Designing robust products using a combination of simulation, experimental and statistical techniques

Probabilistic simulation methodology combines the simulation, experimental and statistical techniques in solving real life problems. In this paper the probabilistic design methodology is illustrated on a particular failure mode that was observed while testing a cell phone in an accelerated life test (ALT) environment. The failure mode encountered was the screw pull out during prototype testing a finite element model (FEM, FEA) was developed and used to predict the tensile force in the screw. The distribution of the stress (tensile force) was estimated using statistical methods such as DOE and response surface models (RSM) as a function of drop angle and friction that were the input parameters used in FEA model. Distributions of strength and drop angle were experimentally determined. Using the distribution of the drop angle and the RSM prediction equation from FEA model, the p.d.f. of the force distribution at the test condition was empirically determined. For known strength distribution but unknown stress distribution there is no analytical solution to calculate failure probability. Therefore, failure probability was calculated by using Monte-Carlo simulations, in which the probability of stress (force) larger than strength was estimated. The failure probability estimates from Monte Carlo Simulation were compared with the drop test results from actual ALT testing and were found to be in very good agreement. An alternative design was proposed and using the Monte-Carlo simulation probability of failure was estimated without doing any retooling, and prototype testing. With the new design it was predicted and later verified that this failure mode was eliminated in the ALT test environment. In conclusion, a practical methodology has been developed that integrates the FEA with statistical methods to predict up front, the reliability of the product. Application of this methodology at an early phase in the design process has the potential for reducing developmental cycle times and improving product reliability.