Beyond SPC: a nonlinear state-space model for explainable prediction of linac output drift

Long-term output drift in linear accelerators arises primarily from gradual aging of the monitor chamber. Current QA practice relies on fixed calibration schedules or corrective actions after tolerance breaches, without exploiting the predictive information contained in daily QA records. This work develops and validates a nonlinear, physically interpretable state-space model of chamber sensitivity to enable proactive forecasting of calibration-threshold exceedance.

Monitor-chamber sensitivity was modelled as a first-order relaxation process driven by cumulative delivered monitor units (MU). The latent sensitivity and its long-term parameters were estimated using an Extended Kalman Filter (EKF) in square-root form, with noise covariances tuned through a physics-guided and data-driven strategy. To account for structural uncertainty in (a₀,λ₀), a bank of 36 EKF instances was generated. Forecasting performance was evaluated by predicting the MU at which the output deviation crossed thresholds of 2-8%, for horizons ranging from 60 to 4 working days before the true event.

The EKF accurately reconstructed the exponential sensitivity decay and produced stable parameter estimates with contracting covariance. Forecast accuracy improved monotonically as the horizon shortened. At 55-60 working days (∼11-12 weeks), the mean absolute error (MAE) was 7-9 days; between 25 and 40 days (∼5-8 weeks), the MAE decreased to 3-4 days. For horizons < 15 days, predictions were highly reliable, with MAE < 2 days.

The proposed framework provides an explainable, uncertainty-aware method for anticipating calibration needs several weeks in advance, supporting the transition toward predictive QA and data-driven maintenance planning.