Goal-seeking problem in discrete event systems simulation

For most complex stochastic systems such as microelectronic systems, the Mean Time To Failure (MTTF) is not available in analytical form. We resort to Monte-Carlo Simulation (MCS) to estimate MTTF function for some specific values of underlying density function parameter(s). MCS models, although simpler than a real-world system, are still a very complex way of relating input parameter(s) to MTTF. This study develops a polynomial model to be used as an auxiliary to an MCS model. The estimated metamodel is a Taylor expansion of the MTTF function in the neighbourhood of the nominal value for the parameter(s). The Score Function methods estimate the needed sensitivities (i.e. gradient, Hessian, etc.) of the MTTF function with respect to the input parameter in a single simulation run. The explicit use of this metamodel is the target-setting problem in Taguchi's product design concept: given a desired target MTTF value, find the input parameter(s). A stochastic approximation algorithm of the Robbins–Monro type uses a linear metamodel to estimate the necessary controllable input parameter within a desired accuracy. The potential effectiveness is demonstrated by simulating a reliability system with a known analytical solution.