### International Journal of Mathematical, Engineering and Management Sciences

#### ISSN: 2455-7749

Stochastic Analysis of a Computer System with Unit Wise Cold Standby Redundancy and Failure of Service Facility

#### Stochastic Analysis of a Computer System with Unit Wise Cold Standby Redundancy and Failure of Service Facility

Department of Statistics, M. D. University, Rohtak - 124001, India.

S. C. Malik
Department of Statistics, M. D. University, Rohtak- 124001, India.

;
Accepted on January 27, 2020

Abstract

Here, we analyze stochastically a computer system by taking one more similar unit (called computer system) in cold standby redundancy. The computer system consists of hardware and software components together. The provision of a single service facility has been made for repairing hardware and up-grading the software. The failure of the service facility is considered which resumes the jobs with full efficiency as new after availing treatment. The failure rates of hardware and software components as well as failure rate of the service facility are taken as constant and thus follow negative exponential distribution. The treatment rate of the service facility, repair rate of the hardware and up-gradation rate of the software follow arbitrary distributions with different probability density functions. Efforts have been made to determine reliability measures in steady state by using SMP and RPT. The behavior of MTSF, availability and also the profit function is observed graphically for some particular situations of the parameters.

Keywords- Computer system, Unit wise redundancy, Failure of service facility, Reliability measures, Stochastic analysis, Profit analysis.

Citation

Yadav, R. K., & Malik, S. C. (2020). Stochastic Analysis of a Computer System with Unit Wise Cold Standby Redundancy and Failure of Service Facility. International Journal of Mathematical, Engineering and Management Sciences, 5(3), 529-543. https://doi.org/10.33889/IJMEMS.2020.5.3.044.

Conflict of Interest

The work is original and has not been submitted anywhere for publication.

Acknowledgements

The authors sincerely appreciate the editor and reviewers for their time and valuable comments.

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