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

• Autores: Joby K. Jose, Mottammal Drisya
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 44, Nº. 1, 2021, págs. 201-223
• Idioma: inglés
• DOI: 10.15446/rce.v44n1.86519
• Títulos paralelos:
  • 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
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen 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.

  • English

    Abstract 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.

• Referencias bibliográficas
  • Asmussen, S.,Nerman, O.,Olsson, M. (1996). 'Fitting phase-type distributions via the em algorithm'. Scandinavian Journal of Statistics....
  • Baklizi, A. (2008). 'Estimation of pr(x < y) using record values in the one and two parameter exponential distributions'. Communications...
  • Barron, Y.,Frostig, E.,Levikson, B. (2004). 'Analysis of r-out-of-n repairable systems: The case of phase-type distribution'. Advances...
  • Barron, Y.,Yechiali, U. (2017). 'Generalized control-limit preventive repair policies for deteriorating cold and warm standby markovian...
  • Birnbaum, Z. M. (1956). 'On a use of the mann-whitney statistic'. Proceedings of the Third Berkeley Symposium on Mathematical Statistics...
  • Bladt, M.,Esparza, L. J. R.,Nielsen, B. F. (2011). 'Fisher information and statistical inference for phase-type distributions'. Journal...
  • Eryilmaz, S. (2018). 'Phase type stress-strength models with reliability applications'. Communications in Statistics-Simulation and...
  • Ghitany, M. E.,Al-Mutairi, D. K.,Aboukhamseen, S. M. (2015). 'Estimation of the reliability of a stress-strength system from power lindley...
  • Gopalan, M. N.,Venkateswarlu, P. (1982). 'Reliability analysis of time-dependent cascade system with deterministic cycle times'. MicroelectronicsReliability....
  • Gopalan, M. N.,Venkateswarlu, P. (1983). 'Reliability analysis of time-dependent cascade system with random cycle times'. Microelectronics...
  • Huang, K.,Mi, J.,Wang, Z. (2012). 'Inference about reliability parameter with gamma strength and stress'. Journal of Statistical Planning...
  • Jose, J. K.,Drisya, M.,Manoharan, M. (2020). 'Estimation of stress-strength reliability using discrete phase type distribution'. Communications...
  • Jose, J. K.,Xavier, T.,Drisya, M. (2019). 'Estimation of stress strength reliability using Kumaraswamy half-logistic distribution'....
  • Kizilaslan, F.,Nadar, M. (2015). 'Classical and bayesian estimation of reliability in multi-component stress-strength model based on Weibull...
  • Kotz, S.,Pensky, M. (2003). The stress-strength model and its generalizations: theory and applications. World Scientific.
  • Kundu, D.,Raqab, M. Z. (2009). 'Estimation of r = pr(y < x) for three-parameter Weibull distribution'. Statistics and Probability...
  • Lomnicki, Z. A. (1966). 'A note on the Weibull renewal process'. Biometrica. 53. 375
  • Neuts, M. F. (1975). 'Liber Amicorum'. University of Louvain. Belgium.
  • Rao, G. S. (2012). 'Estimation of reliability in multicomponent stress-strength based on generalized exponential distribution'. Revista...
  • Rao, G. S.,Aslam, M.,Kundu, D. (2014). 'Burr type XII distribution parametric estimation and estimation of reliability in multi-component...
  • Rezaei, S.,Tahmasbi, R.,Mahmoodi, M. (2010). 'Estimation of p(y < x) for generalized Pareto distribution'. Journal of Statistical...
  • Siju, K. C.,Kumar, M. (2016). 'Reliability analysis of time dependent stress-strength model with random cycle times'. Perspectives...
  • Siju, K. C.,Kumar, M. (2017). 'Reliability computation of a dynamic stress-strength model with random cycle times'. International...
  • Wong, A. (2012). 'Interval estimation of P(Y < X) for generalized Pareto distribution'. Journal of Statistical Planning and Inference....
  • Xavier, T.,Jose, J. K. (2020). 'A study of stress-strength reliability using a generalization of power transformed half-logistic distribution'....
  • Yadav, R. P. S. (1973). 'A reliability model for stress strength problem'. Microelectronics Reliability. 12. 119