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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.v44n1.86519Keywords:
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)
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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.
References
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
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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. Joby K. Jose, Drisya M, Kulathinal Sangita, Sebastian George. (2023). Phase-type stress-strength reliability models under progressive type-II right censoring. Communications in Statistics - Theory and Methods, , p.1. https://doi.org/10.1080/03610926.2023.2292968.
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