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

• Autores: Carlos M. Lopera Gómez, Nelfi González-Alvarez
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 41, Nº. 1, 2018, págs. 1-30
• Idioma: inglés
• DOI: 10.15446/rce.v41n1.59929
• Títulos paralelos:
  • Bandas de confianza simultáneas para la estimación del costo medio de garantía descontado para un sistema coherentes bajo reparo mínimo
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen 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.

  • English

    Abstract 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.

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