A second derivative of a second-order differential equation is calculated at a reference variable value. This beam spot is generated by irradiating the predetermined position on the coordinate input screen with light coming from a pointing tool, or corresponds to a light-emitting portion provided to the distal end of the pointing tool located near the coordinate input screen. A slit control section alternately switches each slit region between a transmitting state and a shielding state at a predetermined cycle. The data is screened to uncover patterns though which the faults of interest manifest in sensor data and the patterns are analyzed and combined with available physical system information to develop an underlying principle that links failures to measured sensor responses. Also included are methods of making and using such compounds.