The fatigue damages in structural details of offshore plants can be accumulated due to various environmental loadings such as swell, wave, wind and current. It is known that load histories acting on mooring and riser systems show stationary and ergodic bimodal wide-banded process. This paper provides refined approach to obtain time signals representing stress range histories from wide-banded bimodal spectrum which consists of ideally narrow-banded and fully separated two spectrums. Variations of the probabilistic characteristics for time signals according to frequency and sampling time increments are compared with the reference data to be the probabilistic characteristics such as zero-crossing period, peak period, and irregularity factor obtained from an assumed ideal spectrum. It is proved that the sampling time increment more affects on the probabilistic characteristics than frequency increment. The fatigue damages according to the frequency and sampling time increments are also compared with the ones with minimum increment condition which are thought to be exact fatigue damage. It is concluded that the maximum sampling time increment to obtain reliable time signals should be determined that ratio of applied maximum sampling time increment and minimum period is less than approximately 0.08.