Device-parameter estimation sensors inside a chip are gaining its importance as the post-fabrication tuning is becoming of a practical use. In estimation of variational parameters using on-chip sensors, it is often assumed that the outputs of variation sensors are not affected by random variations. However, random variations can deteriorate the accuracy of the estimation result. In this paper, we propose a device-parameter estimation method with on-chip variation sensors explicitly considering random variability. The proposed method derives the global variation parameters and the standard deviation of the random variability using the maximum likelihood estimation. We experimentally verified that the proposed method improves the accuracy of device-parameter estimation by 11.1 to 73.4% compared to the conventional method that neglects random variations.