Published

2015-07-01

Aproximación al uso de una regla de parada óptima sobre sus sistemas coherentes

Approximation to the use of an optimal stopping rule for coherent systems

DOI:

https://doi.org/10.15446/rev.fac.cienc.v4n2.50637

Keywords:

Modelo general de tiempo de vida, reparo mínimo, semi-martingala regular, sistema coherente, tasa de falla (es)
Coherent system, failure rate, general lifetime model, minimal repair, smooth semimartingale (en)

Downloads

Authors

  • Nelfi Gertrudis González Alvarez Universidad Nacional de Colombia

En este trabajo se introducen varias aplicaciones de la regla de parada óptima denominada regla ILA (Innitesimal Look Ahead rule) en la solución de problemas de optimización en procesos de mantenimiento, de burn-in y de garantías sobre sistemas coherentes observados al nivel de sus componentes. Estas aplicaciones corresponden a extensiones propuestas en este trabajo de problemas formulados previamente en la literatura de conabilidad, con el n de modelar los procesos de falla/reparo y las funciones de costo asociados, cuando el sistema coherente es observado bajo una ltración completa.

In this paper  is introduced some applications of the optimal stopping rule known as ILA rule (Infinitesimal Look Ahead rule) in solving optimization problems in maintenance, burn-in and guarantees processes on coherent systems observed at the level of components. These applications correspond to extensions proposed in this work for problems formulated previously in literature of reliability, in order to model the processes of failure/repair and their associated cost functions, when the system is observed under a complete filtration.

References

Aven, T. and Jensen, U. (2013). Stochastic models in reliability, 2 edn, Springer Science Business Media, New York.

Bai, J. and Pham, H. (2004). Discounted warranty cost of minimally repaired series systems, IEEE Transactions on Reliability 53, 37–42.

Barlow, R. E. and Proschan, F. (1975). Statistical theory of reliability and life testing: Probability models, Holt, Rinehart and Winston, Inc., New York.

Blischke, W. R. and Murthy, D. N. P. (1992a) Product warranty management-1: A taxonomy for warranty policies, European Journal of Operational Research 62, 127–148.

Blischke, W. R. and Murthy, D. N. P. (1992b). Product warranty management-2: An integrated framework for study, European Journal of Operational Research 62, 261–281.

Blischke, W. R. and Murthy, D. N. P. (1992c). Product warranty management-3: A review of mathematical models, European Journal of Operational Research 63, 1–34.

Blischke, W. R. and Murthy, D. N. P. (1994). Warranty cost analysis, Marcel Dekker, Inc., New York.

Blischke, W. R. and Murthy, D. N. P. (1996). Product warranty handbook, Marcel Dekker, Inc., New York.

Block, H. S. and Savits, T. H. (1997). Burn-in, Statistical Science 12, 1–19.

Block, H. W., Borges, W. S. and Savits, T. H. (1985). Age-dependent minimal repair, Journal of Applied Probability 22, 370–385.

Brémaud, P. (1981). Point processes and queues, Martingale dynamics, Springer, New York.

Bueno, V. C. (2007). Burn-in of a coherent system at component information level, Technical Report RT-MAE 2007-15, Universidade de São Paulo, Instituto de Matemática e Estatística, São Paulo.

Cha, J. H. (2000). On a better burn-in procedure, Journal of Applied Probability 12, 1090–1103.

Cha, J. H. (2001). Burn-in procedures for a generalized model, Journal of Applied Probability 38, 542–553.

Cha, J. H. (2003). A further extension of the generalized burn-in model, Journal of Applied Probability 40, 264–270.

Chien, Y. H. (2005). Determining optimal warranty periods from the seller’s perspective and optimal out-of-warranty replacement age from the buyer’s perspective, International Journal of Systems Science 36, 631–637.

Feng, Q., Peng, H. and Coit, D. W. (2010). A degration based-model for joint optimization of burn-in, quality inspection, and maintenance: a light display device application, The International Journal of Advanced Manufacturing Technology 50, 801–808.

González, N. G. (2009). Processos de burn-in e de garantia em sistemas coerentes sob o modelo de tempo de vida geral, Tese De Doutorado, Universidade de São Paulo, Instituto de Matemática e Estatística.

Ja, S. S., Kulkarni, V., Mitra, A. and Patankar, G. (2001). A non-renewable minimal-repair warranty policy with time-dependent costs, IEEE Transactions on Reliability 50, 346–352.

Jensen, F. and Petersen, N. E. (1982). Burn-in, Wiley, New York.

Jensen, U. (1989). Monotone stopping rules for stochastic processes in a semimartingale representation with applications, Optimization 20, 837–852.

Jensen, U. (1990). A general replacement model, ZOR - Methods and Models of Operations Research 34, 423–439.

Kar, T. R. and Nachlas, J. A. (1997). Coordinated warranty & burn-in strategies, IEEE Transactions on Reliability 46, 512–518.

