different maintenance strategies and policies are applied on the components of manufacturing systems. The calculations cover three policy possibilities: internal crew, external service (on-demand) and external service (annual contract). Both scheduled (preventive maintenance, inspection-based maintenance) and unscheduled (corrective maintenance, condition monitoring) strategies are considered. On the basis of the proposed formulae, optimization is carried out with a view to find the best solution in economical aspect. Furthermore, the method takes into account the possibility of clustering the scheduled interventions with the intention of reaching a predefined availability constraint while keeping the costs as low as possible. The paper presents the results of the European FP7 research project EASE-R3 where a specific maintenance planning software tool is being developed implementing the methodologies outlined above. © Published by Elsevier B.V. This © 2016 2015The TheAuthors. Authors. Published by Elsevier B.V.is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of Scientific committee of the 49th CIRP Conference on Manufacturing Systems (CIRP-CMS 2016). Peer-review under responsibility of the scientific committee of the 49th CIRP Conference on Manufacturing Systems Keywords: Maintenance optimisation of manufacturing systems; life cycle cost estimation; maintenance strategy; maintenance policy
1. Introduction The overall life cycle cost estimation is a cradle-to-grave approach, in which all the relevant costs are summarized from inception to disposal for equipment or projects [1]. The objective of LCC analysis is to choose the most cost effective approach from a series of alternatives in order to have longterm benefits. LCC can be mainly divided in acquisition and sustaining costs. Sustaining costs can be further broken down in subgroups, as can be seen in Fig. 1. As underlined in [2] and [3] in many sectors, such as manufacturing, LCC can be reduced with strategic decisions on reliability and proper maintenance plans.
In this framework, this paper aims to present a maintenance planning software platform for manufacturing systems, based on a mathematical model that takes into account the part of LCC connected to R&M, comparing different options to define the optimal maintenance plan, the one accounting for the minimum costs. The maintenance strategies comparison is applied to each item the machine is composed of, according to a hierarchicalmorphological decomposition of the system. As output a matrix grouping the components according to the optimal policy and strategy is obtained. In case of scheduled
2212-8271 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 49th CIRP Conference on Manufacturing Systems doi:10.1016/j.procir.2016.11.117
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maintenance the optimal intervention time will be calculated and provided.
values of the parameters, the Weibull distribution can be used to model a variety of life behaviors. 2.2. Maintainability Maintainability ሺሻ is the probability that a failed machine or system will be restored to operational effectiveness within a given period of time ‘t’ when the repair action is performed in accordance with the prescribed procedures [5]. In this context, the Mean Time To Repair (MTTR) is the average time it takes to restore a system to operational status after it has failed to function and can be calculated by: ஶ
ൌ න ൫ͳ െ ܯሺݐሻ൯ݐ
(4)
Fig. 1 – Main contributions to life cycle costs
This leads to numerous different optimal intervals, one for each component, reducing drastically the system availability. A clusterization method is then proposed, in order to group the components having similar optimal interval, in order to increase the system availability without increasing too much the costs. 2. R&M background 2.1. Reliability In order to assess the optimal maintenance plan, the one that allows minimizing the life cycle costs, it is necessary to know the reliability of each component. Reliability R(t) is defined as the probability that an item will perform adequately a required function, under stated environmental conditions, for a specified period of time ‘t’ [4]. Different probability distribution can be used to describe reliability, but the one that normally fits for mechanical components is the Weibull distribution. According to Weibull distribution: ܴሺݐሻ ൌ ݁
௧ିఊ ഁ ିቀ ఎ ቁ
(1)
The failure rate (or hazard rate) is defined as:
