La simulación de la confiabilidad de activos mediante el método de Monte Carlo. El caso específico de sistemas complejos y coherentes k-de-n, con datos censurados.
Barra lateral del artículo
Contenido principal del artículo
Resumen
Management of the life cycle of physical assets is based on the estimated life of the equipment, whether during the project, installation and start-up or throughout its useful life. In many situations, engineering needs to calculate or simulate equipment's estimated useful life using accurate data, which is often censored or incomplete. In many cases, equipment, regarding failures, can be structurally represented as block diagram systems. For this article, complex and coherent systems (from a reliability point of view) were studied. Censored data usually results in the loss of important information but must be included in the reliability analysis models of these complex systems. The article develops the complex and coherent systems theory and the respective reliability models. With a new and original approach, simulation algorithms were developed to generate random and censored data (right-censored and type I data). Two case studies of complex systems were designed to validate the algorithms. For each case, a set of simulations was developed with the variation of the reliability models' different parameters to compare better, tune and optimize the simulation of these complex systems.
One of the relevant results shows that the more censored data in the sample, the greater the bias and error about the true value. The variation of the parameter β (shape factor) from β = 0:5 to β = 1:5 proportionally increases the bias.
This article aims to validate the use of the Monte Carlo simulation tool and the Weibull statistical distribution and contribute to improving, with more precision and speed, algorithms for simulating the reliability of complex and coherent systems in the presence of censored data.
Descargas
Detalles del artículo
Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.
Citas
Balakrishnan, N., & Aggarwala, R. (2000). Progressive censoring: Theory, methods, and applications. Springer Science & Business Media.
Balakrishnan, N., & Kannan, N. (2001). Ch. 14. Point and interval estimation for parameters of the logistic distribution based on progressively type-II censored samples. In Handbook of statistics (Vol. 20, pp. 431–456). Elsevier. https://doi.org/10.1016/S0169-7161(01)20016-9
Balakrishnan, N., & Mitra, D. (2012). Left truncated and right censored Weibull data and likelihood inference with an illustration. Computational Statistics & Data Analysis, 56(12), 4011–4025.
Barlow, R. E., & Proschan, F. (1975). Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston.
Birolini, A. (2017). Reliability Engineering: Theory and Practice. Springer Berlin Heidelberg.
Childs, A., & Balakrishnan, N. (2000). Conditional inference procedures for the Laplace distribution when the observed samples are progressively censored. Metrika, 52(3), 253–265.
Crespo Marquez, A., et al. (2020). Maintenance Management through Intelligent Asset Management Platforms (IAMP). Emerging Factors, Key Impact Areas and Data Models. Energies, 13(15), 3762. https://doi.org/10.3390/en13153762
Gaspar, D. (2019). The advanced reliability and maintainability analysis using simulation tools. [Ph.D. Thesis]. FEUP, UP.
Genschel, U., & Meeker, W. Q. (2010). A comparison of maximum likelihood and median-rank regression for Weibull estimation. Quality Engineering, 22(4), 236–255.
Gijbels, I. (2010). Censored data. Wiley Interdisciplinary Reviews: Computational Statistics, 2(2), 178–188.
Horst, R. (2009). The Weibull Distribution A Handbook. Taylor and Francis Group.
J. E. Amadi-Echendu. (2004). Managing physical assets is a paradigm shift from maintenance. 2004 IEEE International Engineering Management Conference (IEEE Cat. No.04CH37574), 3, 1156–1160 Vol. 3. https://doi.org/10.1109/IEMC.2004.1408874
Kaufmann, A., Grouchko, D., & Cruon, R. (1977). Mathematical Models for the Study of the Reliability of Systems. Academic Press.
Maletič, D., et al. (2020). An Analysis of Physical Asset Management Core Practices and Their Influence on Operational Performance. Sustainability, 12(21), 9097. https://doi.org/10.3390/su12219097
Mousa, M. A., & Jaheen, Z. (2002). Statistical inference for the Burr model based on progressively censored data. Computers & Mathematics with Applications, 43(10–11), 1441–1449.
Murthy, D. P., Xie, M., & Jiang, R. (2004). Weibull models (Vol. 505). John Wiley & Sons.
Nelson, W. (1985). Weibull analysis of reliability data with few or no failures. Journal of Quality Technology, 17(3), 140–146.
Olteanu, D., & Freeman, L. (2010). The evaluation of median-rank regression and maximum likelihood estimation techniques for a two-parameter Weibull distribution. Quality Engineering, 22(4), 256–272.
Ross, S. M. (2012). Simulation. Elsevier Science.
Soliman, A. A. (2005). Estimation of parameters of life from progressively censored data using Burr-XII model. IEEE Transactions on Reliability, 54(1), 34–42.
Somboonsavatdee, A., Nair, V. N., & Sen, A. (2007). Graphical estimators from probability plots with right-censored data. Technometrics, 49(4), 420–429.
Trindade, M., Almeida, N., Finger, M., & Ferreira, D. (2019). Design and Development of a Value-Based Decision Making Process for Asset Intensive Organizations. In J. Mathew, C. W. Lim, L. Ma, D. Sands, M. E. Cholette, & P. Borghesani (Eds.), Asset Intelligence through Integration and Interoperability and Contemporary Vibration Engineering Technologies (pp. 605–623). Springer International Publishing.
Wang, P., & Coit, D. W. (2005). Repairable systems reliability trend tests and evaluation. Proceedings of the Annual Reliability and Maintainability Symposium, 416–421.