Reliability analysis of process systems, which is often based on a model of Weibull distribution, is semiquantitative at best because it uses constant parameters, requiring assumption of steady state operating conditions. A reliability model based on a variable scale parameter Weibull distribution is proposed in this work, in which a power law, the Arrhenius factor, and instantaneous amplitudes and frequencies of the operating condition variables are introduced. Numerical experiment indicates that when an operating condition variable fluctuates, the assumption of an average steady state operating condition can cause a serious error in reliability analysis. Therefore, the proposed method is expected to contribute to more quantitative risk assessment, and thus more rigorous safety analysis of process systems under changing operating conditions.