ɉሺሻ ൌ
ൌ ஒିଵ ൌ Ⱦ ൬ െ ɀ൰ Ʉ Ʉ ሺሻ
(2)
and the Mean Time To Failure (MTTF) is: ஶ
MTTF ൌ න
୲ିஓ ಊ ିቀ ቁ d
(3)
where Ⱦ is the shape parameter, Ʉ is the characteristic life and ɀ is the location parameter of the distribution. Usually ɀ ൌ Ͳ and the distribution is called 2 parameters Weibull. The Weibull distribution is widely used in reliability and life data analysis due to its versatility. Depending on the
Maintenance can be carried out according to 4 different strategies: I. Corrective Maintenance (CM): a recovery action performed after failure occurs to restore system to its operational status. It is unscheduled and normally it has high application cost. It can be convenient when the equipment failure does not significantly affects the production and does not cause significant collateral damages. Preventive Maintenance (PM): performed II. periodically to reduce the probability of failure of the system. It is scheduled, it can have lower application costs with respect to CM, avoiding collateral damages due to failures, or lost production due to delays in acquiring spare parts or in collecting the crew. Preventive maintenance is effective only in case of items subjected to ageing and wear. Maintenance based on periodic Inspections (IN): III. items are checked at scheduled interval of time and maintenance is carried out only when the inspection reveals that a failure is approaching to prevent it to happen. Maintenance based on real-time Condition IV. Monitoring (CBM): called also predictive maintenance, is based on the past trends to predict failures. It makes use of factors such as continuous monitoring, analysing, detection, diagnosing and responding actions. This maintenance focuses on eliminating the root causes of failure before it leads to a major breakdown. Each of the described maintenance strategies can be carried out according to 3 policies: 1. Internal crew: maintenance is carried out by the technicians employed by the machine user. 2. External service (on demand): maintenance is carried out by external companies that will provide maintenance service when requested by the user. In this case fixed call cost can be applied by the company responsible for maintenance. 3. External service (annual framework contract): maintenance is carried out by an external company that have an annual framework maintenance contract
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with the user (so the cost of the contract is flat and independent on the number of requested actions). 3. Maintenance costs calculation for intervention
ܥெିூே் ሺݐሻ ൌ
Maintenance costs are calculated for each maintenance intervention on each component and are here presented for every maintenance strategies and policies. 3.1. Corrective maintenance
ܮூே் ஶ ͳȀ ܴሺݐሻ݀ݐ
ܥ ߪெ ή ܥௌ ܨெ
ሺ ݐ݊݅ܶܦܯ ߪெ ή ܵ ܶܦ ܴܶܶܯሻ ή ܥ ܥெିா் ൌ ܮா் ή ܴܶܶܯ ܥ ߪெ ή ܥௌ ܨெ ሺ ݐݔ݁ܶܦܯ ߪெ ή ܵ ܶܦ ܴܶܶܯሻ ή ܥ
ܥெିிௐ ൌ
ܮூே் ߪெ ή ܥௌ ܨெ ܶெ ή ܥ ͳȀݐ
ܥெିா் ൌ ܮா் ή ܶெ ߪெ ή ܥௌ ܨெ + ܶெ ή ܥ ܥெିிௐ ሺݐሻ ൌ
First of all it is necessary to split the case of labor cost for internal operators (-INT) from the case of labor cost for external operators (-EXT). In the first case we need to spread the cost of internal salary in each maintenance intervention, in the second case we simple consider the external labor hourly cost multiplied by MTTR. A third case is then considered: maintenance operations are completed in the framework of an annual contract (-FWC). In this case the total cost of the contract is also divided into each intervention. It is worth noting that in case of exponential distribution the integral representing the mean time to failure is equal to MTBF. A coefficient ı multiplies the cost of spare parts and the spare delay time in order to take into account that not each intervention leads to the change of the component. Moreover in case of annual framework contract the coefficient ıFWC is different in order to consider warranties as well. Costs calculation for corrective actions are listed in equation (5) to (7), where L is the labor cost, HY is the number of operative hours per year, CCD is the cost due to collateral damages, CSP is the cost of the spare part, F is fixed costs (consumables, machinery depreciation, call cost in case of external service), MDT is the mean delay time, SDT is the delay time due to spare part acquisition and CLP is the cost for lost production. ܥெିூே் ൌ
As a consequence CPM is function of t, as can be seen in equation (8) to (10).
