The number of smart devices connected to the Internet has been constantly increasing, and as a result, lightweight cryptography (LWC) has become more important in the past decade. The Lightweight Cryptography (LWC) Project is an initiative taken by the National Institute of Standards and Technology (NIST) to standardize such LWC algorithms. Grain128-AEAD, which was submitted to the NIST LWC project, is an encryption algorithm that provides both confidentiality and integrity assurance. Third-party security analysis of the submitted ciphers is an important aspect of the evaluation of the submission to the NIST LWC project. Although several pieces of existing research, such as the bit-flipping attack, random fault attack, and deterministic random fault attack, have examined the security of Grain128-AEAD, there is still room for improvement in the fault attack models of these studies. This work aims to fill this research gap by analyzing the security margin of Grain128-AEAD against a series of improved differential fault attacks. In this study, we developed a probabilistic random fault attack and applied it to Grain128-AEAD. As an improvement of the existing research, a probabilistic approach can be applied to a more relaxed moderate control attack model. The existing moderate control model assumes the fault to be injected within any bit of a given byte, whereas the faults in our improved approach can be injected within any bits of a two-byte/four-byte segment, thereby relaxing the fault precision. The results indicate that the improved moderate control requires 388 keystreams for the two-byte model and 279 for the four-byte model to identify the target fault locations for implementing a state recovery attack. The relaxed fault attack models presented in this work are more practical to implement; hence, the findings of this research have improved the existing studies and narrowed the current research gap on the fault attack models of Grain128-AEAD. % To maintain consistency in terminology, "Grain-128AEAD" has been revised to "Grain128-AEAD" in both the abstract and the main text. Please confirm this revision.