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Abstract.The zero-inflated Poisson (ZIP) distribution is used to model count data with an excessive number of zeros. In this article, we present a double generally weighted moving average control chart for monitoring ZIP processes (regarded as ZIP-DGWMA chart). The run-length distribution of the proposed chart is evaluated by performing Monte Carlo simulations. A comparison study with the ZIP-GWMA chart indicates that the ZIP-DGWMA chart is more effective for shifts in the zero-inflated parameter p and for small shifts in both of the zero-inflated and Poisson parameters. The proposed chart is also applied on an example to demonstrate its application. [ABSTRACT FROM AUTHOR]

In various scenarios where products and services are accompanied by warranties to ensure their reliability over a specified time, the two-parameter (shifted) exponential distribution serves as a fundamental model for time-to-event data. In modern production process, the products often come with warranties, and their quality can be manifested by the changes in the scale and origin parameters of a shifted exponential (SE) distribution. This paper introduces the Max-EWMA chart, employing maximum likelihood estimators and exponentially weighted moving average (EWMA) statistics, to jointly monitor SE distribution parameters. Additionally, we extend two additional charts, namely the Max-DEWMA and Max-TEWMA charts to enhance early-stage shift detection. Performance evaluations under zero-state and steady-state conditions compare these charts with the existing Max-CUSUM chart in terms of expected value and standard deviation of the run length (RL) distribution. Our findings reveal that among the Max-EWMA schemes, the Max-EWMA SE chart outperforms the others in terms of steady-state performance, while the Max-TEWMA chart surpasses the Max-EWMA and Max-DEWMA SE charts in respect to zero-state performance. Moreover, the proposed Max-EWMA schemes demonstrate advantages over Max-CUSUM, especially for small to moderate smoothing constants. We also provide an illustrative example to demonstrate the implementation of the proposed schemes. [ABSTRACT FROM AUTHOR]

The aim of variable selection is the identification of the most important predictors that define the response of a linear system. Many techniques for variable selection use a constrained least squares (LS) formulation in which the constraint is imposed in the 1-norm (the lasso), or the 2-norm (Tikhonov regularisation), or a linear combination of these norms (the elastic net). It is always assumed that a constraint must necessarily be imposed, but the consequences of its imposition have not been addressed. This assumption is considered in this paper and it is shown that the correct application of Tikhonov regularisation to the LS problem min ‖ A x − b ‖ 2 requires that A and b satisfy a condition C. If this condition is satisfied, then the solution of the LS problem with this constraint is numerically stable and the regularisation error e between the solution of this problem and the solution of the LS problem is small. If, however, the condition C is not satisfied, then the error e is large. The condition C is derived from a refined normwise condition number of the solution of the LS problem. The paper includes examples of regularisation and variable selection with correlated variables that illustrate the theory. [ABSTRACT FROM AUTHOR]

Face recognition and identification are very important applications in machine learning. Due to the increasing amount of available data, traditional approaches based on matricization and matrix PCA methods can be difficult to implement. Moreover, the tensorial approaches are a natural choice, due to the mere structure of the databases, for example in the case of color images. Nevertheless, even though various authors proposed factorization strategies for tensors, the size of the considered tensors can pose some serious issues. Indeed, the most demanding part of the computational effort in recognition or identification problems resides in the training process. When only a few features are needed to construct the projection space, there is no need to compute a SVD on the whole data. Two versions of the tensor Golub–Kahan algorithm are considered in this manuscript, as an alternative to the classical use of the tensor SVD which is based on truncated strategies. In this paper, we consider the Tensor Tubal Golub–Kahan Principal Component Analysis method which purpose it to extract the main features of images using the tensor singular value decomposition (SVD) based on the tensor cosine product that uses the discrete cosine transform. This approach is applied for classification and face recognition and numerical tests show its effectiveness. [ABSTRACT FROM AUTHOR]

