Stress-strength reliability analysis of series systems with redundancy : A study utilizing Rayleigh distribution and estimation techniques

Hassan, Marwa KH.; Aslam, Muhammad

doi:10.47974/JSMS-1354

Open Access Research Article

Stress-strength reliability analysis of series systems with redundancy : A study utilizing Rayleigh distribution and estimation techniques

Marwa KH. Hassanmarwa_khalil@edu.asu.edu.egDepartment of MathematicsFaculty of EducationAin Shams UniversityCairo, Egypt0000-0003-3730-7869View full profile → , ^*Muhammad AslamCorresponding authoraslam_ravian@hotmail.comDepartment of StatisticsFaculty of ScienceKing Abdulaziz UniversityJeddah, 21589, Saudi ArabiaView full profile →

* Corresponding author · click or hover a name for details

pp. 151–175Vol. 28Issue 1January 2025DOI: 10.47974/JSMS-1354XML

Received:: 12 Dec 2023
Published Online:: 15 Jan 2025
Article type:: Research Article
Language:: EN
Article no.:: JSMS-1354
Pages:: 151–175

Abstract

The Rayleigh distribution is among the numerous distributions employed as a model for lifetime events, finding appli-cations in survival analysis, reliability, and communications engineering. This study focuses on investigating the stress-strength reliability of a series system with redundancy at both component and system levels, utilizing the Rayleigh dis-tribution with varying parameters. Estimators for model parameters are obtained through the Maximum Likelihood method and Bayesian procedures. A Monte Carlo simulation study is conducted to compare the different estimates. Additionally, a real-world application is presented to demonstrate the validity of our proposed model.

Keywords

Series system Cold standby redundancy system Rayleigh distribution Bayes estimator Maximum likelihood estimator Simulation study

