A Cascade System Reliability Model for Rama Distributed Random Variables

Chumchum Doloi¹ , Jonali Gogoi² , Gitanjali Pradhani³

1. Statistics, Assistant Professor, Pandit Deendayal Upadhyaya Adarsha Mahavidyalaya, Bongaigaon, India.
2. Statistics, Assistant Professor, Assam University, Silchar, India.
3. Statistics, Research Scholar, Assam University, Silchar, India.

Section:Research Paper, Product Type: Journal-Paper
Vol.10 , Issue.1 , pp.1-9, Feb-2023

Online published on Feb 28, 2023

Copyright © Chumchum Doloi, Jonali Gogoi, Gitanjali Pradhani . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
The reliability of a cascade system when the stress and strength are Rama-distributed random variables have been studied in this study. A standby redundancy system known as a "Cascade" replaces a failed component with a standby component that has independently dispersed strength and a lower stress value. A specific kind of stress-strength model is the cascade reliability model. The Cascade model`s system reliabilities for the parameters of this distribution about the cascade variables are calculated using the value of the marginal reliabilities for n=1,2 which is further used to find the system reliability R_2 2 of the Cascade model for the parameters of Rama distribution according to the cascade variables.

Key-Words / Index Term :
cascade system, stress-strength, reliability, hazard rate function, mean residual life function, Rama distribution

References :
[1]. C. Doloi, “Estimation of Cascade Reliability for two Stresses and Single Strength,” Advances and Applications in Statistics, Vol. 2, Issue 70, pp.129-136, 2021.
[2]. D. Reddy, “Cascade and System Reliability for Exponential Distribution,” DJ Journal of Applied Mathematics, vol.2, issue 2, pp.1-5, 2016, doi: 10.18831/djmaths.org/2016021001.
[3]. H. Dong, L. Cui, “System Reliability Under Cascading Failure Models,” IEEE Trans. Reliability, vol.65, issue 2, pp.929-940, 2016, doi:10.1109/TR.2015.2503751.
[4]. K. C. Kapur, L. R. Lamberson, “Reliability in Engineering Design,” Wiley, 1991.
[5]. M. Maryam, R. Kannan, Shabir A. Dar, “Improving the Reliability of System by Standby Redundancy Method,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue 1, pp.76-82, 2021.
[6]. P. V. Pandit, K. N., “Estimation of Stress Strength Reliability for Transmuted Exponentiated Inverse Rayleigh Distribution,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.5, pp.57-62, 2019.
[7]. R. E. Schafer, N. D. Singpurwalla, “Methods of Statistical Analysis of Reliability and Life Data,” Wiley-Blackwell, 1975.
[8]. R. Shanker, “Rama Distribution and Its Application,” International Journal of Statistics and Applications, Vol.1, No.7, pp.26-35, 2017.
[9]. S. N. N. Pandit, G. L. Sriwastav, “Studies in Cascade Reliability II,” IEEE Transactions on Reliability, Vol. 2, No. 27, pp.166-168, 1978.