Defining Optimal Maintenance Scope for Multiple k-out-of-n Load-Sharing Production Systems Connected in Series Based on RUL Predictions
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Published
Nov 13, 2020
Leonardo R. Rodrigues
Abstract
This paper presents a method to define the optimal maintenance scope of a production system consisting of multiple k-out-of-n systems connected in series. Maintenance recommendations are based on Remaining Useful Life (RUL) predictions obtained from a Prognostics and Health Management (PHM) system for each production unit within the production system. Defining the techniques applied in order to estimate the degradation level of production units is out of the scope of this paper. It is assumed here that a PHM system is available and provides the degradation level and RUL estimates for each production unit. The goal is to find the maintenance scope that minimizes the expected total cost per cycle until the next maintenance activity. A k-out-of-n load-sharing system is assumed, which means that the failure of a production unit results in a higher load (and consequently a higher degradation rate) on the surviving production units. The total cost comprises the production cost and the maintenance cost. Production cost of each k-out-of-n system is also affected by the number of surviving production units. A preventive maintenance cost is incurred to maintain a degraded but still functional production unit. A corrective maintenance cost is incurred
to maintain a failed production unit. An Ant Colony Optimization (ACO) approach is adopted, which allows the proposed method to deal with large instances of the problem. A numerical example is presented to illustrate the application of the proposed method.
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Keywords
condition-based maintenance optimization, production systems, k-out-of-n systems, load-sharing systems
References
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Afac, H., & Saini, S. (2011). On the solutions to the travelling salesman problem using nature inspired computing techniques. International Journal of Computer Science Issues, 8(2), 326–334.
Ahmad, R., & Kamaruddin, S. (2012). A review of conditionbased maintenance decision-making. European Journal of Industrial Engineering, 6(5), 519–541.
Amari, S. V., & Bergman, R. (2008, January). Reliability analysis of k-out-of-n load-sharing systems. In Proceedings of the 2008 annual reliability and maintainability symposium (RAMS) (pp. 440–445). Las Vegas.
Barajas, L. G., & Srinivasa, N. (2008, October). Realtime diagnostics, prognostics and health management for large-scale manufacturing maintenance systems. In Proceedings of the ASME 2008 international manufacturing science and engineering conference (pp. 85–94). Evanston.
Bernarden, J. (2012). Indirect jobs: A direct way to talk about why we need smart manufacturing (Tech. Rep.). Rockwell Automation.
Brodsky, A., Krishnamoorthy, M., Menascé, D. A., Shao, G., & Rachuri, S. (2014, June). Toward smart manufacturing using decision analytics. In Proceedings of the 2014 ieee international conference on big data (pp. 967–977). Anchorage.
Camci, F. (2009). System maintenance scheduling with prognostics information using genetic algorithm. IEEE Transactions on Reliability, 58(3), 539–552.
Chmait, N., & Challita, K. (2013). Using simulated annealing and ant-colony optimization algorithms to solve the scheduling problem. Computer Science and Information Technology, 1(3).
Colorni, A., Dorigo, M., & Maniezzo, V. (1991, December). Distributed optimization by ant colonies. In Proceedings of the european conference on artificial life (pp.134–142). Paris.
Cordon, O., Herrera, F., & St¨utzle, T. (2002). A review on the ant colony optimization metaheuristic: Basis, models and new trends. Mathware & Soft Computing, 9, 141–175.
Gaertner, D., & Clark, K. (2005, July). On optimal parameters for ant colony optimization algorithms. In Proceedings of the international conference of artificial intelligence (pp. 83–89). Pittsburgh.
Gebraeel, N. (2010). Prognostics-based identification of the top k units in a fleet. IEEE Transactions on Automation and Science Engineering, 7, 37–48.
Ghonaim, W., Ghenniwa, H., & Shen, W. (2011, June). Towards an agent oriented smart manufacturing system. In Proceedings of the 2011 15th international conference on computer supported cooperative work in design (pp. 636–642). Lausanne.
Heddy, G., Huzaifa, U., Beling, P., Haimes, Y., Marvel, J., Weiss, B., & LaViers, A. (2015, October). Linear temporal logic (LTL) based monitoring of smart manufacturing systems. In Proceedings of the 2015 annual conference of the prognostics and health management society (pp. 640–649). San Diego.
Huynh, K. T., Barros, A., & Bérenguer, C. (2015). Multilevel decision-making for the predictive maintenance of k-out-of-n:F deteriorating systems. IEEE Transactions on Reliability, 64(1), 94–117.
