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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
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    References listed on IDEAS

    as
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    2. 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.
    3. 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.
    4. 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.
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    6. 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.
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