The effectiveness of Max-half-Mchart over Max-Mchart in simultaneously monitoring process mean and variability of individual observations

Control charts are widely used in industrial environments for the simultaneous or separate monitoring of the process mean and process variability. The Max-Mchart is a multivariate Shewhart-type simultaneous control chart that is used when monitoring subgroups. While this sampling design allows the computation of the generalized variance (GV) used to calculate the process variability, a GV chart cannot be plotted for individual observations. Hence, we cannot compute the single statistic in the Max-Mchart. This study aims to overcome the aforementioned issue. To this end, first, we develop a new Max-Mchart for individual observations by utilizing the statistic in the dispersion control chart. Second, instead of the standard normal distribution, we propose a new transformation using a half-normal distribution to calculate the statistic for the process mean and process variability. Thus, the proposed chart is called the Max-Half-Mchart, whose control limit is calculated using the bootstrap approach. An evaluation based on the average run length values shows the robustness of the Max-Half-Mchart for the simultaneous monitoring of the process mean and process variability. The single statistic in the Max-Half-Mchart is more consistent with the statistic in Hotelling's T² and the dispersion chart than that of the Max-Mchart.     

An Algorithm to Reduce Compression Ratio in Multimedia Applications

In recent years, it has been evident that internet is the most effective means of transmitting information in the form of documents, photographs, or videos around the world. The purpose of an image compression method is to encode a picture with fewer bits while retaining the decompressed image’s visual quality. During transmission, this massive data necessitates a lot of channel space. In order to overcome this problem, an effective visual compression approach is required to resize this large amount of data. This work is based on lossy image compression and is offered for static color images. The quantization procedure determines the compressed data quality characteristics. The images are converted from RGB to International Commission on Illumination CIE La^*b^*; and YCbCr color spaces before being used. In the transform domain, the color planes are encoded using the proposed quantization matrix. To improve the efficiency and quality of the compressed image, the standard quantization matrix is updated with the respective image block. We used seven discrete orthogonal transforms, including five variations of the Complex Hadamard Transform, Discrete Fourier Transform and Discrete Cosine Transform, as well as thresholding, quantization, de-quantization and inverse discrete orthogonal transforms with CIE La^*b^*; and YCbCr to RGB conversion. Peak to signal noise ratio, signal to noise ratio, picture similarity index and compression ratio are all used to assess the quality of compressed images. With the relevant transforms, the image size and bits per pixel are also explored. Using the (n, n) block of transform, adaptive scanning is used to acquire the best feasible compression ratio. Because of these characteristics, multimedia systems and services have a wide range of possible applications.