Publicado

2021-01-15

Stress-Strength Reliability Estimation of Time-Dependent Models with Fixed Stress and Phase Type Strength Distribution

Estimación de la confiabilidad de resistencia a la tensión de modelos dependientes del tiempo con estrés fijo y distribución de fuerza de tipo de fas

DOI:

https://doi.org/10.15446/rce.v44n1.86519

Palabras clave:

Stress-Strength Reliability, Phase Type distribution, Exponential distribution, Gamma distribution, Weibull distribution, EM algorithm (en)
Algoritmo EM, Distribución de tipo de fase, Distribución Gamma, Distribución exponencial, Distribución de Weibull, Fiabilidad de resistencia al estrés (es)

Descargas

Autores/as

The time-dependent stress-strength reliability models deal with systems whose strength or the stress imposed on it or both are time-dependent. In this paper, we consider time-dependent stress-strength reliability model which is subjected to constant stress and it causes a change in the strength of the system over each run of the system. Assuming a continuous phase- type distribution for the initial strength and exponential distribution for the duration of each run of the system called cycle time we derived the expression for the stress-strength reliability of the system at time t. The model is further extended to the cases where cycle time distribution is Gamma and Weibull. Simulation studies are conducted to assess the variations in stress-strength reliability, R(t) at different time points, corresponding to the changes in the initial strength distribution and cycle time distribution.

Los modelos de confiabilidad tensión-resistencia dependientes del tiempo tratan con sistemas cuya fuerza o el estrés que se le impone o ambos dependen de tiempo. En este artículo, consideramos modelos de confiabilidad de resistencia-tensión dependientes del tiempo que está sometido a un estrés constante y provoca un cambio en la fuerza del sistema después de cada
ejecución del sistema. Asumiendo una fase continua distribución de tipo para la fuerza inicial y distribución exponencial para la duración de cada ejecución del sistema llamado tiempo de ciclo que obtuvimos la expresión de la fiabilidad tensión-resistencia del sistema en el tiempo t. El modelo se amplía aún más a  los casos en los que la distribución del tiempo de ciclo es Gamma y Weibull. Se realizan
estudios de simulación para evaluar las variaciones en la confiabilidad tensión-resistencia, R(t) en diferentes puntos de tiempo, correspondiente a los cambios en la distribución y el ciclo de la fuerza inicial distribución del tiempo.

Referencias

Asmussen, S., Nerman, O. & Olsson, M. (1996), ‘Fitting phase-type distributions via the em algorithm’, Scandinavian Journal of Statistics 23, 419–441.

Baklizi, A. (2008), ‘Estimation of pr(x < y) using record values in the one and two parameter exponential distributions’, Communications in Statistics-Theory and Methods 37, 692–698. DOI: https://doi.org/10.1080/03610920701501921

Barron, Y., Frostig, E. & Levikson, B. (2004), ‘Analysis of r-out-of-n repairable systems: The case of phase-type distribution’, Advances in Applied Probability 36, 692–698. DOI: https://doi.org/10.1239/aap/1077134467

Barron, Y. & Yechiali, U. (2017), ‘Generalized control-limit preventive repair policies for deteriorating cold and warm standby markovian systems’, IISE Transactions 49, 1031–1049. DOI: https://doi.org/10.1080/24725854.2017.1335919

Birnbaum, Z. M. (1956), ‘On a use of the mann-whitney statistic’, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability 1, 13–17. DOI: https://doi.org/10.1525/9780520313880-005

Bladt, M., Esparza, L. J. R. & Nielsen, B. F. (2011), ‘Fisher information and statistical inference for phase-type distributions’, Journal of Applied Probability 48(A), 277–293. DOI: https://doi.org/10.1239/jap/1318940471

Eryilmaz, S. (2018), ‘Phase type stress-strength models with reliability applications’, Communications in Statistics-Simulation and Computation 47(4), 954–963. DOI: https://doi.org/10.1080/03610918.2017.1300266

Ghitany, M. E., Al-Mutairi, D. K. & Aboukhamseen, S. M. (2015), ‘Estimation of the reliability of a stress-strength system from power Lindley distributions’, Communications in Statistics-Simulation and Computation 44, 118–136. DOI: https://doi.org/10.1080/03610918.2013.767910

Gopalan, M. N. & Venkateswarlu, P. (1982), ‘Reliability analysis of time-dependent cascade system with deterministic cycle times’, Microelectronics Reliability 22, 841–872. DOI: https://doi.org/10.1016/S0026-2714(82)80198-4

