Проверка значимости случайного эффекта для винеровской деградационной модели

Abstract

This paper considers the Wiener degradation model with random effects. Random-effect models take into account the unit-to-unit variability of the degradation index. It is assumed that a random parameter has a truncated normal distribution. During the research, the expression for the maximum likelihood estimates and the reliability function has been obtained. Two statistical tests have been proposed to reveal the existence of random effects in degradation data corresponding to the Wiener degradation model. The first test is a well-known likelihood ratio test, and the second one is based on the variance estimate of the random parameter. These tests have been compared in terms of power with the Monte-Carlo simulation method. The result of the research has shown that the criterion based on the variance estimate of the random parameter is more powerful than the likelihood ratio test in the case of the considered pairs of competing hypotheses. An example of the analysis using the proposed tests for the turbofan engine degradation data has been considered. The data set includes the measurements recorded from 18 sensors for 100 engines. Before constructing the degradation model, the single degradation index has been obtained using the principal component method. The hypothesis of the random effect insignificance in the model has been rejected for both tests. It has been shown that the random-effect Wiener degradation model describes the failure time distribution more accurately than the fixed-effect Wiener degradation model.