Estimation of the survival fractions of cells irradiated with various particles over a wide linear energy transfer (LET) range is of great importance in the treatment planning of charged-particle therapy. Two computational models were developed for estimating survival fractions based on the concept of the microdosimetric kinetic model. They were designated as the double-stochastic microdosimetric kinetic and stochastic microdosimetric kinetic models. The former model takes into account the stochastic natures of both domain and cell nucleus specific energies, whereas the latter model represents the stochastic nature of domain specific energy by its approximated mean value and variance to reduce the computational time. The probability densities of the domain and cell nucleus specific energies are the fundamental quantities for expressing survival fractions in these models. These densities are calculated using the microdosimetric and LET-estimator functions implemented in the Particle and Heavy Ion Transport code System (PHITS) in combination with the convolution or database method. Both the double-stochastic microdosimetric kinetic and stochastic microdosimetric kinetic models can reproduce the measured survival fractions for high-LET and high-dose irradiations, whereas a previously proposed microdosimetric kinetic model predicts lower values for these fractions, mainly due to intrinsic ignorance of the stochastic nature of cell nucleus specific energies in the calculation. The models we developed should contribute to a better understanding of the mechanism of cell inactivation, as well as improve the accuracy of treatment planning of charged-particle therapy.