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This work develops a statistical framework to estimate stabilization time for core tablet batches produced by continuous roller compaction. Using simulated data from multiple production runs of a representative product, the project focuses on characterizing concentration stability during start-up and identifying an optimal start-up duration to guarantee product quality and consistency. The current approach employs a two-component segmented linear model (broken-stick) implemented via the gslnls package in R to separate a transient phase of rapid concentration change from a subsequent stable phase. Although this model captures overall process behavior, practical application has revealed limitations: stabilization-time estimates and their confidence intervals are sometimes unacceptably large, reducing interpretability for operational decision-making. These issues likely arise from sparse transient-phase sampling, within-batch variability, and model inflexibility for complex dynamics. To address these shortcomings, alternative techniques will be investigated with a focus on robustness and precision of estimated change times.
The two-component linear (broken stick) model is given as:
$$Y_i = \beta_1 + \beta_2\left(\left(1 - \frac{1}{1+\exp(-\gamma (time_i - \tau))}\right)\,time_i + \left(\frac{1}{1+\exp(-\gamma (time_i - \tau))}\right)\,\tau \right) + \epsilon_i$$ Where: $Y_i$ is the concentration at time i $\gamma$ is the numeric smoothness of transition between linear model components. Higher value gives a sharper changepoint. $\beta_1$, $\beta_2$, $\tau$ are the parameters of the model which defines the components of interest (see below), $\epsilon_i\sim N(0,\sigma^2)$ is the residual error with $\sigma^2$ variance.
| Classification | Mainly application |
|---|---|
| Keywords | stabilization, broken-stick model, continuous manufacturing |