Random coefficient TVARMA model with application to reliability assessment from degradation data

Time-varying autoregressive moving average (TVARMA) model is widely used in non-stationary signal processing such as fault diagnosis, performance test, automatic control and finance analysis, etc. However, the traditional TVARMA model can almost do nothing about multi-sample non-stationary time series in nonergodic condition, In this paper, random coefficient TVARMA models is established by randomizing coefficients of time-varying function, and used for reliability assessment from degradation data. In addition, the sample periodgram and multi-point averaging method is introduced to determine the function form of the time-varying coefficients, and then the integral function of the trend and the variance terms can be synthesized. The approach is an effective way to assess the reliability of highly reliable components and systems with small sample by monitoring performance degradation, as it is the most significant advantage that model building for degradation data is completely independent of degradation paths. Consequently, it can be applicable to a broad class of degradation models. An example of reliability assessment from crack propagation data is given at last, which can illustrate the superiority of the presented methodology.