Measurement models need to properly delineate the real aspect of examinees' response processes for measurement accuracy purposes. To avoid invalid inferences, fit of examinees' response data to the model is studied through "person-fit" statistics. Misfit between the examinee response data and measurement model may be due to invalid models and/or examinee's aberrant response behavior such as cheating, creative responding, and random responding. Hierarchy consistency index (HCI) was introduced as a person-fit statistics to assess classification reliability of particular cognitive diagnosis models. This study examines the HCI in terms of its usefulness under nonhierarchical attribute conditions and under different item types. Moreover, current form of HCI formulation only considers the information based on correct answers only. We argue and demonstrate that more information could be obtained by incorporating the information that may be obtained from incorrect responses. Therefore, this study considers the full-version of the HCI (i.e., FHCI). Results indicate that current form of HCI is sensitive to misfitting item types (i.e., basic or more complex) and examinee attribute patterns. In other words, HCI is affected by the attribute pattern an examinee has as well as by the item s/he aberrantly responded. Yet, FHCI is not severely affected by item types under any examinee attribute pattern.