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The paper studies the expectation of the inspection time in complex agingsystems. Under reasonable assumptions, this problem is reduced to studying theexpectation of the length of the shortest path in the directed degradationgraph of the systems where the parameters are given by a pool of experts. Theexpectation itself being sometimes out of reach, in closed form or even throughMonte Carlo simulations in the case of large systems, we propose an easilycomputable lower bound. The proposed bound applies to a rather general class oflinear programs with random nonnegative costs and is directly inspired from theupper bound of Dyer, Frieze and McDiarmid [Math.Programming {\bf 35} (1986),no.1,3--16].

A lower bound on the expected optimal value of certain random linear programs and application to shortest paths and reliability