Sequential tests constructed from images

A method is described for constructing sequential test boundaries for which the sample size distribution is easily computed. Assuming a diffusion approximation to be adequate, a few suitably placed images with negative weights are added to a basic unit source at the origin to create absorbing boundaries with intuitively desirable properties. A simple family of closed boundaries generated in this way is compared with Ferebee's (1980) reversed parabolic boundaries and Anderson's (1960) trapezoidal boundaries with regard to minimax expected sample size. The use of a delayed image to generate two-lobed closed boundaries is also briefly described.