Degradation analysis method based on regression time series model under equal and unequal variances

A degradation analysis method based on regression time series model is presented. The degradation path expressed by the linear, exponential and power laws are discussed in detail, respectively. For linear path, a linear regression-autoregression model under equal variances is given. And for exponential and power path, a heteroscedastic quasi-linear regression-autoregression model is established, since the path linearization leads the random errors with unequal variances. During the quasi-linearization of exponential and power path, an approximate process based on Taylor expansion is presented to obtain the error variance function over time. For the above regression-autoregression models, both conditional and exact maximum likelihood method of model parameters are discussed, particularly for simple and practical first-order models. After model parameter estimate, the failure probability is forecasted for the given threshold value. In these methods, regression can grasp the degradation trend in long term which is the main part of the degradation process, and time series can model the residual part that cannot be fully explained by the independent variables in regression and that is caused by pure randomicity. As regression and time series respectively have forecast precision advantage respectively in long and short term, the presented method is helpful to make good decision in PHM of products.