A new approach of statistical model for prediction of fuel element failure is developed to take into account the effects of overall operating history and damaging environmental conditions. It is accomplished by the application of dynamic reliability function and entropy minimax principles. the degradation of material properties of fuel cladding is mainly caused by the combined effects of accumulated dynamic stresses, neutron irradiation, and chemical and stress corrosion at operating temperatures. Since the degradation of material properties due to these effects can be considered as a Markov process, a dynamic reliability function is derived based on the Markov process. It is utilized to describe the effects on fuel elements failure of damaging environmental conditions and overall operating history. Four damage parameters, namely dynamic stress, the magnitude of power increase from the preceding power level and with ramp rate, and fatigue cycles are used to build this statistical prediction model. The dynamic reliability function and damage parameters are used to obtain effective damage parameters. The entropy maximization principle is applied to generate probability density function of effective damage parameters. The entropy minimization principle is applied to determine weighting factors for combination of the failure probabilities of the respective failure modes. In this way, the effects of operating history and damaging environmental conditions and damage sequence are more fully take into account in model.