Vibration induced fatigue failures (VIFF) of pipework small bore connections (SBCs) due to turbulent flow excitation continue to occur in process piping systems, resulting in elevated safety risks and costly interruptions to normal operations. One of the primary causes of these failures is poor design. When the valve and pipe components in an SBC assembly combine to produce a fundamental natural frequency that is low, the SBC can readily be excited into a high vibration condition. In this high vibration condition, the threat of VIFF increases significantly. One of the primary design goals for SBCs should therefore be to achieve a high natural frequency, however, this is very rarely considered in the existing design process. Reasons for this include the lack of understanding of the importance of natural frequency to the vulnerability of the design and a lack of information on how high this target natural frequency must be when it is considered. In this paper, the concept of a cut-off natural frequency is defined, above which the probability of VIFF of SBCs is negligible. If this concept is incorporated into the design process for SBCs a decrease in the number of failures of SBCs due to vibration should be realised.