IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v4y2002i4d10.1023_a1023570718955.html
   My bibliography  Save this article

System-Wide Probabilities for Systems with Runs and Scans Rules

Author

Listed:
  • Galit Shmueli

    (University of Maryland)

Abstract

Systems that include multiple decision rules are encountered in many fields. We focus on systems with several states or levels where the rules determining when and how to move between the levels are based on runs or scans. Our target is to evaluate the proportion of time spent at each level. This information is valuable since it is required for constructing various cost functions. In this paper we address two questions: How to incorporate the system of levels and decision rules into a probabilistic setting and which measures to use in order to evaluate the proportion of time spent at each level. We take a waiting-time approach, and use special features of runs and scans distributions in order to investigate long and short-term measures of the time spent at the different levels of a system. We introduce a short term per-cycle measure and compare it with the finite-time measure. We find that the two measures can differ significantly.

Suggested Citation

  • Galit Shmueli, 2002. "System-Wide Probabilities for Systems with Runs and Scans Rules," Methodology and Computing in Applied Probability, Springer, vol. 4(4), pages 409-419, December.
    • Handle: RePEc:spr:metcap:v:4:y:2002:i:4:d:10.1023_a:1023570718955
    DOI: 10.1023/A:1023570718955
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1023570718955
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1023570718955?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. Sigeo Aki, 1992. "Waiting time problems for a sequence of discrete random variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(2), pages 363-378, 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. Sotiris Bersimis & Markos V. Koutras & George K. Papadopoulos, 2014. "Waiting Time for an Almost Perfect Run and Applications in Statistical Process Control," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 207-222, March.

    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. Markos V. Koutras & Sotirios Bersimis & Demetrios L. Antzoulakos, 2006. "Improving the Performance of the Chi-square Control Chart via Runs Rules," Methodology and Computing in Applied Probability, Springer, vol. 8(3), pages 409-426, September.
    2. Ourania Chryssaphinou & Eutichia Vaggelatou, 2002. "Compound Poisson Approximation for Multiple Runs in a Markov Chain," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 411-424, June.
    3. Masayuki Uchida, 1998. "On Generating Functions of Waiting Time Problems for Sequence Patterns of Discrete Random Variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(4), pages 655-671, December.
    4. Yu-Fei Hsieh & Tung-Lung Wu, 2013. "Recursive equations in finite Markov chain imbedding," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 513-527, June.
    5. Milienos, F.S. & Koutras, M.V., 2008. "A lower bound for the reliability function of multiple failure mode systems," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1639-1648, September.
    6. Michael V. Boutsikas & Markos V. Koutras, 2000. "Reliability Approximation for Markov Chain Imbeddable Systems," Methodology and Computing in Applied Probability, Springer, vol. 2(4), pages 393-411, December.
    7. Demetrios Antzoulakos & Andreas Philippou, 1997. "Probability Distribution Functions of Succession Quotas in the Case of Markov Dependent Trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 531-539, September.
    8. Dheeraj Sharma & Mir Ghulam Talpur, 2016. "An Examination of One Dimension Marginal Distributions: Selling and Non - Selling Activities of a Salesperson," Working Papers id:10970, eSocialSciences.
    9. Sharma, Dheeraj & Talpur, Mir Ghulam Haider, 2016. "An Examination of One Dimension Marginal Distributions: Selling and Non-selling Activities of a Salesperson," IIMA Working Papers WP2016-03-48, Indian Institute of Management Ahmedabad, Research and Publication Department.
    10. Masayuki Uchida & Sigeo Aki, 1995. "Sooner and later waiting time problems in a two-state Markov chain," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 415-433, September.
    11. R. L. Shinde & K. S. Kotwal,, 2008. "Distributions of scan statistics in a sequence of Markov Bernoulli trials," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 135-155.
    12. Inoue, Kiyoshi & Aki, Sigeo, 2010. "On the conditional and unconditional distributions of the number of success runs on a circle with applications," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 874-885, May.
    13. Michael V. Boutsikas & Markos V. Koutras, 2002. "On a class of multiple failure mode systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(2), pages 167-185, March.
    14. K. K. Kamalja, 2017. "Markov binomial distribution of order k and its applications," Statistical Papers, Springer, vol. 58(3), pages 831-853, September.
    15. Yung-Ming Chang & James Fu & Han-Ying Lin, 2012. "Distribution and double generating function of number of patterns in a sequence of Markov dependent multistate trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(1), pages 55-68, February.
    16. Demetrios Antzoulakos, 1999. "On Waiting Time Problems Associated with Runs in Markov Dependent Trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(2), pages 323-330, June.
    17. S. Aki & N. Balakrishnan & S. Mohanty, 1996. "Sooner and later waiting time problems for success and failure runs in higher order Markov dependent trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(4), pages 773-787, December.

    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:spr:metcap:v:4:y:2002:i:4:d:10.1023_a:1023570718955. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.