Trend Autoregressive Model Exact Run Length Evaluation on a Two-Sided Extended EWMA Chart

The Extended Exponentially Weighted Moving Average (extended EWMA) control chart is one of the control charts and can be used to quickly detect a small shift. The performance of control charts can be evaluated with the average run length (ARL). Due to the deriving explicit formulas for the ARL on a two-sided extended EWMA control chart for trend autoregressive or trend AR(p) model has not been reported previously. The aim of this study is to derive the explicit formulas for the ARL on a two-sided extended EWMA control chart for the trend AR(p) model as well as the trend AR(1) and trend AR(2) models with exponential white noise. The analytical solution accuracy was obtained with the extended EWMA control chart and was compared to the numerical integral equation (NIE) method. The results show that the ARL obtained by the explicit formula and the NIE method is hardly different, but the explicit formula can help decrease the computational (CPU) time. Furthermore, this is also expanded to comparative performance with the Exponentially Weighted Moving Average (EWMA) control chart. The performance of the extended EWMA control chart is better than the EWMA control chart for all situations, both the trend AR(1) and trend AR(2) models. Finally, the analytical solution of ARL is applied to real-world data in the health field, such as COVID-19 data in the United Kingdom and Sweden, to demonstrate the efficacy of the proposed method.     

Effects of Grafting Maleic Anhydride onto Poly-ɛ-caprolactone on Facilitative Enzymatic Hydrolysis

Plastic waste is a global issue because it causes overflowing landfills and pollution, leading to environmental concerns. To address this crisis, materials that can be decomposed in the natural environment are introduced to replace conventional plastics. Poly-ɛ-caprolactone (PCL) is a commonly used plastic that can degrade in natural environments. However, owing to its hydrophobicity, its natural decomposition rate is low. In this study, PCL is modified with maleic anhydride (MA) (PCL-g-MA) to increase hydrophilicity and amorphous region for faster decomposition. To assess the hydrolysis in seawater, lipase hydrolysis is performed to compare the decomposition of PCL-g-MA and PCL. Consequently, in a Pseudomonas lipase-containing PBS solution, it takes 72 and 120 h for complete hydrolyze of PCL-g-MA and PCL, respectively. MA grafted onto PCL increases the amorphous region, where lipase can easily diffuse into PCL-g-MA. Morphological (FESEM and POM images), thermal (TGA and DSC), and structural (FTIR, XRD, and XPS) analyzes support the hydrolysis reaction. The mechanisms proposed in this study confirm that lipase hydrolysis starts in the amorphous regions and then transfers to the crystal regions. This hydrolysis progress is expected to facilitate the creation of eco-friendly low-cost PCL-g-MA composites with high-rate hydrolysis, such as bio-plastics and bio-fibers.