Published

2018-01-01

Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair

Bandas de confianza simultáneas para la estimación del costo medio de garantía descontado para un sistema coherentes bajo reparo mínimo

DOI:

https://doi.org/10.15446/rce.v41n1.59929

Keywords:

Central Limit Theorem, Coverage Probability, Point Process, Resampling, Semimartingales, Weak Convergence (en)
convergencia débil, probabilidad de cobertura, proceso puntual, remuestreo, semimartingalas, teorema de límite central (es)

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Authors

  • Carlos Mario Lopera Gómez Universidad Nacional de Colombia, Sede Medellín
  • Nelfi Gertrudis Gónzalez Álvarez Universidad Nacional de Colombia, Sede Medellín
This paper develops simultaneous confidence bands using computer intensive methods based on resampling, for the expected discounted warranty costs in coherent systems under physical minimal repair, that is, when the system is observed at its components level and only the component that causes the fault is minimally repaired. For this purpose, it is shown that, under the framework of the Martingale processes and the central limit resampling theorem (CLRT) over stochastic processes, the discounted warranty cost processes satisfy the conditions set by the central limit resampling theorem (CLRT). Additionally, a simulation study is performed on the most relevant variables, such that the finite sample features of the proposed bands may be assessed, based on their actual coverage probabilities. The results in the considered scenarios show that resampling-based simultaneous confidence bands have coverage probabilities that are close to the nominal coverage. In particular, the agreement is good when there are 100 systems or more where a large number of resamples are used for the approximation.
Este trabajo desarrolla bandas de confianza simultáneas usando métodos computacionales intensivos basados en remuestreo, para el costo medio de garantía descontado en sistemas coherentes bajo reparo mínimo físico, esto es, cuando el sistema es observado al nivel de sus componentes y sólo la componente que causa la falla es reparada mínimamente. Para ello se prueba que, bajo el marco teórico de los procesos martingala, los procesos de costos de garantía descontados cumplen las condiciones del teorema de límite central de remuestreo (CLRT). Un estudio de simulación Monte Carlo se realiza para evaluar, a través de las probabilidades de cobertura alcanzadas, el desempeño de las bandas propuestas en muestras finitas. Los resultados en los escenarios considerados muestran que las bandas de confianza basadas en remuestreo tienen probabilidades de cobertura con valores cercanos a los esperados, en particular para aquellas basadas en muestras con más de 100 sistemas donde el número de remuestras usado para la aproximación es grande.

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How to Cite

APA

Lopera Gómez, C. M. & Gónzalez Álvarez, N. G. (2018). Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair. Revista Colombiana de Estadística, 41(1), 1–30. https://doi.org/10.15446/rce.v41n1.59929

ACM

[1]
Lopera Gómez, C.M. and Gónzalez Álvarez, N.G. 2018. Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair. Revista Colombiana de Estadística. 41, 1 (Jan. 2018), 1–30. DOI:https://doi.org/10.15446/rce.v41n1.59929.

ACS

(1)
Lopera Gómez, C. M.; Gónzalez Álvarez, N. G. Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair. Rev. colomb. estad. 2018, 41, 1-30.

ABNT

LOPERA GÓMEZ, C. M.; GÓNZALEZ ÁLVAREZ, N. G. Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair. Revista Colombiana de Estadística, [S. l.], v. 41, n. 1, p. 1–30, 2018. DOI: 10.15446/rce.v41n1.59929. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/59929. Acesso em: 13 nov. 2025.

Chicago

Lopera Gómez, Carlos Mario, and Nelfi Gertrudis Gónzalez Álvarez. 2018. “Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair”. Revista Colombiana De Estadística 41 (1):1-30. https://doi.org/10.15446/rce.v41n1.59929.

Harvard

Lopera Gómez, C. M. and Gónzalez Álvarez, N. G. (2018) “Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair”, Revista Colombiana de Estadística, 41(1), pp. 1–30. doi: 10.15446/rce.v41n1.59929.

IEEE

[1]
C. M. Lopera Gómez and N. G. Gónzalez Álvarez, “Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair”, Rev. colomb. estad., vol. 41, no. 1, pp. 1–30, Jan. 2018.

MLA

Lopera Gómez, C. M., and N. G. Gónzalez Álvarez. “Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair”. Revista Colombiana de Estadística, vol. 41, no. 1, Jan. 2018, pp. 1-30, doi:10.15446/rce.v41n1.59929.

Turabian

Lopera Gómez, Carlos Mario, and Nelfi Gertrudis Gónzalez Álvarez. “Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair”. Revista Colombiana de Estadística 41, no. 1 (January 1, 2018): 1–30. Accessed November 13, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/59929.

Vancouver

1.
Lopera Gómez CM, Gónzalez Álvarez NG. Simultaneous Confidence Bands for the Estimation of Expected Discounted Warranty Costs for Coherent Systems under Minimal Repair. Rev. colomb. estad. [Internet]. 2018 Jan. 1 [cited 2025 Nov. 13];41(1):1-30. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/59929

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