Green hydrogen represents a promising solution for renewable energy application and carbon footprint reduction. However, its production through renewable energy powered water electrolysis is hindered by significant cost, arising from repair, maintenance, and economic losses due to unexpected downtimes. Although reliability engineering is highly effective in addressing such issues, there is limited research on its application in the hydrogen field. To present the state-of-the-art research, this study aims to explore the potential of reducing these events through reliability engineering, a widely adopted approach in various industries. For this purpose, it examines past accidents occurred in water electrolysis plants from the hydrogen incident and accident database (HIAD 2.1). Besides, a literature review is performed to analyze the state-of-the-art application of reliability engineering techniques, such as failure analysis, reliability assessment, and reliability-centered maintenance, in the hydrogen sector and similar industries. The study highlights the contributions and potentials of reliability engineering for efficient and stable green hydrogen production, while also discussing the gaps in applying this approach. The unique challenges posed by hydrogen's physical properties and innovative technologies in water electrolysis plants necessitate advancement and specialized approaches for reliability engineering.