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

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 fa...

Full description

Autores:
Lopera Gómez, Carlos Mario
Gónzalez Álvarez, Nelfi Gertrudis
Tipo de recurso:
Article of journal
Fecha de publicación:
2018
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/66490
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/66490
http://bdigital.unal.edu.co/67518/
Palabra clave:
51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Central Limit Theorem
Coverage Probability
Point Process
Resampling
Semimartingales
Weak Convergence
convergencia débil
probabilidad de cobertura
proceso puntual
remuestreo
semimartingalas
teorema de límite central
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
Description
Summary: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.