• Reliability analysis
• Risk analysis

Industrial plants handling dangerous substances pose substantial risks to the environment and human safety due to potential accidental releases. Accidents within these plants, caused by internal factors like failures and external events, have resulted in catastrophic consequences over the years. Thus, researchers have concentrated on enhancing the safety of various industries, including Oil & Gas, chemical, and petrochemical sectors. Reliability and risk analyses, evaluations, and assessments have emerged as critical components in ensuring the safety of these installations. Estimating the probability and risk associated with undesired events like equipment failures and containment losses is fundamental to implementing effective safety measures. Additionally, Prognostic and Health Management (PHM) technologies, encompassing failure diagnosis and prediction, have gained prominence in maintaining reliable and safe operations while considering economic efficiency. However, as safety requirements and system complexity continue to evolve, traditional reliability and risk methods could be inadequate. Researchers have embarked on developing innovative frameworks to enhance the safety of hazardous plants and installations. Nevertheless, there is still space to propose other frameworks to deal with typical challenges and issues. This work aims to propose a set of frameworks to address common issues that could affect reliability analysis, risk analysis, and failure diagnosis, such as limited information or nonlinear and non-stationary Process Variables (PVs). These frameworks can function independently or be integrated as needed. The developed approaches are applied to critical equipment in hazardous plants, particularly within the Oil & Gas industry. The proposed frameworks could be useful to enhance the safety of critical installations facing similar challenges.