# Performability Evaluation of Autonomous Underwater Vehicles Using Phased Fault Tree Analysis
## 2 Literature Review  
Safety-critical systems (SCSs) have to complete assigned tasks precisely and on schedule. Conventional reliability represents the viability of a task in terms of a binary view. Numerous studies are currently underway to ensure the stable operation of Autonomous Underwater Vehicles (AUVs), which are safety-critical systems [12; 13; 14]. In reliability research, system-level reliability analyses are carried out for preventive maintenance [15], and reliability analyses of individual components are carried out by examining their properties and operating environment [16]. Performance typically describes the system's capabilities under the assumption of a condition free from failures [17]. It is crucial to complete a task in an SCS even in the event of a failure [18]. Even in the event of a partial failure, a fault-tolerant system can still function at a lower level of performance [19]. Consequently, it is possible to assess the likelihood that a system will function at a specific performance level in the event of a breakdown through a performability analysis. The performability refers to the unified performance-dependability measure. It is the probability that a system will operate at a certain level, which corresponds to a predetermined range of achievement levels that represent system performance [20]. Dependability is a measure of the user's degree of trust based on a number of factors, including availability, reliability, security, and safety [21]. Availability and reliability are the two main concepts used in performability analyses. The performability of an SCS can be assessed using a variety of techniques, including analysis techniques, probability-distribution-based methodologies, stochastic modeling, etc. [22]. There are several ways to evaluate the performance and dependability of a system. Among these, performability analyses of stochastic modeling methodologies are easy to conduct. Performability can be analyzed by analytical models using parameter-based formulation, while modeling-based performability approaches make use of the system's structure. The system's intrinsic reliability, failure, MTT, etc., for a system in a normal condition are all used by analytical approaches to assess performability [23]. State-based modeling methods like Petri nets [24; 25; 26], stochastic activity networks (SANs) [27], and Markov chains [28; 29; 30] are used in behavioral probabilistic modeling [31]. The semi-Markov process (SMP) model was used to model the reliability and mean and variation of web service response times [32]. Dependability and performance models were used to simulate an electronic funds transfer system considering failures and repairs, and the performability was evaluated [33]. A continuous-time Markov chain with a Markov reward model was employed to assess the fault-tolerant SCS's performability. The reliability, availability, average failure frequency, and system throughput were used to evaluate the system's performability [29]. The system's performability in terms of availability and dependability was analyzed using Markov and regenerative processes [34]. In order to identify key components, the capabilities of the three pumps were compared and examined. Via sensitivity analyses, parameters that impact system dependability were found. In order to analyze the impact of availability and reliability, a stochastic Petri net model was developed that takes into account the system's hardware and software [35]. Additionally, a performability evaluation technique was proposed that addresses the redundancy issue in fault-tolerant systems. To guarantee the autonomy of a UAV in risky operating scenarios, a framework for modeling and assessing the system's performability was proposed [36]. This framework used hierarchically structured stochastic Petri nets (SPNs) to examine performability and suggested new operating strategies. To represent the architecture for the two-level recovery technique, an extended Markov chain was used.