To find the cause of a functional or non-functional defect (bug) in software running on a multi-processor System-on-Chip (MPSoC), developers need insight into the chip. Tracing systems provide this insight non-intrusively, at the cost of high off-chip bandwidth requirements. This I/O bottleneck limits the observability, a problem becoming more severe as more functionality is integrated on-chip. In this paper, we present DiaSys, an MPSoC diagnosis system with the potential to replace today's tracing systems. Its main idea is to partially execute the analysis of observation data on the chip; in consequence, more information and less data is sent to the attached host PC. With DiaSys, the data analysis is performed by the diagnosis application. Its input are events, which are generated by observation hardware at interesting points in the program execution (like a function call). Its outputs are events with higher information density. The event transformation is modeled as dataflow application. For execution, it is mapped in part to dedicated and distributed on-chip components, and in part to the host PC; the off-chip boundary is transparent to the developer of the diagnosis application. We implement DiaSys as extension to an existing SoC with four tiles and a mesh network running on an FPGA platform. Two usage examples confirm that DiaSys is flexible enough to replace a tracing system, while significantly lowering the off-chip bandwidth requirements. In our examples, the debugging of a race-condition bug, and the creation of a lock contention profile, we see a reduction of trace bandwidth of more than three orders of magnitude, compared to a full trace created by a common tracing system.