IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i4p390-d499923.html
   My bibliography  Save this article

A Complex Model via Phase-Type Distributions to Study Random Telegraph Noise in Resistive Memories

Author

Listed:
  • Juan E. Ruiz-Castro

    (Department of Statistics and O.R. and Math Institute, University of Granada, 18071 Granada, Spain)

  • Christian Acal

    (Department of Statistics and O.R. and Math Institute, University of Granada, 18071 Granada, Spain)

  • Ana M. Aguilera

    (Department of Statistics and O.R. and Math Institute, University of Granada, 18071 Granada, Spain)

  • Juan B. Roldán

    (Department of Electronics and Computing Technology, University of Granada, 18071 Granada, Spain)

Abstract

A new stochastic process was developed by considering the internal performance of macro-states in which the sojourn time in each one is phase-type distributed depending on time. The stationary distribution was calculated through matrix-algorithmic methods and multiple interesting measures were worked out. The number of visits distribution to a determine macro-state were analyzed from the respective differential equations and the Laplace transform. The mean number of visits to a macro-state between any two times was given. The results were implemented computationally and were successfully applied to study random telegraph noise (RTN) in resistive memories. RTN is an important concern in resistive random access memory (RRAM) operation. On one hand, it could limit some of the technological applications of these devices; on the other hand, RTN can be used for the physical characterization. Therefore, an in-depth statistical analysis to model the behavior of these devices is of essential importance.

Suggested Citation

  • Juan E. Ruiz-Castro & Christian Acal & Ana M. Aguilera & Juan B. Roldán, 2021. "A Complex Model via Phase-Type Distributions to Study Random Telegraph Noise in Resistive Memories," Mathematics, MDPI, vol. 9(4), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:390-:d:499923
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/4/390/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/4/390/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Alonso, F.J. & Maldonado, D. & Aguilera, A.M. & Roldán, J.B., 2021. "Memristor variability and stochastic physical properties modeling from a multivariate time series approach," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Aguilera-Morillo, M. Carmen & Aguilera, Ana M. & Jiménez-Molinos, Francisco & Roldán, Juan B., 2019. "Stochastic modeling of Random Access Memories reset transitions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 159(C), pages 197-209.
    3. Ruiz-Castro, Juan Eloy, 2020. "A complex multi-state k-out-of-n: G system with preventive maintenance and loss of units," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    4. Visser, Ingmar & Speekenbrink, Maarten, 2010. "depmixS4: An R Package for Hidden Markov Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 36(i07).
    5. Ruiz-Castro, Juan Eloy, 2016. "Complex multi-state systems modelled through marked Markovian arrival processes," European Journal of Operational Research, Elsevier, vol. 252(3), pages 852-865.
    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. Tuo Shi & Lili Gao & Yang Tian & Shuangzhu Tang & Jinchang Liu & Yiqi Li & Ruixi Zhou & Shiyu Cui & Hui Zhang & Yu Li & Zuheng Wu & Xumeng Zhang & Taihao Li & Xiaobing Yan & Qi Liu, 2025. "Memristor-based feature learning for pattern classification," Nature Communications, Nature, vol. 16(1), pages 1-13, December.
    2. Junjun Zheng & Hiroyuki Okamura & Tadashi Dohi, 2021. "Availability Analysis of Software Systems with Rejuvenation and Checkpointing," Mathematics, MDPI, vol. 9(8), pages 1-15, April.
    3. Gabriel Ciobanu, 2023. "Analyzing Non-Markovian Systems by Using a Stochastic Process Calculus and a Probabilistic Model Checker," Mathematics, MDPI, vol. 11(2), pages 1-17, January.

