Published

2019-01-01

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

Estimación Bayesiana de la disponibilidad límite en un sistema reparable uni-componente

DOI:

https://doi.org/10.15446/rce.v42n1.66279

Keywords:

Exponential and Gamma Distributions, Generalized Beta Distribution, Conjugate Analysis, Gibbs Sampling (en)
Análisis conjugado, Distribuciones Exponencial y Gamma, Distribución Beta generalizada, Sistema coherente. (es)

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Authors

  • Cristian A. Vásquez Escuela de Administración, Facultad de Ciencias Económicas y Administrativas, Pontificia Universidad Católica de Chile (Santiago, Chile)
  • Víctor H. Salinas Torres U. de Santiago de Chile https://orcid.org/0000-0001-9770-9662
  • José S. Romeo

 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.

En este trabajo se presenta un enfoque bayesiano para estimar la disponbilidad límite de un sistema reparable uni-componente. Un análisis bayesiano es desarrollado considerando distribuciones a priori informativa y poco informativa, respectivamnete. 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.

References

Abraham, B. & Balakrishna, N. (2000), ‘Estimation of limiting availability for a stationary bivariate process’, Journal of Applied Probability 37(3), 696–704.

Ananda, M. (1999), ‘Estimation and testing of availability of a parallel system with exponential failure and repair times’, Journal of Statistical Planning and Inference 77(2), 237–246.

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 re-

newal function and the point availability’, Scandinavian Journal of Statistics

, 277–287.

Baxter, L. & Li, L. (1996), ‘Nonparametric estimation of the limiting availability’, Lifetime Data Analysis 2, 391–402.

Chen, J. & Novick, M. (1996), ‘Bayesian analysis for binomial models with generalized Beta prior distributions’, Journal of Educational Statistics 9, 163–175.

Huang, K. & Mi, J. (2013), ‘Properties and computation of interval availability of system’, Statistics and Probability Letters 83, 1388–1396.

Jeffreys, H. (1996), Theory of Probability, 3 edn, Oxford University Press, Oxford.

Kaplan, E. & Meier, P. (1958), ‘Nonparametric estimation from incomplete observations’, Journal of the American Statistical Association 53, 457–481.

Libby, D. & Novick, M. (1982), ‘Multivariate generalized beta-distributions with applications to utility assessment’, Journal of Educational Statistics 7, 271–294.

Lu, M. & Mi, J. (2011), ‘ Statistical inference about availability of system with gamma lifetime and repair time’, Statistics and Probability Letters 18, 1–24.

Marsan, M., Balbo, G., Conte, G., Donatelli, S. & Franceschinis, G. (1995), Modelling with Generalised Stochastic Petri Net, Dipartimento d´Informatica, Universit degli Studi di Torino, Torino, Italy.

Mathew, A. & Balakrishna, N. (2014), ‘Nonparametric estimation of the interval reliability’, Journal of Statistical Theory and Applications 13, 356–366.

How to Cite

APA

Vásquez, C. A., Salinas Torres, V. H. & Romeo, J. S. (2019). Bayesian Estimation of the Limiting Availability in a Repairable One-Unit System. Revista Colombiana de Estadística, 42(1), 123–142. https://doi.org/10.15446/rce.v42n1.66279

ACM

[1]
Vásquez, C.A., Salinas Torres, V.H. and Romeo, J.S. 2019. Bayesian Estimation of the Limiting Availability in a Repairable One-Unit System. Revista Colombiana de Estadística. 42, 1 (Jan. 2019), 123–142. DOI:https://doi.org/10.15446/rce.v42n1.66279.

ACS

(1)
Vásquez, C. A.; Salinas Torres, V. H.; Romeo, J. S. Bayesian Estimation of the Limiting Availability in a Repairable One-Unit System. Rev. colomb. estad. 2019, 42, 123-142.

ABNT

VÁSQUEZ, C. A.; SALINAS TORRES, V. H.; ROMEO, J. S. Bayesian Estimation of the Limiting Availability in a Repairable One-Unit System. Revista Colombiana de Estadística, [S. l.], v. 42, n. 1, p. 123–142, 2019. DOI: 10.15446/rce.v42n1.66279. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/66279. Acesso em: 9 nov. 2025.

Chicago

Vásquez, Cristian A., Víctor H. Salinas Torres, and José S. Romeo. 2019. “Bayesian Estimation of the Limiting Availability in a Repairable One-Unit System”. Revista Colombiana De Estadística 42 (1):123-42. https://doi.org/10.15446/rce.v42n1.66279.

Harvard

Vásquez, C. A., Salinas Torres, V. H. and Romeo, J. S. (2019) “Bayesian Estimation of the Limiting Availability in a Repairable One-Unit System”, Revista Colombiana de Estadística, 42(1), pp. 123–142. doi: 10.15446/rce.v42n1.66279.

IEEE

[1]
C. A. Vásquez, V. H. Salinas Torres, and J. S. Romeo, “Bayesian Estimation of the Limiting Availability in a Repairable One-Unit System”, Rev. colomb. estad., vol. 42, no. 1, pp. 123–142, Jan. 2019.

MLA

Vásquez, C. A., V. H. Salinas Torres, and J. S. Romeo. “Bayesian Estimation of the Limiting Availability in a Repairable One-Unit System”. Revista Colombiana de Estadística, vol. 42, no. 1, Jan. 2019, pp. 123-42, doi:10.15446/rce.v42n1.66279.

Turabian

Vásquez, Cristian A., Víctor H. Salinas Torres, and José S. Romeo. “Bayesian Estimation of the Limiting Availability in a Repairable One-Unit System”. Revista Colombiana de Estadística 42, no. 1 (January 1, 2019): 123–142. Accessed November 9, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/66279.

Vancouver

1.
Vásquez CA, Salinas Torres VH, Romeo JS. Bayesian Estimation of the Limiting Availability in a Repairable One-Unit System. Rev. colomb. estad. [Internet]. 2019 Jan. 1 [cited 2025 Nov. 9];42(1):123-42. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/66279

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