(5)
(6)
(7)
3.2. Preventive maintenance For preventive maintenance, similarly as already discussed for corrective maintenance, it is necessary to split the cost function in three cases. TPM, which is the time needed to carry out the preventive task can roughly be estimated as 0.7-0.8 times the MTTR. In this case the number of preventive action is strictly connected to the optimal maintenance interval, ݐை் ; results of the optimization process are described in section 4.
ଵȀ௧
ߪெିிௐ ή ܥௌ +ܶெ ή
ܥ
(9)
(10)
3.3. Maintenance based on periodic inspection In order to spread the internal labor cost or the cost of external annual contract on each intervention it is necessary to identify the number of intervention per year, that means, it is necessary to define the expected replacement cycle length for inspection based maintenance. Being p1 the percentage of life of the component in which it is possible to make decisions about its replacement, the cycle length can be defined according to equation (11) [7]: ௫
ܧሺݐ௬ିூே ሺሻሻ ൌ න ݂ݐሺݐሻ݀ ݐ ௫ భ
ெ
ሺାଵሻ௫
න ሺ݇ݔሻ݂ሺݐሻ݀ ݐ න ୀଵ
௫ భ
௫
න
ሺெାଵሻ௫ భ
න
௫ ୀெାଵ భ
݂ݐሺݐሻ݀ݐ (11)
ሾሺ ܯ ͳሻݔሿ݂ሺݐሻ݀ ݐ
ሺெାଵሻ௫ ሺାଵሻ௫ ஶ భ
ሾሺ݇ ͳሻݔሿ݂ሺݐሻ݀ݐ
A second distinction considers that this maintenance action can be done with or without the need to stop the system. For this reason a coefficient ɒ is introduced, representing the percentage of intervention carried out causing the machine downtime. In few cases (ıIN) the intervention requires the substitution of the component. Equation (12) to (14) give the cost for intervention related to inspection based maintenance, being TIN the time required for maintenance in this case.
ܮிௐ Ȁܪ
ܥ ߪெିிௐ ή ܥௌ ஶ ͳȀ ܴሺݐሻ݀ݐ ሺ ݐݔ݁ܶܦܯ ܴܶܶܯሻ ή ܥ
ಷೈ Ȁுೊ
(8)
ܮூே் ߪூே ή ܥௌ ͳȀܧூே ሺ݄ݐ݃݊݁ܮ݈݁ܿݕܥሻ ߬ ή ܶூே ή ܥ ܨூே
(12)
୍ିଡ଼ ൌ ୍ ή ଡ଼ ɒ ή ୍ ή ɐ୍ ή ୗ ୍
(13)
ܥூேିூே் ൌ
ܮிௐ ͳȀܧூே ሺ݄ݐ݃݊݁ܮ݈݁ܿݕܥሻ ߬ ή ܶூே ή ܥ ߪூே̴ிௐ ή ܥௌ
ܥூேିிௐ ൌ
(14)
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3.4. Maintenance based on real time condition monitoring The possibility to apply predictive maintenance strictly depends on the existence of a prognostic characteristic, which is a property, or an ensemble of properties changing gradually from an initial value to a “fatal limit”. The fatal limit is the value at which the unit enters the failed state. Certain simple measures such as drop of oil pressure, can be extrapolated over time with fair accuracy. This information can be used to estimate the remaining life of the component. In the ideal situation, the measurement of the prognostic characteristic predicts the moment of failure sufficiently in advance to carry out preventive replacement. Nevertheless, some sources of uncertainty can arise. The measurement itself may be affected by uncertainty, the value of the prognostic characteristic may show random oscillation or the relationship between prognostic characteristic and remaining life may not be known with enough confidence. In order to calculate the expected replacement cycle length to spread internal labor cost in each predictive maintenance action, it is necessary to