Luan Jaupi

Multivariate Control Charts for Complex Processes

This paper deals with multivariate control problems and the use of influence function is proposed to distinguish between chance and special causes of variation. The influence function of mean is proposed to monitor the process mean. To investigate process variability, the control charts based on the influence functions of eigenvalues are suggested. Finally, in order to describe process orientation, control charts based on the influence functions of eigenvectors are employed. A real application illustrating the proposed control charts is presented.

Multivariate Process Control Through the Means of Influence Functions

A diversity of multivariate control charts for the process mean and dispersion have been proposed recently to distinguish between random and assignable causes of process variability. This paper deals with the same problem and the use of influence function is proposed to distinguish between chance and special causes of process variability. When the process has reached a state of statistical control, the process mean and the structure of dispersion matrix should be stable over time. The effect of observations or subgroups on these parameters may be evaluated, among others, by the means of influence functions. Hence, special causes of variation could be identified by an unusual influence of observations or subgroups on the process mean and/or dispersion parameters.

Different approaches for the texture classification of a remote sensing image bank

In this paper, we summarize and compare two different approaches used by the authors, to classify different natural textures. The first approach, which is simple and inexpensive in computing time, uses a data bank image and an expert system able to classify different textures from a number of rules established by discipline specialists. The second method uses the same database and a neural networks approach.

Application and Generation of the Univariate Skew Normal Random Variable

In this paper, for the generating the Skew normal random variables, we propose a new method based on the combination of minimum and maximum of two independent normal random variables. The estimation of parameters using the maximum likelihood estimation and the methods of moments estimation method. A real data set has been considered to illustrate the practical utility of the paper.

Various uses of statistical tools for texture analysis

The tools developed by the School of geostatistical have many applications for image segmentation . First, it is very suited to the analysis of natural images eg from remote sensing images and medical images. secondly, they are less expensive in time calculation, as can the methods, from Fourier analysis or matrices coocurrences. We offer reviews of various works of authors to segment natural textures.

Modeling synthetic radar image from a digital terrain model

In this paper we propose to simulate SAR radar images that can be acquired by aircraft or satellite. This corresponds to a real problematic, in fact, an airborne radar data acquisition campaign, was conducted in the south east of France. We want to estimate the geometric deformations that a digital terrain model can be subjected. By extrapolation, this construction should also allow to understand the image distortion if a plane is replaced by a satellite. This manipulation allow to judge the relevance of a space mission to quantify geological and geomorphological data. The radar wave is an electromagnetic wave, they have the advantage of overcoming atmospheric conditions since more wavelength is large is better crossing the cloud layer. Therefore imaging radar provides continuous monitoring.

Construction of Radar SAR Images from Digital Terrain Model and Geometric Corrections

We propose in this paper an original method to correct the geometric distortions of a radar image. The comparison of satellite data, reveals specific problems. Data can be noisy, but especially the geometry of their acquisition requires corrections for comparaisons between them. In this paper we show how highly deformed radar images can be geometrically corrected and compared to map data coming from digital terrain models and also with data coming from SPOT satellite. Radar images used, are from the sensor airborne radar Varan, which is used for data acquisition campaign in the South-East of France. Applications include both structural geology, land cover or study of coastline. We propose a solution to rectify radar image in the geometry of a numerical terrain model. The method adopted here, is to produce a synthesis radar image by encoding all flight parameters of aircraft or satellite from a digital terrain model; radar image can then be compared to the synthetic image because points of landmarks can be clearly identified. Finally, we obtain a correspondence between the points of real radar image distorted, and those in the land or map.

Variable Selection Methods for Process Monitoring

In the first stage of a manufacturing process a large number of variables might be available. Then, a smaller number of measurements should be selected for process monitoring. At this point in time, variable selection methods for process monitoring have focused mainly on explained variance performance criteria. However, explained variance efficiency is a minimal notion of optimality and it does not necessarily result in an economically desirable selected subset, as it makes no statement about the measurement cost or other engineering criteria. Without measuring cost many decisions will be impossible to make. In this article, we propose two new methods to select a reduced number of relevant variables for multivariate statistical process control that makes use of engineering, cost and variability evaluation criteria. In the first method we assume that a two-class system is used to classify the variables as primary and secondary based on different criteria. Then a double reduction of dimensionality is applied to select relevant primary variables that represent well the whole set of variables. In the second methodology a cost-utility analysis is used to compare different variable subsets that may be used for process monitoring. The objective of carrying out a cost–utility analysis is to compare one use of resources with other possible uses. To do this, to any process monitoring procedure is assigned a score calculated as ratio of the cost at which it might be obtained to explained variance that it might provide. The subset of relevant variables is selected in a manner that retains, to some extent, the structure and information carried by the full set of original variables.

Automatic segmentation of textures on a database of remote-sensing images and classification by neural network

Analysis and automatic segmentation of texture is always a delicate problem. Objectively, one can opt, quite naturally, for a statistical approach. Based on higher moments, these technics are very reliable and accurate but expensive experimentally. We propose in this paper, a well-proven approach for texture analysis in remote sensing, based on geostatistics. The labeling of different textures like ice, clouds, water and forest on a sample test image is learned by a neural network. The texture parameters are extracted from the shape of the autocorrelation function, calculated on the appropriate window sizes for the optimal characterization of textures. A mathematical model from fractal geometry is particularly well suited to characterize the cloud texture. It provides a very fine segmentation between the texture and the cloud from the ice. The geostatistical parameters are entered as a vector characterize by textures. A neural network and a robust multilayer are then asked to rank all the images in the database from a learning set correctly selected. In the design phase, several alternatives were considered and it turns out that a network with three layers is very suitable for the proposed classification. Therefore it contains a layer of input neurons, an intermediate layer and a layer of output. With the coming of the learning phase the results of the classifications are very good. This approach can bring precious geographic information system. such as the exploitation of the cloud texture (or disposal) if we want to focus on other thematic deforestation, changes in the ice ...

Control Charts for Multivariate Processes Based on Influence Functions

Every product possesses a number of elements that jointly describes its fitness for use. These parameters are called quality characteristics and generally p quality characteristics are necessary for an adequate description of each item quality. Because of the inherent variability of a process, these quality characteristics are random variables. There are many causes of variability, but in statistical process control is useful to think of variability as arising from two sources. First, there are random causes and second there are assignables causes. When assignable causes are present in a multivariate process they may affect different process parameters: the process mean, and/or orientation and/or variability. Special causes that affect one of these parameters do not necessarily effect the others. Therefore control charts for different situations are necessary. This paper deals with on-line methods for quality improvement where the influence function is used to build up control charts to monitor process variability and orientation. Our aim is to quickly detect the time when special causes are present in a manufacturing process, so investigation of the process and corrective actions may be undertaken before very many noconforming units are produced. Our idea is, that subgroups taken when special causes are present in the process, tend to have an unduly large influence on process parameter estimators. Therefore the influence function can be used to tailor control charts for different parameters. In section 2 we derive the influence measures to monitor process dispersion and orientation. Shewhart control charts for process variability and process orientation are given in section 3. In section 4 we give a numerical example to illustrate our control charts.