Reliability analysis of vibrating electronic assemblies using analytical solutions and response surface methodology

This paper introduces a reliability performance study of electronic assemblies subjected to harmonic vibration loading using analytical solutions and response surface methodology (RSM). The work involved a modification of a previously published analytical solution for the vibrating assembly problem. This solution is employed to calculate the fundamental resonant frequency of the system and the ball grid array (BGA) solder interconnect axial deflections. Using RSM, the geometric parameters of an electronic package, the size and thickness of the printed circuit board (PCB) and the component as well as the solder height and radius, effects on the assembly first natural frequency and the most-critical solder joint axial deflection is investigated and hence presented. The results showed that the natural frequency of the system as well as the critical solder deformations and thus reliability can be effectively affected by such geometric variables. The results of this study can be very useful for the design of electronic products in vibration loading environments.