Mean Residual Life (MRL) of Gnedenko-Weibull Distribution. Estimates of Residual Life Time of Submersible Pump Equipment

The Asymptotics of Moments for the Remaining Time of Heavy-Tail Distributions

“…The physical application of the MRL to the reliability of the "well-pump" system has been reported in [2].…”

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

“…Typical distributions that describe the service life of aging equipment are, for example, the Weibull-Gnedenko distributions and the gamma distribution. If the lifetime of pump submersible equipment [1] lasts long and is modeled by the Weibull-Gnedenko distribution, then it behaves asymptotically as if not ageing. A natural question arises about the set of equipment's lifetime distributions such that the normalized residual lifetime distributions asymptotically have the property of being memoryless.…”

“…1 e −t dt is the lower incomplete gamma function, and Γ(•) denotes complete gamma function. The generalized gamma distribution is extremely useful for parametric models in survival analysis.…”