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System-Wide Probabilities for Systems with Runs and Scans Rules

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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