take into account the uncertainty that can arise. First, a conservative lower confidence limit of the predicted time to failure is considered, assuming that each time-replacement takes place at 75% of the MTTF of the unit in service. Then it is necessary to consider a coefficient, p1,as in inspection based maintenance to take into account the percentage of life of the component in which it is possible to make a decision about its replacement. Finally, p2 is introduced as the small fraction of failures that can happen without being recognized by the instrument. MTTF results then reduced of a fraction that, considering the lower boundary, is the probability that the failure happens at a fraction (1-p2) of the MTTF. The expected replacement cycle length for predictive maintenance is: ൫ݐ௬ିெ ሺݔሻ൯ ൌ ܨܶܶܯή ͲǤͷ ή ଵ ή ሺͳ െ ଶ ሻ
(15)
Now it is possible to spread the internal labor cost in each maintenance intervention, considering the 3 selected policies. ܮூே் ͳȀ ܨܶܶܯή ͲǤͷ ή ଵ ή ሺͳ െ ଶ ሻ ܶெ ή ܥ ܥௌ ܨெ
ܥெିூே் ൌ
ܥெିா் ൌ ܶெ ή ܮா் ܶெ ή ܥ ܥௌ ܨெ ܥெିிௐ ൌ
ܮிௐ ͳȀ ܨܶܶܯή ͲǤͷ ή ଵ ή ሺͳ െ ଶ ሻ ܶெ ή ܥ ܥௌ
(16)
(17)
(18)
4. Maintenance costs calculation for unit time Formulas for calculation of maintenance costs for unit time are here proposed considering that they are applied for each maintenance intervention and for each component. These
formulas enable comparison of different strategies since the number of interventions varies from one to another. 4.1. Preventive maintenance Minimizing the maintenance cost per unit time is the most popular objective to adopt a preventive replacement strategy. In this case an item can be replaced either at the time of failure or at the time of the scheduled maintenance interval, and the expected cycle length is: ௫
൫ݐ௬ିெ ሺݔሻ൯ ൌ න ݂ݐሺݐሻ݀ ݐ ܴሺݔሻݔ
௫
(19)
ൌ න ܴሺݐሻ݀ݐ
The expected cost per cycle is: ܧ ൫ݐ௬ିெ ሺݔሻ൯ ൌ ܥெ ܴሺݔሻ ܥெ ሺͳ െ ܴሺݔሻሻ
(20)
Therefore the expected cost per unit time is [6]: ܥெ ܷܶሺݔሻ ൌ
ܧ ൫ݐ௬ିெ ሺݔሻ൯ ൫ݐ௬ିெ ሺݔሻ൯ ܥெ ܴሺݔሻ ܥெ ሺͳ െ ܴሺݔሻሻ ൌ ௫ ܴሺݐሻ݀ݐ
(21)
The optimal preventive maintenance interval (topt) is the value x which minimizes the CPMUT in equation (21). 4.2. Maintenance based on periodic inspection Inspection is often used to test if a device is working properly, therefore signs of a device’s impending failure can be detected via inspection. The component can then be replaced before the failure actually occurs. If a failure cannot be detected during the inspection, it will occur, and the component will be replaced at the time of the failure. Defining M as the largest inspection interval where no overlap happens between detection zones of 2 adjunct inspections [7]: ܯൌ ݈ܽ ݎ݁݃݁ݐ݊݅ ݐݏ݁݃ݎ൏ ͳെ െ ͳ݂݅݅݊ݎ݁݃݁ݐ ͳെ ൌ൞ ඐ ݂݅݊ݎ݁݃݁ݐ݊݅ݐ ඌ ͳെ
(22)
It is possible to calculate the cycle length as in equation (11) and the cost per cycle as in equation (23), and therefore the expected cost per unit time CINUT in the ratio between the cost per cycle length and the cycle length itself. The optimal inspection interval time will be the value x which minimizes the cost for inspection based maintenance per unit time [7].
