Profile control chart based on maximum entropy

Monitoring a process over time is so important in manufacturing processes to reduce the wastage of money and time. The purpose of this article is to monitor profile coefficients instead of a process mean. In this paper, two methods are proposed for monitoring the intercept and slope of the simple linear profile, simultaneously. The first one is linear regression, and another one is the maximum entropy principle. A simulation study is applied to compare the two methods in terms of the second type of error and average run length. Finally, two real examples are presented to demonstrate the ability of the proposed chart

New statistical control limits using maximum copula entropy

Statistical quality control methods are noteworthy to produced standard production in manufacturing processes. In this regard, there are many classical manners to control the process. Many of them have a global assumption around distributions of the process data. They are supposed to be normal, which is clear that it is not always valid for all processes. Such control charts made some false decisions that waste funds. So, the main question while working with multivariate data set is how to find the multivariate distribution of the data set, which saves the original dependency between variables. Up to our knowledge, a copula function guarantees the dependence on the result function. But it is not enough when there is no other functional information about the statistical society, and we have just a data set. Therefore, we apply the maximum entropy concept to deal with this situation. In this paper, first of all, we find out the joint distribution of a data set, which is from a manufacturing process that needs to be control while running the production process. Then, we get an elliptical control limit via the maximum copula entropy. In the final step, we represent a practical example using the stated method. Average run lengths are calculated for some means and shifts to show the ability of the maximum copula entropy. In the end, two real data examples are presented

Lithospheric structure beneath NW Iran using regional and teleseismic travel-time tomography

We compute a 2-D tomogram using the P wave arrival time readings from a temporary seismic experiment to study the seismic structure of the crust and upper mantle in NW Iran. The study area includes the western margins of the South Caspian Basin (SCB), and the Sahand and Sabalan post-collisional volcanoes in NW Iran. We invert 2780 regional and teleseismic relative P wave arrival times recorded by 23 stations along the seismic profile extending from the western shoreline of the Caspian Sea to Lake Urumieh. Our tomographic results show a higher-velocity region beneath the SCB. The observed higher velocities strongly correlate with the observed positive gravity anomalies over the southwestern margins of the Caspian Sea, suggesting an oceanic like nature for the SCB lithosphere. The tomographic results also show several lower-velocity anomalies in the crust. The Sabalan volcano is underlain by a low-velocity zone in the lower crust, which is most likely thermal in nature. In the Sahand region, the lower velocities are considerably shallower in depth and might be controlled by shallow sedimentary structures, as well as an anomalously warm upper crust. The shallow low-velocity regions are connected with deeper low-velocity zones 60–100 km deep in the upper mantle. This pattern points to a possible mantle source of post-collisional volcanism in NW Iran, i.e. the melting of a subducted slab