Bayesian Estimation of the Limiting Availability in a Repairable One-Unit System

• Autores: Cristián A. Vásquez, Víctor H Salinas-Torres, José S. Romeo
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 42, Nº. 1, 2019, págs. 123-142
• Idioma: inglés
• DOI: 10.15446/rce.v42n1.66279
• Títulos paralelos:
  • Estimación Bayesiana de la disponibilidad límite en un sistema reparable uni-componente
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen En este trabajo se presenta un enfoque bayesiano para estimar la disponibilidad límite de un sistema reparable uni-componente. Un análisis bayesiano es desarrollado considerando distribuciones a priori informativa y poco informativa, respectivamente. Simulaciones son presentadas para estudiar el desempeño de las soluciones bayesianas. El método de máxima verosimilitud también es reconsiderado. Finalmente, un caso de estudio es considerado, la metodología bayesiana es aplicada para estimar la disponibilidad límite de un paletizador. el cual es usado en el embalaje de botellas de vidrio. Extensiones a un sistema coherente, también son discutidas.

  • English

    Abstract This work presents a Bayesian approach for estimating the limiting availability of an one-unit repairable system. A Bayesian analysis is developed considering an informative prior and a less informative prior distribution, respectively. Simulations are presented to study the performance of the Bayesian solutions. The maximum likelihood method is also revisited. Finally, a case study is considered, the Bayesian methodology is applied to estimate the limiting availability of a palletizer, which is used in the packaging of glass bottles. Extensions to a coherent system are also discussed.

• Referencias bibliográficas
  • Abraham, B.,Balakrishna, N. (2000). Estimation of limiting availability for a stationary bivariate process. Journal of Applied Probability....
  • Ananda, M. (1999). Estimation and testing of availability of a parallel system with exponential failure and repair times. Journal of Statistical...
  • Barlow, R.,Proschan, F. (1996). Mathematical Theory of Reliability, classics in applied probability EDN. SIAM. New York.
  • Baxter, L.,Li, L. (1994). Non-parametric confidence intervals for the renewal function and the point availability. Scandinavian Journal of...
  • Baxter, L.,Li, L. (1996). Nonparametric estimation of the limiting availability. Lifetime Data Analysis. 2. 391
  • Chen, J.,Novick, M. (1996). Bayesian analysis for binomial models with generalized Beta prior distributions. Journal of Educational Statistics....
  • Huang, K.,Mi, J. (2013). Properties and computation of interval availability of system. Statistics and Probability Letters. 83. 1388
  • Jeffreys, H. (1996). Theory of Probability. 3. Oxford University Press. Oxford.
  • Kaplan, E.,Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association. 53. 457
  • Libby, D.,Novick, M. (1982). Multivariate generalized beta-distributions with applications to utility assessment. Journal of Educational Statistics....
  • Lu, M.,Mi, J. (2011). Statistical inference about availability of system with gamma lifetime and repair time. Statistics and Probability Letters....
  • Marsan, M.,Balbo, G.,Conte, G.,Donatelli, S.,Franceschinis, G. (1995). Modelling with Generalised Stochastic Petri Net. Dipartimento d-Informatica,...
  • Mathew, A.,Balakrishna, N. (2014). Nonparametric estimation of the interval reliability. Journal of Statistical Theory and Applications. 13....
  • Mi, J. (1991). Interval estimation of availability of a series system. IEEE Transactions on Reliability R-40. 541
  • Mi, J. (2006). Limiting availability of system with non-identical lifetime distributions and non-identical repair time distributions. Statistics...
  • Mishra, A.,Jain, M. (2013). Availability of k-out-of-n: F secondary subsystem with general repair time distribution. International Journal...
  • (2007). R Development Core Team. R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing.
  • Ross, S. (1996). Stochastic Processes. 2. Wiley. New York.
  • Sarkar, J.,Chandhuri, G. (1999). Availability of a system with gamma life and exponential repair time under a perfect repair policy. Statistics...
  • (2017). SAS SAS software, Version [9.4] of the SAS System for [Microsoft Windows Workstation for x64]. SAS Institute Inc. North Caroline,...
  • Sethuraman, J.,Hollander, M. (2009). Nonparametric Bayes estimation in repair models. Journal of Statistical Planning and Inference. 139....
  • Sobolewski, R. (2016). Implication of availability of an electrical system of a wind farm for the farm's output power estimation. Advances...
  • Thompson, W.,Palicio, P. (1975). Bayesian confidence limits for the availability of systems. IEEE Transactions on Reliability R-24.
  • Vásquez, C. (2006). Estimation of the limiting availability in a reliability system. Universidad de Santiago de Chile, Facultad de Ciencia....
  • Zacks, S. (1971). The Theory of Statistical Inference. 1. Wiley. New York.