IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i24p5001-d1302480.html
   My bibliography  Save this article

Semi-Markov Models for Process Mining in Smart Homes

Author

Listed:
  • Sally McClean

    (School of Computing, Ulster University, Belfast BT15 1AP, Northern Ireland, UK
    These authors contributed equally to this work.)

  • Lingkai Yang

    (Research Institute of Mine Big Data, Chinese Institute of Coal Science, Beijing 100013, China
    These authors contributed equally to this work.)

Abstract

Generally, these days people live longer but often with increased impairment and disabilities; therefore, they can benefit from assistive technologies. In this paper, we focus on the completion of activities of daily living (ADLs) by such patients, using so-called Smart Homes and Sensor Technology to collect data, and provide a suitable analysis to support the management of these conditions. The activities here are cast as states of a Markov-type process, while changes of state are indicated by sensor activations. This facilitates the extraction of key performance indicators (KPIs) in Smart Homes, e.g., the duration of an important activity, as well as the identification of anomalies in such transitions and durations. The use of semi-Markov models for such a scenario is described, where the state durations are represented by mixed gamma models. This approach is illustrated and evaluated using a publicly available Smart Home dataset comprising an event log of sensor activations, together with an annotated record of the actual activities. Results indicate that the methodology is well-suited to such scenarios.

Suggested Citation

  • Sally McClean & Lingkai Yang, 2023. "Semi-Markov Models for Process Mining in Smart Homes," Mathematics, MDPI, vol. 11(24), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:5001-:d:1302480
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/24/5001/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/24/5001/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. P.-C. G. Vassiliou & T. P. Moysiadis, 2010. "$\boldsymbol{\mathcal{G}-}$ Inhomogeneous Markov Systems of High Order," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 271-292, June.
    2. Stewart, T. & Strijbosch, L.W.G. & Moors, J.J.A. & van Batenburg, P., 2007. "A Simple Approximation to the Convolution of Gamma Distributions (Revision of DP 2006-27)," Discussion Paper 2007-70, Tilburg University, Center for Economic Research.
    3. Rafael Lorenz & Julian Senoner & Wilfried Sihn & Torbjørn Netland, 2021. "Using process mining to improve productivity in make-to-stock manufacturing," International Journal of Production Research, Taylor & Francis Journals, vol. 59(16), pages 4869-4880, August.
    4. Jennifer Gillespie & Sally McClean & Lalit Garg & Maria Barton & Bryan Scotney & Ken Fullerton, 2016. "A multi-phase DES modelling framework for patient-centred care," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(10), pages 1239-1249, October.
    5. Sally McClean & Erin Montgomery & Fidelis Ugwuowo, 1997. "Non‐homogeneous continuous‐time Markov and semi‐Markov manpower models," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 13(3‐4), pages 191-198, September.
    6. B Shaw & A H Marshall, 2007. "Modelling the flow of congestive heart failure patients through a hospital system," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(2), pages 212-218, February.
    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. Zhai, Yue & Hua, Guowei & Cheng, Meng & Cheng, T.C.E., 2023. "Production lead-time hedging and order allocation in an MTO supply chain," European Journal of Operational Research, Elsevier, vol. 311(3), pages 887-905.
    2. Ortiz-Barrios, Miguel & Arias-Fonseca, Sebastián & Ishizaka, Alessio & Barbati, Maria & Avendaño-Collante, Betty & Navarro-Jiménez, Eduardo, 2023. "Artificial intelligence and discrete-event simulation for capacity management of intensive care units during the Covid-19 pandemic: A case study," Journal of Business Research, Elsevier, vol. 160(C).
    3. Miguel Ortiz-Barrios & Juan-José Alfaro-Saiz, 2020. "An integrated approach for designing in-time and economically sustainable emergency care networks: A case study in the public sector," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-28, June.
    4. Harper, P.R. & Knight, V.A. & Marshall, A.H., 2012. "Discrete Conditional Phase-type models utilising classification trees: Application to modelling health service capacities," European Journal of Operational Research, Elsevier, vol. 219(3), pages 522-530.
    5. Patrick Carmack & Jeffrey Spence & William Schucany, 2012. "Generalised correlated cross-validation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 269-282.
    6. Casucci, Sabrina & Lin, Li & Nikolaev, Alexander, 2018. "Modeling the impact of care transition programs on patient outcomes and 30 day hospital readmissions," Socio-Economic Planning Sciences, Elsevier, vol. 63(C), pages 70-79.
    7. Jesús Isaac Vázquez-Serrano & Rodrigo E. Peimbert-García & Leopoldo Eduardo Cárdenas-Barrón, 2021. "Discrete-Event Simulation Modeling in Healthcare: A Comprehensive Review," IJERPH, MDPI, vol. 18(22), pages 1-20, November.
    8. Brecht Verbeken & Marie-Anne Guerry, 2021. "Discrete Time Hybrid Semi-Markov Models in Manpower Planning," Mathematics, MDPI, vol. 9(14), pages 1-13, July.
    9. Jabari, Saif Eddin & Zheng, Jianfeng & Liu, Henry X., 2014. "A probabilistic stationary speed–density relation based on Newell’s simplified car-following model," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 205-223.
    10. Carter, Michael W., 2018. "High-fidelity whole-system patient flow modeling to assess health care transformation policiesAuthor-Name: Esensoy, Ali Vahit," European Journal of Operational Research, Elsevier, vol. 266(1), pages 221-237.
    11. Bégin Jean-François & Bédard Mylène & Gaillardetz Patrice, 2015. "Simulating from the Heston model: A gamma approximation scheme," Monte Carlo Methods and Applications, De Gruyter, vol. 21(3), pages 205-231, September.
    12. Felix Oberdorf & Myriam Schaschek & Sven Weinzierl & Nikolai Stein & Martin Matzner & Christoph M. Flath, 2023. "Predictive End-to-End Enterprise Process Network Monitoring," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 65(1), pages 49-64, February.
    13. Yiting Xing & Ling Li & Zhuming Bi & Marzena Wilamowska‐Korsak & Li Zhang, 2013. "Operations Research (OR) in Service Industries: A Comprehensive Review," Systems Research and Behavioral Science, Wiley Blackwell, vol. 30(3), pages 300-353, May.

    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:gam:jmathe:v:11:y:2023:i:24:p:5001-:d:1302480. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.