This paper proposes individual computation processes of the partial demodulation reference signal (DM-RS) sequence in a synchronization signal (SS)/physical broadcast channel (PBCH) block to be used to detect the radio frame timing based on SS/PBCH block index detection for New Radio (NR) initial access. We present the radio frame timing detection probability using the proposed partial DM-RS sequence detection method that is applied subsequent to the physical-layer cell identity (PCID) detection in five tapped delay line (TDL) models in both non-line-of-sight (NLOS) and line-of-sight (LOS) environments. Computer simulation results show that by using the proposed method, the radio frame timing detection probabilities of almost 100% and higher than 90% are achieved for the LOS and NLOS channel models, respectively, at the average received signal-to-noise power ratio (SNR) of 0dB with the frequency stability of a local oscillator in a set of user equipment (UE) of 5ppm at the carrier frequency of 4GHz.