Damage in a structure can be detected using vibration measurements under unknown random excitation. Structural health monitoring (SHM) systems must be often designed before knowledge about future damage. Also, the excitation characteristics are unknown and may vary between measurements. The objective of the present paper is to facilitate the design of an SHM system, when autocovariance functions (ACFs) are used as damage-sensitive features. Since the ACFs have the same form as a free decay of the system for a stationary random process, they are spatiotemporally correlated. Therefore, it is possible to achieve redundant measurement data. The data space can then be divided into two subspaces, a signal space and the noise space. The information lies in the signal space, while the noise space consists mostly of measurement errors. If the structure is damaged, the new data also hit the noise space, where damage can be detected. To this end, the objective is to pursue data redundancy. The degree of redundancy of the ACF data depends on three design parameters: (1) the number of active modes, (2) the number of sensors, and (3) the model order used in the data analysis. It is also shown that with a proper choice of the design parameters, the variability of the excitation statistics has no effect on redundancy. To help with the selection of the parameters, a design map is provided. It has four different regions, depending on the number of sensors and the model order: (1) both frequency and mode shape changes can be detected, (2) frequency changes can only be detected, (3) mode shape changes can only be detected, and (4) damage is not detected. A numerical experiment was conducted to verify the regions of the design map. The rank of the noiseless data matrix was used to indicate the degree of redundancy. With the help of the design map, the user can select the number of sensors and the model order to detect both frequency and mode shape changes.