Multivariate control charts based on Bayesian state space models

This paper develops a new multivariate control charting method for vector autocorrelated and serially correlated processes. The main idea is to propose a Bayesian multivariate local level model, which is a generalization of the Shewhart-Deming model for autocorrelated processes, in order to provide the predictive error distribution of the process and then to apply a univariate modified EWMA control chart to the logarithm of the Bayes' factors of the predictive error density versus the target error density. The resulting chart is proposed as capable to deal with both the non-normality and the autocorrelation structure of the log Bayes' factors. The new control charting scheme is general in application and it has the advantage to control simultaneously not only the process mean vector and the dispersion covariance matrix, but also the entire target distribution of the process. Two examples of London metal exchange data and of production time series data illustrate the capabilities of the new control chart.Comment: 19 pages, 6 figure

Topographic and subterranean structural mapping utilizing aerial magnetic and remote sensing data

The current investigation focuses on conducting surface and subsurface structural mapping of Warana River basin’s Rafin Rewa’s warm spring area and its surroundings utilizing airborne magnetic and topographic datasets. To fulfill this objective, the residual magnetic data underwent reduction to the magnetic pole, and two methods of source edge detection were implemented: the first vertical derivative (FVD) and 3D Euler deconvolution. SRTM data was transformed into hillshade maps employing four distinct solar elevations and a constant azimuth of 450. From the FVD map, discernible structures traversing the study area were delineated, with one significant structure intersecting Rafin Rewa’s warm spring. These delineated FVD structures were superimposed on the Euler solution map with a structural index of one for further structural delineation. The Euler solutions unveiled most major structures trending in the NE-SW and NW-SE directions, with Rafin Ruwa Warm Spring located within an Euler solution cluster, suggesting its shallow-seated structural origin at depths ranging from 200 m to 400 m. Moreover, a surface structure trending NW-SE was observed to intersect Rafin Rewa’s warm spring, potentially representing a subsurface structure reflection. The magnetic structure intersecting with the topographic structure was hypothesized to be responsible for upward fluid migration, leading to the warm spring’s evolution during the Mesozoic era coinciding with the emplacement of Nigeria’s younger granite series. Statistical trend analysis revealed that 38.76% of magnetic structures trended in the NE-SW direction, followed by NNW-SSE at 33.72%, NNE-SSW at 18.22%, and NW-SE at 7.75%. Similarly, surface topographic structural trend analysis indicated that the most predominant trend was NNW-SSE at 38.57%, followed by NW-SE at 34.38%, NNE-SSW at 19.71%, WNW-ESE at 6.38%, and NE-SW at 1.05%

Multivariate Quality Control Chart for Autocorrelated Processes

Traditional multivariate statistical process control (SPC) techniques are based on the assumption that the successive observation vectors are independent. In recent years, due to automation of measurement and data collection systems, a process can be sampled at higher rates, which ultimately leads to autocorrelation. Consequently, when the autocorrelation is present in the data, it can have a serious impact on the performance of classical control charts. This paper considers the problem of monitoring the mean vector of a process in which observations can be modelled as a first-order vector autoregressive VAR (1) process. We propose a control chart called Z-chart which is based on the single step finite intersection test (Timm, 1996). An important feature of the proposed method is that it not only detects an out of control status but also helps in identifying variable(s) responsible for the out of control situation. The proposed method is illustrated with the help of suitable illustrations.Multivariate statistical process control, autocorrelation,