Failure modes and effects analysis (FMEA) is a popular reliability tool in petroleum engineering. In FMEA, potential failure modes or corrective actions are evaluated, each assigned a Risk Priority Number (RPN) score, and prioritized for decision making. FMEA is also known as Failure Modes, Effects, and Criticality Analysis (FMECA), while focuses on failure modes prioritization. Despite of the popularity of FMEA and FMECA, it is not clear, how potential failure modes and corrective actions could be represented systematically, for effective decision making. In this paper, two new representations (i.e., a tree representation and a vector representation), for potential failure modes and corrective actions, are proposed. The tree representation for a potential failure mode allows its root cause(s), effect(s) and corrective action(s), together with their severity, occurrence and detection rating(s), to be represented as a three-layer tree model. The tree representation for a corrective action with similar contents is outlined too. The RPN model, together with its score, is represented as a node of the tree model. These tree models can also be represented as their associated equivalence layered-vector representations. In this paper, the usefulness of the proposed approaches is illustrated with benchmark FMEA worksheets pertaining to petroleum engineering.