<s>[INST] This problem was reported in [22] for a production facility where linear trajectory was tracked (forced) before an impending failure occurred. Our system actually contains three modes: pre-failure (1), impending failure (2), and post-failure (3). We can model each of the three situations by a second-order AR model. These AR parameters are different for each situation. Intuitively, if the variation of the system response to the impending failure is regarded as residuals, we can track this impending failure by observing and monitoring its residuals.[/INST]