Surveillance problems: Wiener processes

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Abstract
This paper extends the results presented by I. R. Savage in a previous paper [8]. That paper studied economically optimal policies for inspecting and repairing production processes which behave as Poisson processes. Similar results are presented here for production processes which behave as Wiener processes.With continuous surveillance, methods are presented which permit the computation of exactly optimal strategies and the optimal income per unit of time. With costly surveillance, a functional equation is presented. The solution of this equation would yield the optimal strategy. Explicit solutions do not seem feasible but many qualitative properties of the solutions are found. The most interesting of these says, roughly (see Proposition 12 for exact statement), that the time between inspections decreases as the observed quality decreases.

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