Tadashi Dohi
Department of Information Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 739-8527, Japan.

Junjun Zheng
Department of Information Science and Engineering, Ritsumeikan University, 1-1-1 Nojihigashi Kusatsu 525-8577, Japan.

Hiroyuki Okamura
Department of Information Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 739-8527, Japan.

DOI https://doi.org/10.33889/IJMEMS.2021.6.1.002

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Abstract

In this paper, we consider a two-unit parallel redundant system with deterioration on a lattice, where each unit has multi-stage deterioration levels, say, n levels. The transition from one deterioration level to the subsequent level occurs following the well-known Marshall-Olkin bivariate exponential distribution. We derive the closed form of the Laplace transform of the time to system failure in the two-unit parallel redundant system with deterioration on n×n lattice without repair and simultaneous failure, as well as the simple system on 3×3 lattice.

Keywords- Two-unit parallel redundant system, Marshall-Olkin bivariate exponential distribution, Time to system failure, Laplace transform, Deterioration on a lattice.

Citation

Dohi, T., Zheng, J., & Okamura, H. (2021). A Note on the Time to Failure of a Two-Unit Parallel Redundant System with Deterioration on a Lattice. International Journal of Mathematical, Engineering and Management Sciences, 6(1), 3-14. https://doi.org/10.33889/IJMEMS.2021.6.1.002.