To verify fixed-time constraints in grid workflow systems, the consistency and inconsistency conditions have been defined in the conventional work. However, in this paper, we argue that although the conventional consistency condition is reasonable, the conventional inconsistency condition is too rigorous and covers several different situations. These situations which are handled conventionally by the same exception handling should be handled differently for cost saving. Therefore, we divide the conventional inconsistency into weak consistency,weak inconsistency and strong inconsistency and treat the conventional consistency as strong consistency. Correspondingly, we discuss how to verify them. Especially, for the weak consistency, we present a method on how to adjust it to the strong consistency. For the weak inconsistency, we analyse why it can be handled by simpler and more economical exception handling. The final comparison and discussion further demonstrate that our research can achieve better cost effectiveness than the conventional work.