Gopalan, M. N. & Venkateswarlu, P. (1983), ‘Reliability analysis of time-dependent cascade system with random cycle times’, Microelectronics Reliability 23(2), 355–366. DOI: https://doi.org/10.1016/0026-2714(83)90346-3

Huang, K., Mi, J. & Wang, Z. (2012), ‘Inference about reliability parameter with gamma strength and stress’, Journal of Statistical Planning and Inference 142(4), 848–854. DOI: https://doi.org/10.1016/j.jspi.2011.10.005

Jose, J. K., Drisya, M. & Manoharan, M. (2020), ‘Estimation of stress-strength reliability using discrete phase-type distribution’, Communications in Statistics - Theory and Methods 17(2), 141–154. DOI: https://doi.org/10.1080/03610926.2020.1749663

Jose, J. K., Xavier, T. & Drisya, M. (2019), ‘Estimation of stress strength reliability using Kumaraswamy half-logistic distribution’, Journal of Probability and Statistical Science 17(2), 141–154.

Kizilaslan, F. & Nadar, M. (2015), ‘Classical and bayesian estimation of reliability in multi-component stress-strength model based on Weibull distribution’, Revista Colombiana de Estadística 38(2), 467–484. DOI: https://doi.org/10.15446/rce.v38n2.51674

Kotz, S. & Pensky, M. (2003), The stress-strength model and its generalizations: theory and applications, World Scientific. DOI: https://doi.org/10.1142/9789812564511

Kundu, D. & Raqab, M. Z. (2009), ‘Estimation of r = pr(y < x) for threeparameter Weibull distribution’, Statistics and Probability Letters 79, 1839–1846. DOI: https://doi.org/10.1016/j.spl.2009.05.026

Lomnicki, Z. A. (1966), ‘A note on the Weibull renewal process’, Biometrica 53, 375–381. DOI: https://doi.org/10.1093/biomet/53.3-4.375

Neuts, M. F. (1975), Probability distributions of phase-type, in E. H. Florin, ed., ‘Liber Amicorum’, University of Louvain, Belgium, pp. 173–206.

Rao, G. S. (2012), ‘Estimation of reliability in multicomponent stress-strength based on generalized exponential distribution’, Revista Colombiana de Estadística 35, 67–76.

Rao, G. S., Aslam, M. & Kundu, D. (2014), ‘Burr type XII distribution parametric estimation and estimation of reliability in multi-component stress strength model’, Communication in Statistics-Theory and Methods 44(23), 4953–4961. DOI: https://doi.org/10.1080/03610926.2013.821490

Rezaei, S., Tahmasbi, R. & Mahmoodi, M. (2010), ‘Estimation of p(y < x) for generalized Pareto distribution’, Journal of Statistical Planning and Inference 140, 480–494. DOI: https://doi.org/10.1016/j.jspi.2009.07.024

Siju, K. C. & Kumar, M. (2016), ‘Reliability analysis of time-dependent stress-strength model with random cycle times’, Perspectives in Science 8, 654–657. DOI: https://doi.org/10.1016/j.pisc.2016.06.049

Siju, K. C. & Kumar, M. (2017), ‘Reliability computation of a dynamic stress strength model with random cycle times’, International Journal of Pure and Applied Mathematics 117, 309–316.

Wong, A. (2012), ‘Interval estimation of p(y < x) for generalized Pareto distribution’, Journal of Statistical Planning and Inference 142, 601–607. DOI: https://doi.org/10.1016/j.jspi.2011.04.024

Xavier, T. & Jose, J. K. (2020), ‘A study of stress-strength reliability using a generalization of power transformed half-logistic distribution’, Communications in Statistics - Theory and Methods. 10.1080/03610926.2020.1716250 DOI: https://doi.org/10.1080/03610926.2020.1716250

Yadav, R. P. S. (1973), ‘A reliability model for stress strength problem’, Microelectronics Reliability 12(2), 119–123. DOI: https://doi.org/10.1016/0026-2714(73)90456-3

Cómo citar

APA

Jose, J. K. y M., D. (2021). Stress-Strength Reliability Estimation of Time-Dependent Models with Fixed Stress and Phase Type Strength Distribution. Revista Colombiana de Estadística, 44(1), 201–223. https://doi.org/10.15446/rce.v44n1.86519

ACM

[1]
Jose, J.K. y M., D. 2021. Stress-Strength Reliability Estimation of Time-Dependent Models with Fixed Stress and Phase Type Strength Distribution. Revista Colombiana de Estadística. 44, 1 (ene. 2021), 201–223. DOI:https://doi.org/10.15446/rce.v44n1.86519.

