Published

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

Keywords:

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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Authors

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.

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How to Cite

APA

Jose, J. K. and 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. and 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 (Jan. 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: 28 mar. 2025.

Chicago

Jose, Joby K, and 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. and 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 and D. M., “Stress-Strength Reliability Estimation of Time-Dependent Models with Fixed Stress and Phase Type Strength Distribution”, Rev. colomb. estad., vol. 44, no. 1, pp. 201–223, Jan. 2021.

MLA

Jose, J. K., and D. M. “Stress-Strength Reliability Estimation of Time-Dependent Models with Fixed Stress and Phase Type Strength Distribution”. Revista Colombiana de Estadística, vol. 44, no. 1, Jan. 2021, pp. 201-23, doi:10.15446/rce.v44n1.86519.

Turabian

Jose, Joby K, and 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 (January 15, 2021): 201–223. Accessed March 28, 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]. 2021 Jan. 15 [cited 2025 Mar. 28];44(1):201-23. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/86519

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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.

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