Definition
Reliability is the probability that a component or system performs its intended function without failure for a specified period under specified conditions. Reliability engineering uses probability distributions — exponential, Weibull, log-normal — to model lifetimes, predict failure rates, and design systems that survive long enough to meet operational requirements.
The hazard rate (instantaneous failure rate) and the survival function (probability of surviving past time t) are the two key descriptions of any reliability model.
Why it matters
How it works
The exponential distribution, with its constant hazard rate, models 'memoryless' components — light bulbs, electronic parts in their useful life. The Weibull extends the model to time-varying hazard rates. For a system, the reliability is computed by combining component reliabilities according to the system structure: components in series multiply (chain is as strong as its weakest link), components in parallel use complement rules (1 - product of failure probabilities).
A simple example: two parallel components each with 90% reliability give system reliability 1 - (0.1 × 0.1) = 99%. That single fact — that redundancy dramatically boosts reliability — drives the architecture of safety-critical systems.