This paper is concerned with (1) an explicit solution of a minimum variance control law for linear time-variant (LTV) processes in the transfer function form, and (2) performance assessment of LTV processes using minimum variance control as the benchmark. It is shown that there exists a time-variant, absolute lower bound of process variance that is achievable under LTV minimum variance control and can be estimated from routine operating data. This lower bound can subsequently be used to assess the benefit of implementing LTV control such as adaptive control. The proposed methods are illustrated through simulated examples and an industrial case study.