The radial velocity method plays a major role in the discovery of nearby exoplanets. To efficiently find planet candidates from the data obtained in high precision radial velocity surveys, we apply a signal diagnostic framework to detect radial velocity signals that are statistically significant, consistent in time, robust to the choice of noise models, and not correlated with stellar activity. Based on the application of this approach to the survey data of the Planet Finder Spectrograph (PFS), we report fifteen planet candidates located in fourteen stellar systems. We find that the orbits of the planet candidates around HD 210193, 103949, 8326, and 71135 are consistent with temperate zones around these stars (where liquid water could exist on the surface). With periods of 7.76 and 15.14 days respectively, the planet candidates around star HIP 54373 form a 1:2 resonance system. These discoveries demonstate the feasibility of automated detection of exoplanets from large radial velocity surveys, which may provide a complete sample of nearby Earth analogs.