Confidence intervals for point-of-stabilization of content uniformity

Within the framework of continuous pharmaceutical manufacturing, we are interested in statistical modeling of the initial behavior of the production line. Assuming a gradually changing sequence of a suitable product quality characteristic (e.g., the content uniformity), we estimate the so-called point-of-stabilization (PoSt) and construct corresponding confidence regions based on appropriate asymptotic distributions and bootstrap. We investigate linear, quadratic, and nonlinear gradual change models both in homoscedastic and heteroscedastic setup. We propose a new nonlinear E_max gradual change model and show that it is applicable even if the true model is linear. Asymptotic distribution of the PoSt estimator is known only in a homoscedastic linear and quadratic model and, therefore, bootstrap approximations are used to construct one-sided PoSt confidence intervals.