Subject Classifications

62N0562F15

References

[1] N. L. Johnson, S. Kotz and S. Balakrishman, Continuous Univariate Distributions (1994).
[2] M. Basirat, S. Baratpour and J. Ahmadi, “Statistical inferences for stress-strength in the proportional hazard models based on progressive Type-II censored samples,” Journal of Statistical Computation and Simulation, vol. 85, no. 3, pp. 431-449 (2015).
[3] C. Cetinkaya and A. I. Genc, “Stress-strength reliability estimation under the standard two-sided power distribution.,” Applied Mathematical Modelling, vol. 65, pp. 72-88 (2019).
[4] M. Jovanovıć, B. Milošević and M. Obradović, “Estimation of stress-strength probability in a multicomponent model based on geometric distribution,” Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 4, pp. 1515-1535 (2020).
[5] M. Hassan and M. Alohali,, “Estimation of Reliability in a Multicomponent Stress- Strength Model Based on Generalized Linear Failure Rate Distribution,” Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 6, pp. 1634-1651 (2018).
[6] S. Rao, S. Mbwambo and A. Pak, “Estimation of Multicomponent Stress-Strength Reliability from Exponentiated Inverse Rayleigh Distribution,” Journal of Statistics and Management Systems, vol. 24, no. 3, pp. 499-519 (2021).
[7] X. Bai, J. Zhang and J. Chai, “Statistical Inference for Multicomponent System Stress-Strength Model with Bounded Strengths,” Journal of Systems Science and Complexity, vol. 36, no. 2, pp. 755-770 (2023).
[8] R. Barlow and F. Proschan, Statistical Theory of Reliability and Life Testing, Holt, Rinehart and Winston Inc: International Series in Decision Processes (1975).
[9] G. Sriwastav and M. Kakati, “A stress-strength model with redundancy,” IAPQR TRANSACTIONS, vol. 6, no. 1, pp. 21-27 (1981).
[10] H. Khan, Adil and T. R. Jan, “Estimation of Multi Component Systems Reliability in Stress-Strength Models,” Journal of Modern, vol. 13, no. 2, pp. 389-398 (2014).
[11] J. B. Ke, W. C. Lee and K. Wang, “Reliability and sensitivity analysis of a system with multiple unreliable service stations and standby switching failures,” Physica A, vol. 380, no. 1, pp. 455-469 (2007).
[12] J. H. Cha, J. Mi and W. Y. Yun, “Modelling a general standby system and evaluation of its performance,” Applied Stochastic Models in Business and Industry, vol. 24, no. 2, pp. 159-169 (2008).
[13] S. Eryilmaz, “Reliability of a k-out-of-n system equipped with a single warm standby component,” IEEE Transactions on Reliability, vol. 62, no. 2, pp. 499-503 (2013).
[14] M. K. Hassan, “On Estimating Standby Redundancy System in a MSS Model with GLFRD Based on Progressive Type II Censoring Data,” Reliability: Theory & Applications, vol. 16, pp. 206-219 (2021).
[15] P. J. Boland and E. El-Neweihi, “Component redundancy vs system redundancy in the hazard rate ordering,” IEEE Transactions on Reliability, vol. 44, no. 4, pp. 614-619 (1995).
[16] J. Chen, Y. Zhang, P. Zhao and S. Zhou, “Allocation strategies of standby redundancies in series/parallel system,” Communications in Statistics - Theory and Methods, vol. 47, no. 3, pp. 708-724 (2018).
[17] S. Eryilmaz,, “Dynamic reliability and performance evaluation of multi-state systems with two components,” Hacettepe Journal of Mathematics and Statistics, vol. 62, no. 1, pp. 125-133 (2011).
[18] S. Eryilmaz, “The effectiveness of adding cold standby redundancy to a coherent system at system and component levels,” Reliability Engineering and System Safety, vol. 165, pp. 331-335 (2017).
[19] N. K. Hazra and A. K. Nanda,, “Component redundancy versus system redundancy in different stochastic orderings,” IEEE Transactions on Reliability, vol. 63, no. 2, pp. 567-582 (2014).
[20] C. S. Kumar, “Standby redundancy at system and component levels-A comparison,” Microelectronics Reliability, vol. 35, no. 4, pp. 751-752 (1995).
[21] K. Shen and M. Xie, “The effectiveness of adding standby redundancy at system and component levels.,” IEEE Transactions on Reliability, vol. 40, no. 1, pp. 53-55 (1991).
[22] R. Yan,, B. Lu and X. Li, “On Redundancy allocation to series and parallel systems of two components,” Communications in Statistics - Theory and Methods, vol. 48, no. 18, pp. 4690-4701 (2019).
[23] P. Zhao, Y. Zhang and L. Li, “Redundancy allocation at component level versus system level.,” European Journal of Operational Research, vol. 241, no. 2, pp. 402-411 (2015).
[24] G. Cüran and F. Kızılaslan, “Statistical inference of the stress-strength reliability and mean remaining strength of series system with cold standby redundancy at system and component levels,” Hacettepe Journal of Mathematics and Statistics, vol. 50, pp. 1739-1821 (2021).
[25] Y. Liu, Y. Shi, X. Bai and P. Zhan, “Reliability estimation of a N-M-cold-standby redundancy system in a multicomponent stress-strength model with generalized half logistic distribution,” Physica A, vol. 490, pp. 231-249 (2018).
[26] K. C. Siju and M. Kumar, “Estimation of stress-strength reliability of a parallel system with active, warm and cold standby components,” Journal of Industrial and Production Engineering, vol. 34, no. 8, pp. 590-610 (2017).
[27] J. O. Berger, Statistical Decision Theory and Bayesian Analysis, Springer (1985).
[28] T. Hecke, “Fuzzy Parameter estimation of Raylieigh Distribution,” Journal of Statistics and Management Systems, vol. 21, no. 7, pp. 1391-1400 (2018).
[29] S. K. Upadhyay and A. Gupta, “A Bayes analysis of modified Weibull distribution via Markov chain Mote Carlo simulation,” Journal of Statistical Computation and Simulation, vol. 80, pp. 3-4 (2010).
[30] A. E. Gelfand and A. M. Smith, “Sampling-based approaches to calculating marginal densities,” Journal of the American Statistical Association, vol. 85, no. 410, pp. 398-409 (1990).
[31] W. K. Hastings, “Monte Carlo sampling methods using Markov chains and their applications,” Biometrika, vol. 57, no. 1, pp. 97-109 (1970).
[32] S. P. Brooks, “Markov chain Monte Carlo method and its application,” Journal of the Royal Statistical Society Series D: The Statistician, vol. 47, no. 1, pp. 69-100 (1998).
[33] J. Lawless, Statistical Models and Methods for Lifetime Data, 2 ed., New York: Wiley (2003).

Views: 135Downloads: 74Citations: 0