IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v63y2016i4p320-334.html
   My bibliography  Save this article

Minimizing the false alarm rate in systems with transient abnormality

Author

Listed:
  • Jue Wang

Abstract

We consider a stochastic partially observable system that can switch between a normal state and a transient abnormal state before entering a persistent abnormal state. Only the persistent abnormal state requires alarms. The transient and persistent abnormal states may be similar in appearance, which can result in excess false alarms. We propose a partially observable Markov decision process model to minimize the false alarm rate, subject to a given upper bound on the expected alarm delay time. The cost parameter is treated as the Lagrange multiplier, which can be estimated from the bound of the alarm delay. We show that the optimal policy has a control‐limit structure on the probability of persistent abnormality, and derive closed‐form bounds for the control limit and present an algorithm to specify the Lagrange multiplier. We also study a specialized model where the transient and persistent abnormal states have the same observation distribution, in which case an intuitive “watchful‐waiting” policy is optimal. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 320–334, 2016

Suggested Citation

  • Jue Wang, 2016. "Minimizing the false alarm rate in systems with transient abnormality," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(4), pages 320-334, June.
    • Handle: RePEc:wly:navres:v:63:y:2016:i:4:p:320-334
    DOI: 10.1002/nav.21690
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.21690
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.21690?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
    ---><---

    References listed on IDEAS

    as
    1. Joel M. Calabrese, 1995. "Bayesian Process Control for Attributes," Management Science, INFORMS, vol. 41(4), pages 637-645, April.
    2. Turgay Ayer & Oguzhan Alagoz & Natasha K. Stout, 2012. "OR Forum---A POMDP Approach to Personalize Mammography Screening Decisions," Operations Research, INFORMS, vol. 60(5), pages 1019-1034, October.
    3. Jue Wang & Chi-Guhn Lee, 2015. "Multistate Bayesian Control Chart Over a Finite Horizon," Operations Research, INFORMS, vol. 63(4), pages 949-964, August.
    4. George E. Monahan, 1982. "State of the Art---A Survey of Partially Observable Markov Decision Processes: Theory, Models, and Algorithms," Management Science, INFORMS, vol. 28(1), pages 1-16, January.
    5. George Tagaras & Yiannis Nikolaidis, 2002. "Comparing the Effectiveness of Various Bayesian X̄ Control Charts," Operations Research, INFORMS, vol. 50(5), pages 878-888, October.
    6. Michael Jong Kim & Viliam Makis, 2013. "Joint Optimization of Sampling and Control of Partially Observable Failing Systems," Operations Research, INFORMS, vol. 61(3), pages 777-790, June.
    7. Lisa M. Maillart & Julie Simmons Ivy & Scott Ransom & Kathleen Diehl, 2008. "Assessing Dynamic Breast Cancer Screening Policies," Operations Research, INFORMS, vol. 56(6), pages 1411-1427, December.
    8. Richard D. Smallwood & Edward J. Sondik, 1973. "The Optimal Control of Partially Observable Markov Processes over a Finite Horizon," Operations Research, INFORMS, vol. 21(5), pages 1071-1088, October.
    9. Sheldon M. Ross, 1971. "Quality Control under Markovian Deterioration," Management Science, INFORMS, vol. 17(9), pages 587-596, May.
    10. Chelsea C. White, 1977. "A Markov Quality Control Process Subject to Partial Observation," Management Science, INFORMS, vol. 23(8), pages 843-852, April.
    Full references (including those not matched with items on IDEAS)