Jung, K., Morris, K. C., Lyons, K. W., Leong, S., & Cho, H. (2015). Mapping strategic goals and operational performance metrics for smart manufacturing systems. Procedia Computer Science, 44, 184–193.
Kacprzynski, G. J., Roemer, M. J., & Hess, A. J. (2002, March). Health management system design: Development, simulation and cost/benefit optimization. In Proceedings of the 2002 IEEE aerospace conference (pp. 3065–3072). Big Sky.
Khatab, A., Nahas, N., & Nourelfath, M. (2009). Availability of k-out-of-n:G systems with non-identical components subject to repair priorities. Reliability Engineering and System Safety, 94, 142–151.
Kuo, W., & Zuo, M. J. (2003). Optimal reliability modeling - principles and applications (1st ed.). New Jersey: Wiley.
Lu, L., & Lewis, G. (2008). Configuration determination for k-out-of-n partially redundant systems. Reliability Engineering and System Safety, 93(11), 1594–1604.
Lu, Y., Morris, K. C., & Frechette, S. (2015, August). Standards landscape and directions for smart manufacturing systems. In Proceedings of the 2011 15th international conference on computer supported cooperative work in design (pp. 998–1005). Gothenburg.
Malinowski, M. L., Beling, P. A., Haimes, Y., LaViers, A. E., Marvel, J. A., & Weiss, B. A. (2015, October). System interdependency modeling in the design of prognostic and health management systems in smart manufacturing. In Proceedings of the 2015 annual conference of the prognostics and health management society (pp. 210–222). San Diego.
Medeiros, I. P., Rodrigues, L. R., Shiguemori, E. H., Santos, R., & Nascimento Jr, C. L. (2014, April). PHMbased multi-UAV task assignment. In Proceedings of the 2014 IEEE systems conference (pp. 42–49). Ottawa.
Moghaddass, R., Zuo, M. J., & Wang, W. (2011). Availability of a general k-out-of-n:G system with nonidentical components considering shut-off rules using quasi-birthdeath process. Reliability Engineering and System Safety, 96, 489–496.
Mohammad, R., Kalam, A., & Amari, S. V. (2013, January). Reliability of load-sharing systems subject to proportional hazards model. In Proceedings of the 2013 annual reliability and maintainability symposium (RAMS) (pp. 1–5). Orlando.
Pozsgai, P., Neher, W., & Bertsche, B. (2003, January). Models to consider load-sharing in reliability calculation and simulation of systems consisting of mechanical components. In Proceedings of the 2003 annual reliability and maintainability symposium (pp. 493–499). Tampa.
Rodrigues, L. R., Gomes, J. P. P., Ferri, F. A. S., Medeiros, I. P., Galvao, R. K. H., & Nascimento Jr, C. L. (2015). Use of PHM information and system architecture for optimized aircraft maintenance planning. IEEE Systems Journal, 9(4), 1197–1207.
Rodrigues, L. R., Medeiros, I. P., & Kern, C. S. (2015, April). Maintenance cost optimization for multiple components using a condition based method. In Proceedings of the 2015 IEEE Systems Conference (pp. 164–169). Vancouver.
Rodrigues, L. R., & Yoneyama, T. (2012, September). Spare parts inventory control for non-repairable items based on prognostics and health monitoring information. In Proceedings of the 2012 annual conference of the prognostics and health management society (pp. 53–62). Minneapolis: PHM society.
Sandborn, P. A., & Wilkinson, C. A. (2007). A maintenance planning and business case development model for the application of prognostics and health management (PHM) to electronic systems. Microelectronics Reliability, 47, 1889–1901.
Vachtsevanos, G., Lewis, F. L., Roemer, M., Hess, A., &Wu, B. (2006). Intelligent fault diagnosis and prognosis for engineering systems (1st ed.). New Jersey: John Wiley & sons.
van der Zwaan, S., & Marques, C. (1999). Ant colony optimization for job shop scheduling. In Proceedings of third workshop on genetic algorithms and artificial life.
van Noortwijk, J. M. (2009). A survey of the application of gamma processes in maintenance. Reliability Engineering and System Safety, 94, 2–21.
Weiss, B. A., Vogl, G., Helu, M., Qiao, G., Pellegrino, J., Justiniano, M., & Raghunathan, A. (2015, October). Measurement science for prognostics and health management for smart manufacturing systems: Key findings from a roadmapping workshop. In Proceedings of the 2015 annual conference of the prognostics and health management society (pp. 232–333). San Diego.
