A small sample Monte Carlo study of four system reliability bounds

Abstract

Four theoretical methods providing approximations to total system reliability bounds from subsystem test data are compared through a Monte Carlo study. The system bounds in question, Kraemer, El Mawazini-Buehler, Grubbs and Mann-Grubbs, are valid asymptotically, i.e. when the number of failures observed is large. However, their small sample properties, and the closed forms of their small sample distributions, are unknown. In practice, when a system cannot be tested as a whole, the number of observed failures may be small. Hence, the practical importance for the study of the small sample properties of these bounds. Lacking this information, we perform a numerical study of these small sample properties, as well as a comparison of the bounds.