Mean time between failures (MTBF) is a common reliability measure used to assess the failure behavior of repairable systems. In order to increase MTBF, in most systems, it is a common practice to perform preventive maintenance activities at periodic intervals. In this paper: We first discuss the validity of a commonly used equation for computing MTBF of systems subjected to periodic maintenance.) For complex systems where this equation is valid, we propose a simple and better approximation than the exponential approximation proposed in a recent paper. In addition, we prove that for systems with increasing failure rate on average (IFRA) distributions, the exponential approximation proposed in a recent paper always underestimates the MTBF; hence, it is a lower bound at best.) The proposed approximation and bounds are applicable for a wide range of systems because systems which contain components with exponential or any increasing failure rate (IFR) distribution (viz., Weibull with beta>1, gamma, Gumbel, s-normal, and uniform) follow an IFRA distribution. As a special case, the proposed bounds & approximations provide better results for systems that contain only exponential failure distributions