timetofailure

Time to failure, also known as time-to-failure (TTF), is a reliability metric that measures the duration of operation or exposure until a component or system fails under specified conditions. TTF is treated as a random variable and is described by a probability distribution that captures variability in failure times caused by wear, defects, and environmental factors. For non-repairable items, the expected TTF is referred to as the mean time to failure (MTTF).

Common models for TTF include the exponential, Weibull, and lognormal distributions. The Weibull distribution is especially versatile for modeling aging and wear, as its hazard function can increase, decrease, or remain constant over time. The exponential model assumes a constant hazard. Analysts use the survival function S(t) = P(T > t) and the hazard function h(t) to summarize reliability over time. In repairable systems, mean time between failures (MTBF) is often used instead of MTTF, since systems are restored after each failure.

Data for TTF analysis come from life testing, field failure records, or accelerated life testing (ALT), where stress is increased to induce failures more quickly. Censored data—records where failure has not yet occurred—are common. Methods include maximum likelihood estimation, survival analysis, and plotting techniques such as the Weibull plot. Modern approaches may combine Bayesian inference with prior information.

Applications of TTF analysis span electronics, automotive, mechanical components, and consumer products. It informs design improvements, maintenance planning, warranty management, and risk assessment. Limitations include sensitivity to operating conditions, sample representativeness, and extrapolation beyond tested environments.