Yinghui, T., & Jing, Z. (2008). New model for load-sharing kout- of-n:G system with different components. Journal of Systems Engineering and Electronics, 19(4), 748–751.
Zhou, R., Lee, H. P., & Nee, A. Y. C. (2008). Applying ant colony optimization (ACO) algorithm to dynamic job shop scheduling problems. International Journal of Manufacturing Research, 3(3), 301–320.
Zhou, Y., Zhang, Z., L´ın, T. R., & Ma, L. (2013). Maintenance optimisation of a multi-state series-parallel system considering dependence and state-dependence inspection intervals. Reliability Engineering and System Safety, 11, 248–259.
Afac, H., & Saini, S. (2011). On the solutions to the travelling salesman problem using nature inspired computing techniques. International Journal of Computer Science Issues, 8(2), 326–334.
Ahmad, R., & Kamaruddin, S. (2012). A review of conditionbased maintenance decision-making. European Journal of Industrial Engineering, 6(5), 519–541.
Amari, S. V., & Bergman, R. (2008, January). Reliability analysis of k-out-of-n load-sharing systems. In Proceedings of the 2008 annual reliability and maintainability symposium (RAMS) (pp. 440–445). Las Vegas.
Barajas, L. G., & Srinivasa, N. (2008, October). Realtime diagnostics, prognostics and health management for large-scale manufacturing maintenance systems. In Proceedings of the ASME 2008 international manufacturing science and engineering conference (pp. 85–94). Evanston.
Bernarden, J. (2012). Indirect jobs: A direct way to talk about why we need smart manufacturing (Tech. Rep.). Rockwell Automation.
Brodsky, A., Krishnamoorthy, M., Menascé, D. A., Shao, G., & Rachuri, S. (2014, June). Toward smart manufacturing using decision analytics. In Proceedings of the 2014 ieee international conference on big data (pp. 967–977). Anchorage.
Camci, F. (2009). System maintenance scheduling with prognostics information using genetic algorithm. IEEE Transactions on Reliability, 58(3), 539–552.
Chmait, N., & Challita, K. (2013). Using simulated annealing and ant-colony optimization algorithms to solve the scheduling problem. Computer Science and Information Technology, 1(3).
Colorni, A., Dorigo, M., & Maniezzo, V. (1991, December). Distributed optimization by ant colonies. In Proceedings of the european conference on artificial life (pp.134–142). Paris.
Cordon, O., Herrera, F., & St¨utzle, T. (2002). A review on the ant colony optimization metaheuristic: Basis, models and new trends. Mathware & Soft Computing, 9, 141–175.
Gaertner, D., & Clark, K. (2005, July). On optimal parameters for ant colony optimization algorithms. In Proceedings of the international conference of artificial intelligence (pp. 83–89). Pittsburgh.
Gebraeel, N. (2010). Prognostics-based identification of the top k units in a fleet. IEEE Transactions on Automation and Science Engineering, 7, 37–48.
Ghonaim, W., Ghenniwa, H., & Shen, W. (2011, June). Towards an agent oriented smart manufacturing system. In Proceedings of the 2011 15th international conference on computer supported cooperative work in design (pp. 636–642). Lausanne.
Heddy, G., Huzaifa, U., Beling, P., Haimes, Y., Marvel, J., Weiss, B., & LaViers, A. (2015, October). Linear temporal logic (LTL) based monitoring of smart manufacturing systems. In Proceedings of the 2015 annual conference of the prognostics and health management society (pp. 640–649). San Diego.
Huynh, K. T., Barros, A., & Bérenguer, C. (2015). Multilevel decision-making for the predictive maintenance of k-out-of-n:F deteriorating systems. IEEE Transactions on Reliability, 64(1), 94–117.
Jung, K., Morris, K. C., Lyons, K. W., Leong, S., & Cho, H. (2015). Mapping strategic goals and operational performance metrics for smart manufacturing systems. Procedia Computer Science, 44, 184–193.
Kacprzynski, G. J., Roemer, M. J., & Hess, A. J. (2002, March). Health management system design: Development, simulation and cost/benefit optimization. In Proceedings of the 2002 IEEE aerospace conference (pp. 3065–3072). Big Sky.
Khatab, A., Nahas, N., & Nourelfath, M. (2009). Availability of k-out-of-n:G systems with non-identical components subject to repair priorities. Reliability Engineering and System Safety, 94, 142–151.
