Rubber lifetime prediction for ADT data considering non-arrhenius behavior

Abstract

In reliability engineering, accelerated degradation test (ADT) has been widely used to obtain adequate data within a reasonable period of time. All test units are exposed on higher-than-usual stress levels so that extrapolation is needed to predict actual performance in normal condition. When the accelerated stress is temperature, the commonly used extrapolation methods are based on linear Arrhenius model which has been proved inadequacy over a wide range of temperatures in recent literatures. Therefore this paper focuses on the non-Arrhenius model due to two competing processes which is consistent with our experience that there were two competitive reactions, cross-link or degradation during the aging of rubber. Motivated by a rubber degradation data, we introduce a lifetime prediction method for ADT data taking non-Arrhenius behavior into consideration, and the lifetime distribution of the rubber under normal condition is obtained. Then the validity of non-Arrhenius ADT model is illustrated based on the rubber data and the result indicates a good fit for the degradation data. Finally, we investigate the effects of model misspecification. The results reveal that in normal condition the p-quantile under an incorrect model is overestimated. Meanwhile, the effect resulted by incorrect acceleration model on degradation model parameter is quite severe under temperatures higher than 120o C or lower than 50o C. Moreover, there are still some points should be emphasize: (1) The non-Arrhenius behavior is discovered in a part of polymers, but it doesn't mean the phenomenon is inevitable. In addition, this behavior manifests in a relatively wide range of temperatures, so the non-Arrhenius model is not suitable for tests conducted over a small temperature region. (2) The degradation path model used in this paper can be extended to similar degradation path models as well as stochastic process models according to the practical requirement. (3) In this paper, we concluded that the non-Arrhenius ADT model considering two competing processes fits better for the degradation paths through statistical method. This conclusion should be further demonstrated by degradation mechanism analysis. (4) There are various non-Arrhenius models, such as the quadratic Arrhenius model [15]. Consequently, a procedure discriminating among different non-Arrhenius models will be very useful for further research