The detection of instants of change in random process properties, a problem with a variety of applications in technical and medical diagnostics, control, and image processing, is considered. The focus in this study is on the detection of a jump change in the mean and/or variance of an observed random sequence. The problem is to detect the jump as quickly as possible after its occurrence while avoiding an excessive false alarm rate (i.e. declaring a change before it occurs). For this purpose, the Neyman-Pearson criterion for the design of a disruption detector is used. An optimal design formula is derived for limiting cases. Using a Neyman-Pearson criterion, the designer can determine an optimal window size and an optimal detector sensitivity.