We have developed a directed self-assembly process for the fabrication of three-dimensional (3D) microsystems that contain non-identical parts and a statistical model that relates the process yield to the process parameters. The self-assembly process uses geometric-shape recognition to identify different components, and surface tension between liquid solder and metal-coated areas to form mechanical and electrical connections. The concept is used to realize self-packaging microsystems that contain non-identical subunits. To enable the realization of microsystems that contain more than two non-identical subunits, sequential self-assembly is introduced, a process that is similar to the formation of heterodimers, heterotrimers, and higher aggregates found in nature, chemistry, and chemical biology. The self-assembly of three-component assemblies is demonstrated by sequentially adding device segments to the assembly solution including two hundred micrometer-sized light-emitting diodes (LEDs) and complementary metal oxide semiconductor (CMOS) integrated circuits. Six hundred AlGaInP/GaAs LED segments self-assembled onto device carriers in two minutes, without defects, and encapsulation units self-assembled onto the LED-carrier assemblies to form a 3D circuit path to operate the final device. The self-assembly process is a well-defined statistical process. The process follows a first-order, non-linear differential equation. The presented model relates the progression of the self-assembly and yield with the process parameters-component population and capture probability-that are defined by the agitation and the component design.