Technical Note—On the Rate of Expansion of Gamma Search Plans

In the paper “Optimal Search With Uncertain Sweep Width” Richardson and Belkin derive the optimal search plan (gamma plan) for a stationary target with bivariate normal prior location distribution when the search sensor sweep width has a gamma distribution. The claim is then made that increasing the level of uncertainty in prior knowledge of sweep width (by increasing variance with mean fixed) slows the rate of expansion of this gamma plan. In this note we show that this statement is correct only after the search has proceeded unsuccessfully for some time. Earlier in the search, an increase in the level of sweep width uncertainty would actually accelerate the rate of expansion of the gamma plan.