Mathematical Modeling of Survivability Function for Thermoelectric Module

Abstract

Developing an optimized reliability model for thermoelectric module at the stress where the probability of module to functions without abruptive failure is a challenging aspect. One of the major reasons is the mismatch of thermal expansion coefficient, which has severe effects on segmented moduli compared to unsegmented moduli. The likelihood of a thermoelectric module to survive at certain level of thermo-mechanical stresses varies by varying number of component (layers) in thermoelectric leg. On another hand, selection of an adequate distribution model to predict reliability and sustainability of the thermoelectric module requires development of new optimized stress-strength-based model. In this paper the predictive reliability model for high temperature segmented module is derived from parametric Lognormal mean residual life and nonparametric Lognormal-kernel survival function to measure probability of module to survive at certain thermo-mechanical stress. A comprehensive comparative discussion has been done to illustrate the maximum likelihood based on Bayesian nonparametric lognormal-Kernel inference method regarding to Monte Carlo simulation, Weibull’s distribution, and Lognormal mean residual life for various shapes for the survival function. It has been demonstrated that nonparametric lognormal-kernel survival function has high ratio of probability to predict the survival of module at higher discrete thermo-mechanical stress data.