Mathematical Modeling for Performance Analysis and Inference of k-out of-n Repairable System Integrating Human Error and System Failure

Vishwa Nath Maurya^{1, 2,}

¹Department of Mathematics, School of Science & Technology, University of Fiji, Saweni, Fiji

²Vision Institute of Technology Aligarh, G.B. Technical University, India

Cite this paper:
Vishwa Nath Maurya. Mathematical Modeling for Performance Analysis and Inference of k-out of-n Repairable System Integrating Human Error and System Failure. American Journal of Modeling and Optimization. 2014; 2(1):16-24. doi: 10.12691/ajmo-2-1-3

Abstract

Present paper demonstrates mathematical modeling and evaluation of performance measures of k-out of-n repairable system wherein the most influencing constraints of human error and common-cause failure have been taken into consideration. Firstly the mathematical modeling is developed for performance analysis of k-out of-n repairable system with standby units involving human and common-cause failure. Then, a successful attempt has been made to evaluate various important performance measures such as availability of system, steady state availability and mean time of system failure (MTSF), mean operational time(MOT), expected busy period (EBP) and steady state busy period etc. Using the supplementary variable technique, Laplace transforms of various state probabilities are explored. Moreover, a particular case when repair rate follows exponential distribution has also been discussed. In addition, numerical illustration has also been presented in order to enable a better mode for understanding and testing the outcomes explored herein. Finally, tables and graphs for investigated results are displayed for drawing some significant conclusive observations for testing their validity and consistency.

Keywords:
Mathematical modeling repairable system human error common-cause failure steady state availability Laplace transform supplementary variable technique performance analysis

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