Two-dimensional diffusion processes as models in lifetime studies

Mario Lefebvre and Djilali Ait Aoudia

International Journal of Systems Science, 2012, vol. 43, issue 10, 1943-1949

Abstract: Let X(t) denote the remaining useful lifetime of a machine, and Y(t) be a standard Brownian motion. Assume that the derivative ρ[X(t), Y(t)] of X(t) is a deterministic function of (at least) Y(t). We consider the two-dimensional degenerate diffusion process (X(t), Y(t)). We obtain explicit expressions for the expected value of the random variable T(x, y) denoting the first time the machine must be replaced, or repaired, for various functions ρ[X(t), Y(t)].

Date: 2012
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DOI: 10.1080/00207721.2011.563870

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