Inspections for Log-Convex Failure Distributions

Giovanni Parmigiani
Duke University

Nov 30 1990

This paper discusses the theory of optimal scheduling of inspections for the early detection of failures when the distribution of the failure time is log-convex. The interest of the results is in the intrinsic importance of log-convex distributions as well as in the analysis of failure distributions not fully known. It is shown that, within the classes of log-convex densities, times between successive inspections increase with time. The case of exponential failures with unknown failure rate is explore in detail, with discussion of the issues of learning and of sensitivity to the specification of the prior distribution.


Optimal inspection schedule, log-convex failure distributions, unknown failure rate


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