Phase-Type distributionscomputational aspects andapplications in electronics

  1. Ruiz Castro, Juan Eloy 1
  2. Acal González, Christian J. 1
  3. Aguilera del Pino, Ana María 1
  1. 1 Universidad de Granada
    info

    Universidad de Granada

    Granada, España

    ROR https://ror.org/04njjy449

Revista:
BEIO, Boletín de Estadística e Investigación Operativa

ISSN: 1889-3805

Año de publicación: 2021

Volumen: 37

Número: 1

Páginas: 3-18

Tipo: Artículo

Otras publicaciones en: BEIO, Boletín de Estadística e Investigación Operativa

Resumen

Reliability is an area of statistics that analyzes the behaviour of sys-tems subject to failures where probability plays a fundamental role inmodeling, solving and optimization problems. It is usual to develop me-thodologies that allow a detailed study through classic distributions. Animportant aspect is the estimation of the parameters. A class of non-negative distributions, called phase-type distributions, makes it possibleto model complex problems with well-structured results, thanks to itsmatrix-algebraic form. The computational aspects of the estimation inthis field, through statistical programmes or applications such as R, Mat-lab or EMpht, are revised and applied to a real data set from RRAMmemories in order to prove that this approach is better than the classicstatistical analysis employed in this area.

Referencias bibliográficas

  • Acal C., Ruiz-Castro J.E. y Aguilera A.M. (2019a). Distribuciones tipo faseen un estudio de fiabilidad.TEMat,3, 63-74.
  • Acal C., Ruiz-Castro J.E., Aguilera A.M., et al. (2019b). Phase-type dis-tributions for studying variability in resistive memories.J. Comput. Appl.Math.,345, 23-32.
  • Asmussen S., Nerman O. y Olsson M. (1996). Fitting phase-type distribu-tions via the EM algorithm.Scand. J. Stat.,23(4), 419-441.
  • Asmussen S. (2000).Ruin Probabilities, World Scientific, Hong Kong (Chi-nese).
  • Aslett L. (2012). Package “PhaseType: Inference for Phase-type Distribu-tions”. En:https://cran.r-project.org/web/packages/PhaseType/
  • Buchholz P., Kriege J. y Felko I. (2014).Input modeling with phase-typedistributions and Markov models, Theory and Applications. Springer ChamHeidelberg New York Dordrecht London.
  • BuTools Team. (2015). Tools for Phase-Type Distributions. En:http://webspn.hit.bme.hu/˜telek/tools/butools/doc/ph.html
  • Epstein B. y Sobel M. (1953). Life Testing.J. Am. Stat. Assoc.,48(263),486-502.
  • Goulet V., Auclair S., Dutang C., et al. (2019). Package ’actuar: Ac-tuarial Functions and Heavy Tailed Distributions’. En:https://cran.r-project.org/web/packages/actuar/
  • He Q.M. (2014).Fundamentals of Matrix-Analytic Methods, Springer Scien-ce+Business Media, New York (EEUU).
  • Long S., Cagli C., Ielmini D., et al. (2012). Analysis and modelling ofresistive switching statistics.J. Appl. Phys.,111(7), 074508.
  • Neuts M. F. (1975).Probability Distributions of Phase Type, Liber Amico-rum Professor Emeritus Dr. H. Florin.
  • Neuts M. F. (1994).Matrix-Geometric Solutions in Stochastic Models: anAlgorithmic Approach, Courier Corporation.
  • Okamura H. (2015). Package “mapfit: A Tool for PH/MAP Parameter Es-timation”. En:https://cran.r-project.org/web/packages/mapfit/
  • Pérez E., Maldonado D., Acal C., et al. (2019). Analysis of the statisticsof device-to-device and cycle-to-cycle variability in TiN/Ti/Al:HfO2/TiNRRAMs.Microelectron. Eng.,214, 104-109.
  • The PSF (2019).Python Software, The Python Software Foundation (PSF).URLhttps://www.Python.org/.
  • R Core Team (2019).R: A language and environment for statistical com-puting, R Foundation for Statistical Computing. URLhttps://www.R-project.org/.
  • The Math Works (2020).MATLAB, Natick, MA: The Math Works, Inc.URLwww.mathworks.com