The effects of constructed bivariate copulas on multivariate control charts effectiveness

The average control chart monitors the shifts in the process. The familiar multivariate control charts are used to detect the mean vector of the process such as multivariate cumulative sum (MCUSUM) and Hotelling's T² control charts. In this paper, the effects of constructing bivariate copulas on multivariate control charts, that is, MCUSUM and Hotelling's T² control charts are intensively investigated when observations are drawn from the exponential distribution. Moreover, the dependence levels of observations are classified to be weak, moderate, and strong in both positive and negative values by Kendall's tau. The numerical results were obtained by Monte Carlo simulation to explore the average run length (ARL). The simulation results show that the performance of Hotelling's T² control chart is superior to the MCUSUM control chart for all shifts in the mean vector of process. Furthermore, from applying the presented control chart to two sets of real data, data set of the strength of 1.5 cm glass fibers measured at the National Physical Laboratory, England and data set of the strength of glass of the aircraft window, it was found that for a small shift ($\delta \le 0.1$), the MCUSUM control chart is better than Hotelling's T² control chart.     

A model to develop biological probes from microflora to assure traceability of tilapia

The bacterial community of Suranaree University of Technology (SUT) tilapia was studied with the aim to develop a model for traceable biological markers. Five fish per time were collected from SUT farm and other sources. Total viable counts (TVC) of bacteria from SUT farm were quite similar in all seasons. Seventy three percent of the bacteria were Gram-negative. Total DNA extracted from the fish gills and intestines were used as template to amplify bacterial 16S rDNA V3 region using GC clamp primer to identify specific bacteria of fish origin by PCR-DGGE technique. The results showed 3 DNA bands on DGGE gel that were specific to only bacterial DNA of SUT tilapia when compared to the other sources. The 3 DNA bands were sequenced and identified as uncultured bacteria of different species. Primers were designed from the 3 specific sequences and used to amplify DNA samples from four sources and some pure cultured bacteria. The results indicated that, only one primer pair can amplify DNA samples from SUT farm but not other samples. This primer pair can be used to identify and trace samples from SUT farm. This method can be used as a model to develop bacterial primer specific location for other food products.     

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.