Memristive devices have led to an increased interest in neuromorphic systems. However, different device requirements are needed for the multitude of computation schemes used there. While linear and time-independent conductance modulation is required for machine learning, non-linear and time-dependent properties are necessary for neurobiologically realistic learning schemes. In this context, an adaptation of the resistance switching characteristic is necessary with regard to the desired application. Recently, bi-layer oxide memristive systems have proven to be a suitable device structure for this purpose, as they combine the possibility of a tailored memristive characteristic with low power consumption and uniformity of the device performance. However, this requires technological solutions that allow for precise adjustment of layer thicknesses, defect densities in the oxide layers, and suitable area sizes of the active part of the devices. For this purpose, we have investigated the bi-layer oxide system TiN/TiOx/HfOx/Au with respect to tailored I-V non-linearity, the number of resistance states, electroforming, and operating voltages. Therefore, a 4-inch full device wafer process was used. This process allows a systematic investigation, i.e., the variation of physical device parameters across the wafer as well as a statistical evaluation of the electrical properties with regard to the variability from device to device and from cycle to cycle. For the investigation, the thickness of the HfOx layer was varied between 2 and 8 nm, and the size of the active area of devices was changed between 100 and 2,500 µm2. Furthermore, the influence of the HfOx deposition condition was investigated, which influences the conduction mechanisms from a volume-based, filamentary to an interface-based resistive switching mechanism. Our experimental results are supported by numerical simulations that show the contribution of the HfOx film in the bi-layer memristive system and guide the development of a targeting device.