4 Chapter 1. Introduction As mentioned earlier, this dissertation focuses on relevant aspects within PHM. Figure 1.2 highlights that Reliability Modelling is mainly associated with Stages 1 and 2; Markov Process-based Prognostics with Stage 4, and Maintenance Optimisation with Stage 5. 1.2.2 Reliability Modelling Reliability is the “ability to perform as required, without failure, for a given time interval, under given conditions” (IEC 60050:192-01-24), where “failure is the loss of the ability to perform as required” (IEC 60050:192-03-01). Reliability modelling is the process of developing mathematical models that encapsulate reliability functions and dependencies within a system. The former quantifies the probability that a system or component will perform without failure over a specified period under defined conditions. The latter details the interactions between components that influence the overall system reliability (Assaf, 2018). Reliability modelling provides stochastic-based outcomes (e.g., probabilities) useful for reliability assessment to enhance a system’s lifespan, scheduling maintenance appropriately, and reducing the risk of failures (O’Connor and Kleyner, 2012). The application of reliability modelling spans various industries such as nuclear, aerospace, automotive, electronics, and manufacturing, where reliability is a critical factor (Modarres, Kaminskiy, and Krivtsov, 2016). Reliability (t) Bearing age (t) Failure Reliability over time Nominal behaviour Figure 1.3: Reliability function of a bearing (example). Figure 1.3 exemplifies the reliability function of a bearing as a function of its age. Initially, a new bearing has high reliability, representing nominal behaviour. As the bearing ages and wear occurs, reliability decreases due to the e!ects of deterioration. This means that the older (or more used) the bearing is, the less likely it is to perform nominally. Alternatively, the older the bearing is, the more likely it is to fail. Several models and methods are used in reliability modelling. Statistical-based reliability models, which can be based on Exponential, Weibull, and Log-normal distributions, utilise historical failure data to estimate the probability of failure. Nelson, 2005 provides a comprehensive guide on how these models are used to understand di!erent failure rates and patterns.
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