The Domain of Residual Lifetime Attraction for the Classical Distributions of the Reliability Theory

Abstract

The asymptotic behavior of the residual lifetime of the system and its characteristics are studied for the main distributions of reliability theory. Sufficiently precise and simple conditions for the domain of attraction of the exponential distribution are proposed, which are applicable for a wide class of distributions. This approach allows us to take into account important information about modeling the failure-free operation of equipment that has worked reliably for a long time. An analysis of the domain of attraction for popular distributions with “heavy tails” is given.

Keywords

• Weibull–Gnedenko distribution
• residual lifetime
• domain of attraction
• GG distribution
• log-normal distribution
• Burr distribution