23,646 research outputs found
Finite-Size Effects on Return Interval Distributions for Weakest-Link-Scaling Systems
The Weibull distribution is a commonly used model for the strength of brittle
materials and earthquake return intervals. Deviations from Weibull scaling,
however, have been observed in earthquake return intervals and in the fracture
strength of quasi-brittle materials. We investigate weakest-link scaling in
finite-size systems and deviations of empirical return interval distributions
from the Weibull distribution function. We use the ansatz that the survival
probability function of a system with complex interactions among its units can
be expressed as the product of the survival probability functions for an
ensemble of representative volume elements (RVEs). We show that if the system
comprises a finite number of RVEs, it obeys the -Weibull distribution.
We conduct statistical analysis of experimental data and simulations that show
good agreement with the -Weibull distribution. We show the following:
(1) The weakest-link theory for finite-size systems involves the
-Weibull distribution. (2) The power-law decline of the
-Weibull upper tail can explain deviations from the Weibull scaling
observed in return interval data. (3) The hazard rate function of the
-Weibull distribution decreases linearly after a waiting time , where is the Weibull modulus and is the system size
in terms of representative volume elements. (4) The -Weibull provides
competitive fits to the return interval distributions of seismic data and of
avalanches in a fiber bundle model. In conclusion, using theoretical and
statistical analysis of real and simulated data, we show that the
-Weibull distribution is a useful model for extreme-event return
intervals in finite-size systems.Comment: 33 pages, 11 figure
Reliability analysis of structural ceramic components using a three-parameter Weibull distribution
Described here are nonlinear regression estimators for the three-Weibull distribution. Issues relating to the bias and invariance associated with these estimators are examined numerically using Monte Carlo simulation methods. The estimators were used to extract parameters from sintered silicon nitride failure data. A reliability analysis was performed on a turbopump blade utilizing the three-parameter Weibull distribution and the estimates from the sintered silicon nitride data
Beta-Weibull Distribution: Some Properties and Applications to Censored Data
Some properties of a four-parameter beta-Weibull distribution are discussed. The beta-Weibull distribution is shown to have bathtub, unimodal, increasing, and decreasing hazard functions. The distribution is applied to censored data sets on bus-motor failures and a censored data set on head-and-neck-cancer clinical trial. A simulation is conducted to compare the beta-Weibull distribution with the exponentiated Weibull distribution
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