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Alice Reina et al. / Procedia CIRP 57 (2016) 674 – 679 ௫
ܧ ሺݐ௬ିூே ሺݔሻሻ ൌ න ܥெ ݂ሺݐሻ݀ݐ ெ
௫ భ
න ሾܥெ ݇ܥூே ሿ݂ሺݐሻ݀ݐ ୀଵ
௫
ሺାଵሻ௫
න
௫ భ ሺெାଵሻ௫ భ
න
ሾܥெ ݇ܥூே ሿ݂ሺݐሻ݀ݐ (23) ሾܥெ
ሺெାଵሻ௫
ሺ ܯ ͳሻܥூே ሿ ݂ሺݐሻ݀ݐ ஶ
න
ሺାଵሻ௫ భ
௫ ୀெାଵ భ
ሾܥெ
ሺ݇ ͳሻܥூே ሿ݂ሺݐሻ݀ݐ 4.3. Maintenance based on real time condition monitoring In this case the average interval of time between two maintenance interventions cannot be optimized, as discussed in previous chapters. Nevertheless it is possible to define the equation for cost per unit time in case of predictive replacement as: ܥெ ܥெ ܷܶ ൌ (24) ܨܶܶܯή ͲǤͷ ή ଵ ή ሺͳ െ ଶ ሻ Note that fixed cost for the real time diagnosis device is fully allocated in the whole productive year and then divided by the productive hours per year. 5. Maintenance strategy selection The first step is to calculate the cost for each maintenance intervention for each component, for all the strategies and the policies considered, according to equations (5)-(10), (12)-(14) and (16)-(18). Once the cost calculation is performed for all the maintenance strategies and policies, the policy selection take places: among internal labor, external labor or framework contract, the optimal policy is defined by the minimum cost for the single intervention. This operation is carried out for all the maintenance strategies, and it is worth noting that the policy minimizing cost for one strategy is not necessarily the same that minimizes costs for the other strategies. For example, if the cost for corrective maintenance with external intervention is the minimum value, the policy for corrective maintenance will be external, if the cost for preventive maintenance with internal labor is the minimum value, the policy for preventive maintenance will be internal. Once the optimal policy has been defined for each strategy it is necessary to evaluate the best strategy for each component. The first discriminating parameter for the selection is ȕ, the shape parameter of Weibull equation. If this coefficient is equal to 1, the failure rate becomes constant, which means that failures happen at random, and aging/wear have no effects on the component.
Preventive maintenance or inspection based maintenance in this case are useless as for Ⱦ ൏ ͳ, since in this case the probability to have a failure reduces with increasing time. In this case the optimal maintenance strategy is the one characterized by minimum cost among corrective maintenance and predictive maintenance. For components and systems with increasing failure rates, (Ⱦ ͳ) planned replacements and inspections are often used to prevent failures in order to improve system availability and reduce overall maintenance cost. For example, the commonly used preventive maintenance strategy is to replace an aged item at a given time interval in order to minimize the cost for preventive maintenance for unit time. An optimal time interval exists if the failure rate increases with time (Ⱦ ͳ) and the cost of failure is much higher than the cost of a scheduled replacement. An alternative to preventive maintenance is to use periodic inspection to detect oncoming failures and replace the component when the failure is next to occur. Also for inspection maintenance we can find an optimal time interval to minimize the cost for unit time in a replacement cycle. The third strategy is to adopt a predictive maintenance (condition based real-time monitoring) in this case we cannot define an optimal time interval, but the diagnostic predictive maintenance compared to a preventive maintenance is always convenient, except for the cost of the device that performs the diagnosis. The optimal strategy is the one with minimum cost per unit time. 5.1. Allocation matrix At the end the software tool based on the above presented algorithms, will be able to group the components forming the manufacturing system according to the different maintenance strategies and policies that minimize the LCC. The clusters could be represented for instance using a matrix, as reported in Fig.2.
