Abstract
Interdependence between random variables and processes is analyzed extensively in the literature using different techniques. In this paper, a new direction of analysis to investigate the reliability of systems such as a \( k\hbox {-}out\hbox {-}of\hbox {-}n: G \) system and, in particular serial and parallel systems with interdependence among the components, is introduced. This procedure is through a special case of semi-Markov process. The distribution of the time to failure of serial, parallel and also that of the more general \( k\hbox {-}out\hbox {-}of\hbox {-}n: G \) system, are derived. A theoretical comparison between systems with interdependent components and systems with independent components is provided.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bian L, Wang G, Liu P, Fengjun Duan (1992) Two shock models for single-component systems subject to mutually dependent failure processes. Quality Reliab Eng. https://doi.org/10.1002/qre.3006
Bian L, Wang G, Liu P (2021) Reliability analysis for multi-component systems with interdependent competing failure processes. Appl Math Modell. https://doi.org/10.1016/j.apm.2021.01.009
Dudin AN, Klimenok V, Vishnevsky VM (2020) The theory of queueing systems with correlated flows. Springer, Berlin
Krishnamoorthy A (2020) Analysis of interdependent processes: a semi-markov approach. Bull Kerala Math Assoc 17(1):49–68
Krishnamoorthy A, Ushakumari PV, Lakshmy B (1999) \( k- out - of - n \) - system with repair: The \( N - \) policy. Asia -Pacific J Oper Res 19(1):47
Krishnamoorthy A, Narayanan VC (2021): On a queue with interdependence between arrival and service processes-A semi-Markov approach, under review
Neuts MF (1981) Matrix - geometric solutions in stochastic models: an algorithmic approach. The Johns Hopkins University Press, Baltimore
Ross SM (1992) Applied probability models with optimization applications. Dover, Illinois
Shi H, Wei C, Zhang Z, Liu B, Wen Y (2020) Reliability analysis of dependent competitive failure model with uncertain parameters. Soft Comput. https://doi.org/10.1007/s00500-021-06398-6
Shuyuan G, Zhifang S (2021) Reliability evaluation by a dependent competing failure model including a time-varying rate for sudden degradation increments. Arabian J Sci Eng, Zeitschrift. https://doi.org/10.1007/s13369-021-05438-5
Acknowledgements
The author thanks Ms. Anu Nuthan Joshua, Department of Mathematics, Union Christian College, Aluva, India, for critical reading of the manuscript. Thanks are also due to Professor A.N. Dudin for several suggestions that lead to considerable improvement in the presentation of the paper.
Funding
This research is not supported by any funding agency.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author does not have any conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This paper is dedicated to the memory of my teachers: Professor G. Sankaranarayanan, Professor R.P. Pakshirajan and Professor S. K. Srinivasan. Professor Dandapani Kannan was also a great source of inspiration to me.
Rights and permissions
About this article
Cite this article
Krishnamoorthy, A. Analysis of Reliability of Interdependent Serial, Parallel and The General \( k\hbox {-}out\hbox {-}of\hbox {-}n: G \) System: A New Approach. J Indian Soc Probab Stat 23, 483–496 (2022). https://doi.org/10.1007/s41096-022-00133-6
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41096-022-00133-6