IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v47y1998i2p243-269.html
   My bibliography  Save this article

Analytic approach & Monte Carlo methods for realistic systems analysis

Author

Listed:
  • Dubi, A.

Abstract

The basic concepts of system Engineering are briefly described. The general problem is outlined as that of a `particle' moving in a phase space of states and time. It is shown that this general view leads to a transport equation underlying the behavior of systems. The transport equation is presented with some details and a number of special cases of the equation are discussed in details. The Monte Carlo method is then presented as a general and exclusive means for the solution of this transport equation. While this discussion is highly theoretical an effort is made to maintain the overall perspective that the final purpose is to obtain solutions for realistic industrial problems. A set of unbiased estimators are then presented and proved. Basic methods for variance reduction using transformations of the absorption probability are presented and discussed.

Suggested Citation

  • Dubi, A., 1998. "Analytic approach & Monte Carlo methods for realistic systems analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(2), pages 243-269.
    • Handle: RePEc:eee:matcom:v:47:y:1998:i:2:p:243-269
    DOI: 10.1016/S0378-4754(98)00122-0
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475498001220
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/S0378-4754(98)00122-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. H. W. Block & W. S. Borges & T. H. Savits, 1988. "A general age replacement model with minimal repair," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 365-372, October.
    2. Philip J. Boland & Frank Proschan, 1983. "Optimum Replacement of a System Subject to Shocks," Operations Research, INFORMS, vol. 31(4), pages 697-704, August.
    3. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
    4. Robert Cleroux & Denis J. McConalogue, 1976. "A Numerical Algorithm for Recursively-Defined Convolution Integrals Involving Distribution Functions," Management Science, INFORMS, vol. 22(10), pages 1138-1146, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Olga Fink & Enrico Zio, 2013. "Semi-Markov processes with semi-regenerative states for the availability analysis of chemical process plants with storage units," Journal of Risk and Reliability, , vol. 227(3), pages 279-289, June.
    2. Naseri, Masoud & Baraldi, Piero & Compare, Michele & Zio, Enrico, 2016. "Availability assessment of oil and gas processing plants operating under dynamic Arctic weather conditions," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 66-82.
    3. Raoni, Rafael & Secchi, Argimiro R., 2019. "Procedures to model and solve probabilistic dynamic system problems," Reliability Engineering and System Safety, Elsevier, vol. 191(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shey-Huei Sheu & Chin-Chih Chang & Yu-Hung Chien, 2011. "Optimal age-replacement time with minimal repair based on cumulative repair-cost limit for a system subject to shocks," Annals of Operations Research, Springer, vol. 186(1), pages 317-329, June.
    2. Chien, Yu-Hung & Sheu, Shey-Huei & Zhang, Zhe George & Love, Ernie, 2006. "An extended optimal replacement model of systems subject to shocks," European Journal of Operational Research, Elsevier, vol. 175(1), pages 399-412, November.
    3. Sheu, Shey-Huei & Griffith, William S., 2002. "Extended block replacement policy with shock models and used items," European Journal of Operational Research, Elsevier, vol. 140(1), pages 50-60, July.
    4. Sheu, Shey-Huei & Chang, Chin-Chih & Zhang, Zhe George & Chien, Yu-Hung, 2012. "A note on replacement policy for a system subject to non-homogeneous pure birth shocks," European Journal of Operational Research, Elsevier, vol. 216(2), pages 503-508.
    5. Sheu, Shey-Huei, 1998. "A generalized age and block replacement of a system subject to shocks," European Journal of Operational Research, Elsevier, vol. 108(2), pages 345-362, July.
    6. Sheu, Shey-Huei & Liu, Tzu-Hsin & Zhang, Zhe-George & Tsai, Hsin-Nan, 2018. "The generalized age maintenance policies with random working times," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 503-514.
    7. Sheu, Shey-Huei, 1999. "Extended optimal replacement model for deteriorating systems," European Journal of Operational Research, Elsevier, vol. 112(3), pages 503-516, February.
    8. Sheu, Shey-Huei & Liu, Tzu-Hsin & Zhang, Zhe-George, 2019. "Extended optimal preventive replacement policies with random working cycle," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 398-415.
    9. Juang, Muh-Guey & Anderson, Gary, 2004. "A Bayesian method on adaptive preventive maintenance problem," European Journal of Operational Research, Elsevier, vol. 155(2), pages 455-473, June.
    10. Lim, J.H. & Qu, Jian & Zuo, Ming J., 2016. "Age replacement policy based on imperfect repair with random probability," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 24-33.
    11. Sheu, Shey-Huei & Chien, Yu-Hung, 2004. "Optimal age-replacement policy of a system subject to shocks with random lead-time," European Journal of Operational Research, Elsevier, vol. 159(1), pages 132-144, November.
    12. Shey-Huei Sheu & Griffith, William S. & Toshio Nakagawa, 1995. "Extended optimal replacement model with random minimal repair costs," European Journal of Operational Research, Elsevier, vol. 85(3), pages 636-649, September.
    13. Chien, Yu-Hung & Sheu, Shey-Huei, 2006. "Extended optimal age-replacement policy with minimal repair of a system subject to shocks," European Journal of Operational Research, Elsevier, vol. 174(1), pages 169-181, October.
    14. Yu-Hung Chien & Chin-Chih Chang & Shey-Huei Sheu, 2010. "Optimal age-replacement model with age-dependent type of failure and random lead time based on a cumulative repair-cost limit policy," Annals of Operations Research, Springer, vol. 181(1), pages 723-744, December.
    15. Wang, Hongzhou, 2002. "A survey of maintenance policies of deteriorating systems," European Journal of Operational Research, Elsevier, vol. 139(3), pages 469-489, June.
    16. Shey‐Huei Sheu & William S. Griffith, 1996. "Optimal number of minimal repairs before replacement of a system subject to shocks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(3), pages 319-333, April.
    17. Sheu, Shey-Huei & Jhang, Jhy-Ping, 1997. "A generalized group maintenance policy," European Journal of Operational Research, Elsevier, vol. 96(2), pages 232-247, January.
    18. Sheu, Shey-Huei & Tsai, Hsin-Nan & Wang, Fu-Kwun & Zhang, Zhe George, 2015. "An extended optimal replacement model for a deteriorating system with inspections," Reliability Engineering and System Safety, Elsevier, vol. 139(C), pages 33-49.
    19. Hashemi, M. & Asadi, M. & Zarezadeh, S., 2020. "Optimal maintenance policies for coherent systems with multi-type components," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    20. Won Young Yun & Alfonsus Julanto Endharta, 2016. "A preventive replacement policy based on system critical condition," Journal of Risk and Reliability, , vol. 230(1), pages 93-100, February.

    More about this item

    Keywords

    Monte Carlo methods; System engineering;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:47:y:1998:i:2:p:243-269. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.