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This article presents information on Risk-Based Inservice Inspection and Testing as prescribed by the American Society of Mechanical Engineers (ASME). It is informed that the ASME criteria utilize the Fussell Vesely importance, or FV importance for short, to categorize the risk importance of the components. The FV importance is a measure of the contribution of a given minimal cutset to the risk measure of interest, such as the core damage frequency which the ASME focuses on. Since, to first order, the risk measure is a sum of all the evaluated minimal cutset contributions, the FV importance is the fractional contribution of the minimal cutset. In addition to not assuring that all the risk important contributors are included, the FV importance utilizations have additional deficiencies and sensitivities that can lead to erroneous or even nonsafe conclusions being made. It is opined that the risk importance measures should also not be used in isolation but should be integrated with existing safety and engineering principles.