Kim, C. S., Djamaludin, I. and Murthy, D. N. P. (2001). Warranty cost analysis with heterogeneous usage intensity, International Transactions in Operational Research 8, 337–347.

Kuo, W. and Kuo, Y. (1983). Facing the headaches for early failures. a state of the art review of burn-in decision, Proc. IEEE 71, 1257–1266.

Kurz, D., Lewitschnig, H. & Pilz, J. (2014). Advanced Bayesian estimation of Weibull early life failure distributions, Quality and Reliability Engineering International 30, 363-373.

Mi, J. (1991). Burn-in, PhD thesis, University of Pittsburgh, Department of Mathematics and Statistics, Pittsburgh.

Mi, J. (1994). Burn-in and maintenance policies, Advances in Applied Probability 26, 207–221.

Mi, J. (1997). Warranty policies and burn-in, Naval Research Logistics 44, 199–209.

Murthy, D. N. P. (1990). Optimal reliability choice in product design, Engineering Optimization 15, 280–294.

Nguyen, D. G. and Murthy, D. N. P. (1982). Optimal burn-in time to minimize cost for products sold under warranty, IIE Transactions 14, 167–174.

Raharshi, S. & Raharshi, M. B. (1988). Bathtub distributions: A review, Communications in Statistics - Theory and Methods, 17, 2597-2621.

Sheu, S. H. and Chien, Y. H. (2005). Optimal burn-in time to minimize the cost for general repairable products sold under warranty, European Journal of Operational Research 163(2), 445–461.

Tsai, C.-C., Tseng, S.-T. and Balakrishnan, N. (2011). Optimal burn-in policy for highly reliable products using gamma degradation process, IEEE Transactions on Reliability 60, 234–245.

Ulusoy, S. K., Mazzuchi, T. A., & Perlstein, D. (2011). Bayesian calculation of optimal burn-in time using the joint criteria of cost and delivered reliability, Quality and Reliability Engineering International 27, 569-580.

Xiang, Y., Coit, D. W. and Feng, Q. (2013). n Subpopulations experiencing stochastic degradation: reliability modeling, bur-in, and preventive replacement optimization IEEE Transactions 45, 391–408.

Ye, Z. S., Tang, L. C. and Xie, M. (2011). Performance-based burn-in for products sold with warranty, Proceedings of the 2011 IEEE IEEM, 1544-1548.

Ye, Z. S., Xi, M., Tang, L. C. & Shen, Y. (2012). Degradation-based Burn-in planning under competing risks, Technometrics 54, 159-168.

Yuan, T. & Kuo, Y. (2010). Bayesian analysis of hazard rate, change point, and cost-optimal burn-in time for electronic devices, IEEE Transactions on Reliability 59, 132-138.

Yun, W. Y., Lee, Y. W. and Ferreira, L. (2002). Optimal burn-in time under accumulative free replacement warranty, Reliability Engineering & System Safety 78, 93–100.

Dimensions

PlumX

Article abstract page views

659

Downloads

Download data is not yet available.

How to Cite

González Alvarez, N. G. (2015). Approximation to the use of an optimal stopping rule for coherent systems. Revista De La Facultad De Ciencias, 4(2), 103-136. https://doi.org/10.15446/rev.fac.cienc.v4n2.50637

License

The authors or copyright holders of each paper confer to the Journal of the Faculty of Sciences of Universidad Nacional de Colombia a non-exclusive, limited and free authorization on the paper that, once evaluated and approved, is sent for its subsequent publication in accordance with the following characteristics:

  1. The corrected version is sent according to the suggestions of the evaluators and it is clarified that the paper mentioned is an unpublished document on which the rights are authorized and full responsibility is assumed for the content of the work before both the Journal of the Faculty of Sciences, Universidad Nacional de Colombia and third parties.
  2. The authorization granted to the Journal will be in force from the date it is included in the respective volume and number of the Journal of the Faculty of Sciences in the Open Journal Systems and on the Journal’s home page (https://revistas.unal.edu.co/index.php/rfc/index), as well as in the different databases and data indexes in which the publication is indexed.
  3. The authors authorize the Journal of the Faculty of Sciences of Universidad Nacional de Colombia to publish the document in the format in which it is required (printed, digital, electronic or any other known or to be known) and authorize the Journal of the Faculty of Sciences to include the work in the indexes and search engines deemed necessary to promote its diffusion.
  4. The authors accept that the authorization is given free of charge, and therefore they waive any right to receive any emolument for the publication, distribution, public communication, and any other use made under the terms of this authorization.
  5. All the contents of the Journal of the Faculty of Sciences are published under the Creative Commons Attribution – Non-commercial – Without Derivative 4.0.License 

 

MODEL LETTER OF PRESENTATION and TRANSFER OF COPYRIGHTS

Personal data processing policy

The names and email addresses entered in this Journal will be used exclusively for the purposes set out in it and will not be provided to third parties or used for other purposes.