Fig. 2 – Clusterization matrix for system components
It is also necessary to provide the components that fit into “Preventive Maintenance” and “Maintenance based on Periodic Inspection”, respectively, with the optimal preventive time (how often preventive maintenance actions to be scheduled) and the optimal inspection time (how often the inspections to be planned). Components characterized by similar optimal time must be grouped in order to reduce the
Alice Reina et al. / Procedia CIRP 57 (2016) 674 – 679
number of interventions. In order to have a higher availability without penalizing too much the costs the best intervention time is finally defined for each group.
95% which can be reached with 7 different maintenance intervals.
6. Maintenance planning software tool The software tool which was developed on the basis of the described above is capable of optimizing the maintenance of systems of which components compose serial reliability structure. In Fig. 3 the cost rate resulted by the unscheduled strategies and the cost rate against the interval according to the scheduled strategies are compared in the case of a single component. It worth noting that the costs related to both scheduled strategies tend to the value resulted by the corrective maintenance as the interval increases. For this component the best solution is the application of condition monitoring (CBM).
Fig. 4 – The variation of the cost rate and availability during the optimization
Conclusion The method presented in this paper can be used to determine the optimal maintenance for the components of a manufacturing system. The decision support, which is based on the minimization of the expected cost per unit time, covers four strategies and three policies. On the basis of the described method a software tool was developed which can also take into account a specified availability constraint during the optimization. Acknowledgements
Fig. 3 – Comparison of the cost per unit time according to the different strategies
In general case the optimal maintenance interval of various components which form a system are different. In practice this might lead to low availability due to the frequent interventions, hence some of the components should have common interval. The investigation of the overall cost rate resulted by every contraction possibility cannot be performed in acceptable time if the system consist of large number of components which require scheduled maintenance [8]. In order to overcome this problem the software tool implements agglomerative hierarchical clustering. In the beginning of this process each components form a unique cluster and the optimal maintenance interval are determined for each one. The system level availability which would be resulted by this initial solution is also estimated. Henceforward every pairwise contraction possibility are investigated and the unification of the pair which results the minimum value of the cumulated unit time cost is performed, then a new availability estimation is carried out. This procedure is repeated while a predefined availability constraint is not reached or until every components are placed in one cluster. In the latter case the specified availability constraint cannot be attained due to the low reliability and/or high time requirement of the maintenance tasks. In Fig. 4 the optimization of the maintenance of a system which consist of 32 components with scheduled strategy is illustrated. The achievable availability is
The research leading to these results is part of EASE-R3 project, which has received founds from the European Community’s Seventh Framework Programme FP7/20072013 under grant agreement no 608771. References [1] Barringer HP, A Life Cycle Cost Summary, International Conference on Maintenance Societies, Perth, Australia, May 2003. [2] Society of Automotive Engineers (SAE), Reliability and Maintainability Guideline for Manufacturing Machinery and Equipment, M110.2Warrendale, PA, 1999. [3] Society of Automotive Engineers (SAE), Life Cycle Cost – Reliability, Maintainability, and Supportability Guidebook, 3rd Edition, Warrendale, PA, 1995. [4] Leemis L., Reliability: Probabilistic Models and Statistical Methods, Prentice-Hall, 1995. [5] Ebeling CE, An Introduction to Reliability and Maintainability Engineering, Waveland Press, 2005. [6] Barlow, R.; L. Hunter, Optimum Preventive Maintenance Policies, Operations Research, vol. 8, pp. 90-100, 1960. [7] Guo, H; Szidarovszky, F; Gerokostopoulos, A; Pengying Niu: On determining optimal inspection interval for minimizing maintenance cost, Reliability and Maintainability Symposium (RAMS), pp 1-7, 2015. [8] Kocsis, Á; Németh, I: Clustered preventive maintenance scheduling for production machinery, Proceedings of the International Conference on Innovative Technologies, pp 198-201, 2015. [9] Aggogeri F., Faglia R., Mazzola M., Merlo A. (2015) Automating the simulation of SME processes through a discrete event parametric model. International Journal of Engineering Business Management, Volume 7, Issue 1, 2015, pp 1-10
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