The present day systems are increasing in complexity in terms of both the size and functionality. Also society demands these systems to be ultra-reliable. Reliability evaluation and optimization techniques play a major role in these regards. However reliability evaluation & optimization techniques do not give any idea about maintenance, risk involved and related cost incurred and criticality of system components or subsystems. Important measures (IM) exist in literature that identify the weak components i.e critical components and give ranking to them. Recently some work has appeared on Cost Importance Measure (CIM). There are number of mistakes/short comings in the paper Cost-related importance measure by Ming et.al. Definition of CIM given in general and the same used for computation of CIM of component xi have appeared differently (Different definitions for CIM). PD(xi),Partial derivative of component xi obtained for most of the components are either inexact or are faulty in expression and computations are wrong. All other mistakes also have not only been pointed but have been corrected also. A New CIM (NCIM) proposed, which highlights the above issues and have done desired calculations. The new CIM which has been advanced is computationally simpler and yields the desired ranking of components.