ACS

(1)
Jose, J. K.; M., D. Stress-Strength Reliability Estimation of Time-Dependent Models with Fixed Stress and Phase Type Strength Distribution. Rev. colomb. estad. 2021, 44, 201-223.

ABNT

JOSE, J. K.; M., D. Stress-Strength Reliability Estimation of Time-Dependent Models with Fixed Stress and Phase Type Strength Distribution. Revista Colombiana de Estadística, [S. l.], v. 44, n. 1, p. 201–223, 2021. DOI: 10.15446/rce.v44n1.86519. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/86519. Acesso em: 1 abr. 2025.

Chicago

Jose, Joby K, y Drisya M. 2021. «Stress-Strength Reliability Estimation of Time-Dependent Models with Fixed Stress and Phase Type Strength Distribution». Revista Colombiana De Estadística 44 (1):201-23. https://doi.org/10.15446/rce.v44n1.86519.

Harvard

Jose, J. K. y M., D. (2021) «Stress-Strength Reliability Estimation of Time-Dependent Models with Fixed Stress and Phase Type Strength Distribution», Revista Colombiana de Estadística, 44(1), pp. 201–223. doi: 10.15446/rce.v44n1.86519.

IEEE

[1]
J. K. Jose y D. M., «Stress-Strength Reliability Estimation of Time-Dependent Models with Fixed Stress and Phase Type Strength Distribution», Rev. colomb. estad., vol. 44, n.º 1, pp. 201–223, ene. 2021.

MLA

Jose, J. K., y D. M. «Stress-Strength Reliability Estimation of Time-Dependent Models with Fixed Stress and Phase Type Strength Distribution». Revista Colombiana de Estadística, vol. 44, n.º 1, enero de 2021, pp. 201-23, doi:10.15446/rce.v44n1.86519.

Turabian

Jose, Joby K, y Drisya M. «Stress-Strength Reliability Estimation of Time-Dependent Models with Fixed Stress and Phase Type Strength Distribution». Revista Colombiana de Estadística 44, no. 1 (enero 15, 2021): 201–223. Accedido abril 1, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/86519.

Vancouver

1.
Jose JK, M. D. Stress-Strength Reliability Estimation of Time-Dependent Models with Fixed Stress and Phase Type Strength Distribution. Rev. colomb. estad. [Internet]. 15 de enero de 2021 [citado 1 de abril de 2025];44(1):201-23. Disponible en: https://revistas.unal.edu.co/index.php/estad/article/view/86519

Descargar cita

CrossRef Cited-by

CrossRef citations3

1. Joby K. Jose, M. Drisya, Sebastian George. (2023). Bayesian Inference of the Phase-Type Stress-Strength Reliability Models. American Journal of Mathematical and Management Sciences, 42(1), p.13. https://doi.org/10.1080/01966324.2022.2162465.

2. Dang Duc Trong, Thai Phuc Hung. (2024). Deconvolution of ℙ( X t < Y t ) for stationary processes with supersmooth error distributions . Statistics, 58(6), p.1463. https://doi.org/10.1080/02331888.2024.2407913.

3. Joby K. Jose, Drisya M, Kulathinal Sangita, Sebastian George. (2024). Phase-type stress-strength reliability models under progressive type-II right censoring. Communications in Statistics - Theory and Methods, 53(23), p.8498. https://doi.org/10.1080/03610926.2023.2292968.

Dimensions

PlumX

Plum Print visual indicator of research metrics
  • Citations
  • Scopus - Citation Indexes: 5
  • Usage
  • SciELO - Full Text Views: 266
  • SciELO - Abstract Views: 23
  • Captures
  • Mendeley - Readers: 2
-
see details

Visitas a la página del resumen del artículo

273

Descargas

Licencia

Derechos de autor 2021 Revista Colombiana de Estadística

Creative Commons License

Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.

  1. Los autores/as conservarán sus derechos de autor y garantizarán a la revista el derecho de primera publicación de su obra, el cuál estará simultáneamente sujeto a la Licencia de reconocimiento de Creative Commons (CC Atribución 4.0) que permite a terceros compartir la obra siempre que se indique su autor y su primera publicación esta revista.
  2. Los autores/as podrán adoptar otros acuerdos de licencia no exclusiva de distribución de la versión de la obra publicada (p. ej.: depositarla en un archivo telemático institucional o publicarla en un volumen monográfico) siempre que se indique la publicación inicial en esta revista.
  3. Se permite y recomienda a los autores/as difundir su obra a través de Internet (p. ej.: en archivos telemáticos institucionales o en su página web) antes y durante el proceso de envío, lo cual puede producir intercambios interesantes y aumentar las citas de la obra publicada. (Véase El efecto del acceso abierto).