Vytautas Kazakevičius

Statistical analysis of linear degradation and failure time data with multiple failure modes.

The paper considers linear degradation and failure time models with multiple failure modes. Dependence of traumatic failure intensities on the degradation level are included into the models. Estimators of traumatic event cumulative intensities, and of various reliability characteristics are proposed. Prediction of residual reliability characteristics given a degradation value at a given moment is discussed. Non-parametric, semiparametric and parametric estimation methods are given. Theorems on simultaneous asymptotic distribution of random functions characterising degradation and intensities of traumatic events are proposed. Asymptotic properties of unconditional and residual reliability characteristics estimators are given. Real tire wear and failure time data are analysed.

ON STATIONARITY IN THE ARCH([infty infinity]) MODEL

We continue investigation of the ARCH(∞) model begun in Giraitis, Kokoszka, and Leipus (2000, Econometric Theory 16, 3–22). Nonrestrictive conditions for the existence of a strictly stationary solution are established. The paper generalizes the results of Nelson (1990, Econometric Theory 6, 318–334) and Bougerol and Picard (1992, Journal of Econometrics 52, 115–127) to the ARCH(∞) model.

Stability of random coefficient ARCH models and aggregation schemes

In this paper, we consider ARCH(∞) models with nonnegative random coefficients. Necessary and sufficient conditions for the existence of first and second moments are established. The ARCH models with deterministic coefficients are shown to be always short memory processes. The effect of small perturbations of the parameters is investigated. The results obtained are applied to some aggregation schemes.

Nonparametric Confidence Intervals for the Number of Spares Required for a Renewable System

ABSTRACT Nonparametric estimators of the minimal number of reserved units from non renewable reliability data are given. Cases of stationary and non stationary renewal processes are considered. Numerical methods of estimator computing are proposed. Asymptotic confidence intervals are given. Real tire failure time data are analyzed.