This paper explores safety assessment of self-tuning generalized minimum variance control (GMVC) system by strong stability rate. Strong stability rate is one of the concepts of plant safety and is derived by using coprime factorization approach. Its value is defined by open-loop gain of controlled system through Youla-Kucera parametrization. GMVC is extended by using coprime factorization in this paper. Moreover the extended GMVC is designed so as to make the open-loop gain be closer to the closed-loop gain by new design parameter. In the case that the open-loop gain is closer to the closed-loop one, strong stability rate assesses that the controlled system maintains higher safety in the meaning that the open-loop output will be closer to the closed-loop output even if the feedback signal becomes zero by accident. In this paper numerical example for the self-tuning controller is given in order to verify the validity of the proposed assessment.