    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. Jue Wang & Chi-Guhn Lee, 2015. "Multistate Bayesian Control Chart Over a Finite Horizon," Operations Research, INFORMS, vol. 63(4), pages 949-964, August.
    2. Chiel van Oosterom & Lisa M. Maillart & Jeffrey P. Kharoufeh, 2017. "Optimal maintenance policies for a safety‐critical system and its deteriorating sensor," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(5), pages 399-417, August.
    3. Hao Zhang, 2010. "Partially Observable Markov Decision Processes: A Geometric Technique and Analysis," Operations Research, INFORMS, vol. 58(1), pages 214-228, February.
    4. Turgay Ayer & Oguzhan Alagoz & Natasha K. Stout & Elizabeth S. Burnside, 2016. "Heterogeneity in Women’s Adherence and Its Role in Optimal Breast Cancer Screening Policies," Management Science, INFORMS, vol. 62(5), pages 1339-1362, May.
    5. Makis, Viliam, 2009. "Multivariate Bayesian process control for a finite production run," European Journal of Operational Research, Elsevier, vol. 194(3), pages 795-806, May.
    6. Ali Hajjar & Oguzhan Alagoz, 2023. "Personalized Disease Screening Decisions Considering a Chronic Condition," Management Science, INFORMS, vol. 69(1), pages 260-282, January.
    7. V. Makis & X. Jiang, 2003. "Optimal Replacement Under Partial Observations," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 382-394, May.
    8. Gong, Linguo & Tang, Kwei, 1997. "Monitoring machine operations using on-line sensors," European Journal of Operational Research, Elsevier, vol. 96(3), pages 479-492, February.
    9. Viliam Makis, 2008. "Multivariate Bayesian Control Chart," Operations Research, INFORMS, vol. 56(2), pages 487-496, April.
    10. Wooseung Jang & J. George Shanthikumar, 2002. "Stochastic allocation of inspection capacity to competitive processes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(1), pages 78-94, February.
    11. Malek Ebadi & Raha Akhavan-Tabatabaei, 2021. "Personalized Cotesting Policies for Cervical Cancer Screening: A POMDP Approach," Mathematics, MDPI, vol. 9(6), pages 1-20, March.
    12. Kampitsis, Dimitris & Panagiotidou, Sofia, 2022. "A Bayesian condition-based maintenance and monitoring policy with variable sampling intervals," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    13. Chernonog, Tatyana & Avinadav, Tal, 2016. "A two-state partially observable Markov decision process with three actionsAuthor-Name: Ben-Zvi, Tal," European Journal of Operational Research, Elsevier, vol. 254(3), pages 957-967.
    14. Saghafian, Soroush, 2018. "Ambiguous partially observable Markov decision processes: Structural results and applications," Journal of Economic Theory, Elsevier, vol. 178(C), pages 1-35.
    15. Kuo, Yarlin, 2006. "Optimal adaptive control policy for joint machine maintenance and product quality control," European Journal of Operational Research, Elsevier, vol. 171(2), pages 586-597, June.
    16. Otten, Maarten & Timmer, Judith & Witteveen, Annemieke, 2020. "Stratified breast cancer follow-up using a continuous state partially observable Markov decision process," European Journal of Operational Research, Elsevier, vol. 281(2), pages 464-474.
    17. Turgay Ayer, 2015. "Inverse optimization for assessing emerging technologies in breast cancer screening," Annals of Operations Research, Springer, vol. 230(1), pages 57-85, July.
    18. Turgay Ayer & Oguzhan Alagoz & Natasha K. Stout, 2012. "OR Forum---A POMDP Approach to Personalize Mammography Screening Decisions," Operations Research, INFORMS, vol. 60(5), pages 1019-1034, October.
    19. Alireza Boloori & Soroush Saghafian & Harini A. Chakkera & Curtiss B. Cook, 2020. "Data-Driven Management of Post-transplant Medications: An Ambiguous Partially Observable Markov Decision Process Approach," Manufacturing & Service Operations Management, INFORMS, vol. 22(5), pages 1066-1087, September.
    20. Shoshana Anily & Abraham Grosfeld-Nir, 2006. "An Optimal Lot-Sizing and Offline Inspection Policy in the Case of Nonrigid Demand," Operations Research, INFORMS, vol. 54(2), pages 311-323, April.

    More about this item

    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:wly:navres:v:63:y:2016:i:4:p:320-334. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.