Reliability Estimation of Parallel Systems with Diverse Failure Modes: Semi-Markov Model Approach
DOI:
https://doi.org/10.13052/jrss0974-8024.1725Keywords:
Parallel unit system, semi-Markov process, reliability, sensitivity analysisAbstract
This paper introduces a novel system consisting of two dissimilar units operating in parallel, each with distinct failure modes. This flexibility in units characteristics minimizes the risk of simultaneous failures due to common causes. The system’s mathematical model is developed using a semi-Markov approach, and a numerical method based on the regenerative point technique is applied to estimate various reliability measures, such as the mean time to system failure (MTSF) and system availability. Failure rates are modeled as exponentially distributed, while repair rates are allowed to follow arbitrary distributions. Additionally, the proposed model undergoes graphical analysis to evaluate system performance under varying parameters.
Downloads
References
Kumar, P. and Gupta, R. Reliability analysis of a single unit M/G/1
system model with helping unit. J. Comb. Info. & System Sciences, 32(1–4):209–219, 2007.
Kumar, P. and Sirohi, A. Profit analysis of a two-unit cold standby system with delayed repair of partially failed unit and better utilization of units. Int. J. Comput. Appl., 117(1):41–46, 2015.
Kumar, P. and Sharma, S. K. A two non-identical unit parallel system with inspection and correlated lifetimes. J. Rajasthan Acad. Phys. Sci., 5(3):301–318, 2006.
Singh, V. V. and Poonia, P. K. Probabilistic assessment of two units parallel system with correlated lifetime under inspection using regenerative point technique. Int. J. Reliab. Risk Saf. Theory Appl., 2(1):5–14, 2019.
Kumar, A., Savita, and Shekhar, C. (2024). Cost Analysis of a Finite Capacity Queue with Server Failures, Balking, and Threshold-Driven Recovery Policy. International Journal of Mathematical, Engineering and Management Sciences, 9(5):1198–1209.
Kumar, A., Savita and Shekhar, C. (2024). Optimizing Resource Allocation in M/M/1/N
Queues with Feedback, Discouraged Arrivals, and Reneging for Enhanced Service Delivery. Journal of Reliability and Statistical Studies, 17(1), 1–16.
Shekhar, C., Kumar, A., and Varshney, S. (2020). Load Sharing Redundant Repairable Systems with Switching and Reboot Delay. Reliability Engineering & System Safety, 193:106656.
Shekhar, C., Kumar, A., Varshney, S., and Ammar, S. I. (2022). Fault-Tolerant Redundant Repairable System with Different Failures and Delays. Engineering Computations, 37(3):1043–1071.
Shekhar, C., Raina, A. A., Kumar, A., and Iqbal, J. (2017). A survey on queues in machining system: progress from 2010 to 2017. Yugoslav Journal of Operations Research, 27(4):391–413.
Shekhar, C., Kumar, N., Gupta, A., Kumar, A., and Varshney, S. (2020). Warm-spare provisioning computing network with switching failure, common cause failure, vacation interruption, and synchronized reneging. Reliability Engineering & System Safety, 199:106910.
Lin, Z., Tao, L., Wang, S., Yong, N., Xia, D., Wang, J., and Ge, D. (2024). A subset simulation analysis framework for rapid reliability evaluation of series-parallel cold standby systems. Reliability Engineering & System Safety, 241:109706.
Kumar, A. (2023). Single server multiple vacation queue with discouragement solve by confluent hypergeometric function. Journal of Ambient Intelligence and Humanized Computing, 14(5), 6411–6422.
Bhandari, A. S., Kumar, A., and Ram, M. (2024). Hybrid PSO‐GWO algorithm for reliability redundancy allocation problem with Cold Standby Strategy. Quality and Reliability Engineering International, 40(1):115–130.
Qi, F. Q., Wang, Y. K., and Huang, H. Z. (2024). Optimal maintenance policy considering imperfect switching for a multi‐state warm standby system. Quality and Reliability Engineering International, 40(5):2423–2443.
Hu, Z., Dang, C., Wang, L., and Beer, M. (2024). Parallel Bayesian probabilistic integration for structural reliability analysis with small failure probabilities. Structural Safety, 106:102409.
Ahmadi, R., Castro, I. T., and Bautista, L. (2024). Reliability modeling and maintenance planning for a parallel system with respect to the state-dependent mean residual time. Journal of the Operational Research Society, 75(2):297–313.
Bo, Y., Bao, M., Ding, Y., and Hu, Y. (2024). A DNN-based reliability evaluation method for multi-state series-parallel systems considering semi-Markov process. Reliability Engineering & System Safety, 242:109604.
