Reliability

Reliability is the probability that a system or component will perform its required function under stated conditions for a specified period of time, without failure. It applies to hardware, software, and human-involved processes and is a key consideration in design, production, and operation.

Core concepts include the reliability function R(t) = P(T > t), where T is the time to failure, and the hazard rate λ(t). In simple models, constant failure rate yields exponential reliability R(t) = e^{-λ t}. Real systems are often described by distributions such as the Weibull, which can capture early failures, steady operation, and wear-out. The bathtub curve summarizes these life phases. Average measures include mean time between failures (MTBF) and, for serviceable systems, repair time MTTR, with availability A = MTBF / (MTBF + MTTR) in steady state.

Applications and tools include reliability prediction, accelerated life testing, life data analysis, reliability block diagrams, and fault trees. These support design decisions, testing programs, and maintenance planning. Reliability engineering emphasizes design-for-reliability, component quality, redundancy, fault tolerance, and robust software engineering practices to reduce failure probability.

Maintenance and policy approaches such as reliability-centered maintenance (RCM) use reliability information to determine appropriate inspection, repair, or replacement actions. Reliability is a component of overall quality and is distinct from, but related to, durability and maintainability. It guides product development, risk assessment, and resource allocation across industries.