A Note on the Time to Failure of a Two-Unit Parallel Redundant System with Deterioration on a Lattice

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.