A projection-type display apparatus in accordance with the invention reduces the margin formed around the image forming range of the light valves, and forms a bright projected image. The first tracking element produces a first value indicative of a first estimated speed associated with the circuitry. Pseudo random LBIST patterns are then simulated using standard LBIST tool. When using the detailed inputs, the database composition of each table can be described in great detail, including details about the columns and rows. Once the pattern is obtained, the verifier performs a lookup of the pattern in the database.