Kuo, W., & Zuo, M. J. (2003). Optimal reliability modeling - principles and applications (1st ed.). New Jersey: Wiley.
Lu, L., & Lewis, G. (2008). Configuration determination for k-out-of-n partially redundant systems. Reliability Engineering and System Safety, 93(11), 1594–1604.
Lu, Y., Morris, K. C., & Frechette, S. (2015, August). Standards landscape and directions for smart manufacturing systems. In Proceedings of the 2011 15th international conference on computer supported cooperative work in design (pp. 998–1005). Gothenburg.
Malinowski, M. L., Beling, P. A., Haimes, Y., LaViers, A. E., Marvel, J. A., & Weiss, B. A. (2015, October). System interdependency modeling in the design of prognostic and health management systems in smart manufacturing. In Proceedings of the 2015 annual conference of the prognostics and health management society (pp. 210–222). San Diego.
Medeiros, I. P., Rodrigues, L. R., Shiguemori, E. H., Santos, R., & Nascimento Jr, C. L. (2014, April). PHMbased multi-UAV task assignment. In Proceedings of the 2014 IEEE systems conference (pp. 42–49). Ottawa.
Moghaddass, R., Zuo, M. J., & Wang, W. (2011). Availability of a general k-out-of-n:G system with nonidentical components considering shut-off rules using quasi-birthdeath process. Reliability Engineering and System Safety, 96, 489–496.
Mohammad, R., Kalam, A., & Amari, S. V. (2013, January). Reliability of load-sharing systems subject to proportional hazards model. In Proceedings of the 2013 annual reliability and maintainability symposium (RAMS) (pp. 1–5). Orlando.
Pozsgai, P., Neher, W., & Bertsche, B. (2003, January). Models to consider load-sharing in reliability calculation and simulation of systems consisting of mechanical components. In Proceedings of the 2003 annual reliability and maintainability symposium (pp. 493–499). Tampa.
Rodrigues, L. R., Gomes, J. P. P., Ferri, F. A. S., Medeiros, I. P., Galvao, R. K. H., & Nascimento Jr, C. L. (2015). Use of PHM information and system architecture for optimized aircraft maintenance planning. IEEE Systems Journal, 9(4), 1197–1207.
Rodrigues, L. R., Medeiros, I. P., & Kern, C. S. (2015, April). Maintenance cost optimization for multiple components using a condition based method. In Proceedings of the 2015 IEEE Systems Conference (pp. 164–169). Vancouver.
Rodrigues, L. R., & Yoneyama, T. (2012, September). Spare parts inventory control for non-repairable items based on prognostics and health monitoring information. In Proceedings of the 2012 annual conference of the prognostics and health management society (pp. 53–62). Minneapolis: PHM society.
Sandborn, P. A., & Wilkinson, C. A. (2007). A maintenance planning and business case development model for the application of prognostics and health management (PHM) to electronic systems. Microelectronics Reliability, 47, 1889–1901.
Vachtsevanos, G., Lewis, F. L., Roemer, M., Hess, A., &Wu, B. (2006). Intelligent fault diagnosis and prognosis for engineering systems (1st ed.). New Jersey: John Wiley & sons.
van der Zwaan, S., & Marques, C. (1999). Ant colony optimization for job shop scheduling. In Proceedings of third workshop on genetic algorithms and artificial life.
van Noortwijk, J. M. (2009). A survey of the application of gamma processes in maintenance. Reliability Engineering and System Safety, 94, 2–21.
Weiss, B. A., Vogl, G., Helu, M., Qiao, G., Pellegrino, J., Justiniano, M., & Raghunathan, A. (2015, October). Measurement science for prognostics and health management for smart manufacturing systems: Key findings from a roadmapping workshop. In Proceedings of the 2015 annual conference of the prognostics and health management society (pp. 232–333). San Diego.
Yinghui, T., & Jing, Z. (2008). New model for load-sharing kout- of-n:G system with different components. Journal of Systems Engineering and Electronics, 19(4), 748–751.
Zhou, R., Lee, H. P., & Nee, A. Y. C. (2008). Applying ant colony optimization (ACO) algorithm to dynamic job shop scheduling problems. International Journal of Manufacturing Research, 3(3), 301–320.
Zhou, Y., Zhang, Z., L´ın, T. R., & Ma, L. (2013). Maintenance optimisation of a multi-state series-parallel system considering dependence and state-dependence inspection intervals. Reliability Engineering and System Safety, 11, 248–259.
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