Description:

To discuss some recent advances in Survival or Reliability modeling under the new tendency of innovation and transfer of technology in finance, medicine and industry.

Organizer: Vera L. D. Tomazella, Universidade Federal de São Carlos, Brazil

Speakers:

Title:

Zero-inflated cure rate regression models for lifetime data

Abstract:

Cure rate survival models are widely used in practice, where certain individuals are not susceptible to the occurrence of the event of interest. We extend the cure rate survival models by incorporating excess of zeros in the modeling, the so-called zero-inflated cure rate regression survival models, providing a new general class of survival models with a strong practical appeal. In obstetrical studies, an issue that should be considered in the modeling is the inclusion of women for whom the duration of labor cannot be observed due to fetal death. In banking loans, it is observed the propensity to fraud in lending loans in the presence of straight-to-default customers that never pay their loans. In both cases, generating a proportion of lifetimes equal to zero. Maximum likelihood and Bayesian estimation procedures reach parameter estimation. A comprehensive simulation study is carried out to assess the performance of the estimation procedure. Our modeling is illustrated on real datasets. This work is co-authored by Gleici da Silva Castro Perodoná, Mauro Ribeiro de Oliveira and Hayala Cristina Cavenague de Souza, Pedro Luis Ramos.

Title:

Efficient closed-form MAP estimators for some survival distributions

Abstract:

Nakagami-type distributions play an important role in communication engineering problems, particularly to model fading of radio signals. A maximum a posteriori (MAP) estimator for the Nakagami-type fading parameter is proposed. The MAP estimator has a simple closed-form expression and can be rewritten as a bias-corrected generalized moment estimator. Numerical results demonstrate that the MAP estimation scheme outperforms the existing estimation procedures and produces almost unbiased estimates for the fading parameter even for small sample size. In the second stage of the presentation, we show that the obtained results can be extended to other probability distributions, such as the gamma and Wilson-Hilferty. The potentiality of our proposed methodology is illustrated in a real reliability data set.

Title:

Bayesian study of metallic fatigue behavior considering space Poisson processes

Abstract:

Predicting fatigue in mechanical components is extremely important for preventing hazardous situations. In this work with Babuška, Sawlan, Szabó, and Tempone, we introduce a stochastic model to estimate the survival-probability function of notched and unnotched metallic specimens of 75S-T6 aluminum alloys under high cycle uniaxial fatigue experiments.
The stochastic model is based on spatial Poisson processes with intensity function that combines stress-life (S-N) curves with an averaged effective stress function. The rate function of the process is suitably scaled by a parameterized highly stressed volume. The resulting model is independent of the shape of the specimen and can fit fatigue data from both notched and unnotched specimens.
We analyze the performance of the proposed model via a Bayesian framework by comparing the posterior estimates of pooled data sets with the reference maximum likelihood estimate of each data set. Finally, cross-validation analysis is performed to predict the life of specimens with geometries not considered in the calibration stage.