    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. Ruiz-Castro, Juan E. & Acal, Christian & Aguilera, Ana M. & Aguilera-Morillo, M. Carmen & Roldán, Juan B., 2021. "Linear-Phase-Type probability modelling of functional PCA with applications to resistive memories," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 186(C), pages 71-79.
    2. Juybari, Mohammad N. & Hamadani, Ali Zeinal & Ardakan, Mostafa Abouei, 2023. "Availability analysis and cost optimization of a repairable system with a mix of active and warm-standby components in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    3. Denis S Willett & Justin George & Nora S Willett & Lukasz L Stelinski & Stephen L Lapointe, 2016. "Machine Learning for Characterization of Insect Vector Feeding," PLOS Computational Biology, Public Library of Science, vol. 12(11), pages 1-14, November.
    4. Chen, Wu-Lin & Wang, Kuo-Hsiung, 2018. "Reliability analysis of a retrial machine repair problem with warm standbys and a single server with N-policy," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 476-486.
    5. Yonit Barron, 2018. "Group maintenance policies for an R-out-of-N system with phase-type distribution," Annals of Operations Research, Springer, vol. 261(1), pages 79-105, February.
    6. Davey, Calum & Dirawo, Jeffrey & Mushati, Phillis & Magutshwa, Sitholubuhle & Hargreaves, James R. & Cowan, Frances M., 2019. "Mobility and sex work: why, where, when? A typology of female-sex-worker mobility in Zimbabwe," Social Science & Medicine, Elsevier, vol. 220(C), pages 322-330.
    7. Wu, Hui & Li, Yan-Fu & Bérenguer, Christophe, 2020. "Optimal inspection and maintenance for a repairable k-out-of-n: G warm standby system," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    8. Georges Dionne & Amir Saissi Hassani, 2015. "Endogenous Hidden Markov Regimes in Operational Loss Data: Application to the Recent Financial Crisis," Cahiers de recherche 1516, CIRPEE.
    9. Rob Hayward & Jens Hölscher, 2017. "The Forward-Discount Puzzle in Central and Eastern Europe," Comparative Economic Studies, Palgrave Macmillan;Association for Comparative Economic Studies, vol. 59(4), pages 472-497, December.
    10. Koryazhkina, M.N. & Filatov, D.O. & Shishmakova, V.A. & Shenina, M.E. & Belov, A.I. & Antonov, I.N. & Kotomina, V.E. & Mikhaylov, A.N. & Gorshkov, O.N. & Agudov, N.V. & Guarcello, C. & Carollo, A. & S, 2022. "Resistive state relaxation time in ZrO2(Y)-based memristive devices under the influence of external noise," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    11. Yonit Barron & Chananel Benshimol, 2024. "Emergency Supply Alternatives for a Storage Facility of a Repairable Multi-Component System," Mathematics, MDPI, vol. 12(17), pages 1-37, August.
    12. Ruiz-Castro, Juan Eloy & Dawabsha, Mohammed & Alonso, Francisco Javier, 2018. "Discrete-time Markovian arrival processes to model multi-state complex systems with loss of units and an indeterminate variable number of repairpersons," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 114-127.
    13. Yousefi, Nooshin & Coit, David W. & Song, Sanling, 2020. "Reliability analysis of systems considering clusters of dependent degrading components," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    14. Morteza Amini & Afarin Bayat & Reza Salehian, 2023. "hhsmm: an R package for hidden hybrid Markov/semi-Markov models," Computational Statistics, Springer, vol. 38(3), pages 1283-1335, September.
    15. Maldonado, D. & Aguilera-Pedregosa, C. & Vinuesa, G. & García, H. & Dueñas, S. & Castán, H. & Aldana, S. & González, M.B. & Moreno, E. & Jiménez-Molinos, F. & Campabadal, F. & Roldán, J.B., 2022. "An experimental and simulation study of the role of thermal effects on variability in TiN/Ti/HfO2/W resistive switching nonlinear devices," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    16. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Mission abort and rescue for multistate systems operating under the Poisson process of shocks," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    17. Ahmet Akca & Ethem Çanakoğlu, 2021. "Adaptive stochastic risk estimation of firm operating profit," Economia e Politica Industriale: Journal of Industrial and Business Economics, Springer;Associazione Amici di Economia e Politica Industriale, vol. 48(3), pages 463-504, September.
    18. Melnykov, Volodymyr, 2016. "ClickClust: An R Package for Model-Based Clustering of Categorical Sequences," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 74(i09).
    19. Safaei, Fatemeh & Ahmadi, Jafar & Taghipour, Sharareh, 2022. "A maintenance policy for a k-out-of-n system under enhancing the system’s operating time and safety constraints, and selling the second-hand components," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    20. Tessa J P van Schijndel & Kim Huijpen & Ingmar Visser & Maartje E J Raijmakers, 2018. "Investigating the development of causal inference by studying variability in 2- to 5-year-olds' behavior," PLOS ONE, Public Library of Science, vol. 13(4), pages 1-15, April.

    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:9:y:2021:i:4:p:390-:d:499923. 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.