In this paper, upper and lower bounds are derived for convex reliability functions (or survival functions) with known first n moments. The case where the mean and the variance are given (n = 2) is discussed in details and explicit expressions are provided. Extensions for n >= 3 moments are described. Comparisons with existing bounds are performed.
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Louvain School of Management
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Courtois, C., & Denuit, M. (2007). Bounds on convex reliability functions with known first moments. European Journal of Operational Research, 177, 365-377. https://doi.org/10.1016/j.ejor.2005.08.026 (Original work published 2007)