A significant challenge in statistical process monitoring (SPM) is to find exact and closed-form expressions (CFEs) (i.e. formed with constants, variables and a finite set of essential functions connected by arithmetic operations and function composition) for the run-length properties such as the average run-length (ARL\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ARL$$\end{document}), the standard deviation of the run-length (SDRL\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$SDRL$$\end{document}), and the percentiles of the run-length (PRL\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$PRL$$\end{document}) of nonparametric monitoring schemes. Most of the properties of these schemes are usually evaluated using simulation techniques. Although simulation techniques are helpful when the expression for the run-length is complicated, their shortfall is that they require a high number of replications to reach reasonably accurate answers. Consequently, they take too much computational time compared to other methods, such as the Markov chain method or integration techniques, and even with many replications, the results are always affected by simulation error and may result in an inaccurate estimation. In this paper, closed-form expressions of the run-length properties for the nonparametric double sampling precedence monitoring scheme are derived and used to evaluate its ability to detect shifts in the location parameter. The computational times of the run-length properties for the CFE and the simulation approach are compared under different scenarios. It is found that the proposed approach requires less computational time compared to the simulation approach. Moreover, once derived, CFEs have the added advantage of ease of implementation, cutting off on complex convergence techniques. CFE's can also easily be built into mathematical software for ease of computation and may be recalled for further work. [ABSTRACT FROM AUTHOR]

The moving average (MA) and double moving average (DMA) control charts are a good alternative to the Shewhart chart to detect small to moderate shifts of the process mean more quickly. In this article, we propose the triple moving average (TMA) control chart to improve the detection ability of the MA chart. It is shown that the proposed chart is more effective than the MA and DMA charts in detecting small to moderate shifts for a small value of span w. However, this range of shifts decreases as the value of w increases. The application of the proposed chart is demonstrated through two examples. [ABSTRACT FROM AUTHOR]

In this paper, we study self-dual codes over GF(p) where p=11,13,17,19,23 and 29. A classification of such codes for small lengths is given. The largest minimum weights of these codes are investigated. Many maximum distance separable self-dual codes are constructed. [Copyright &y& Elsevier]

Distribution-free or nonparametric control charts are used for monitoring the process parameters when there is a lack of knowledge about the underlying distribution. In this paper, we investigate a single distribution-free triple exponentially weighted moving average control chart based on the Lepage statistic (referred as TL chart) for simultaneously monitoring shifts in the unknown location and scale parameters of a univariate continuous distribution. The design and implementation of the proposed chart are discussed using time-varying and steady-state control limits for the zero-state case. The run-length distribution of the TL chart is evaluated by performing Monte Carlo simulations. The performance of the proposed chart is compared to those of the existing EWMA-Lepage (EL) and DEWMA-Lepage (DL) charts. It is observed that the TL chart with a time-varying control limit is superior to its competitors, especially for small to moderate shifts in the process parameters. We also provide a real example from a manufacturing process to illustrate the application of the proposed chart., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2023 Informa UK Limited, trading as Taylor & Francis Group.)

In the present article, a double generally weighted moving average (DGWMA) control chart based on a three-parameter logarithmic transformation is proposed for monitoring the process variability, namely the S 2 -DGWMA chart. Monte-Carlo simulations are utilized in order to evaluate the run-length performance of the S 2 -DGWMA chart. In addition, a detailed comparative study is conducted to compare the performance of the S 2 -DGWMA chart with several well-known memory-type control charts in the literature. The comparisons indicate that the proposed one is more efficient in detecting small shifts, while it is more sensitive in identifying upward shifts in the process variability. A real data example is given to present the implementation of the new S 2 -DGWMA chart., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2022 Informa UK Limited, trading as Taylor & Francis Group.)

Control charts are widely known quality tools used to detect and control industrial process deviations in Statistical Process Control. In the current paper, we propose a new single memory-type control chart, called the maximum double generally weighted moving average chart (referred as Max-DGWMA), that simultaneously detects shifts in the process mean and/or process dispersion. The run length performance of the proposed Max-DGWMA chart is compared with that of the Max-EWMA, Max-DEWMA, Max-GWMA and SS-DGWMA charts, using time-varying control limits, through Monte-Carlo simulations. The comparisons reveal that the proposed chart is more efficient than the Max-EWMA, Max-DEWMA and Max-GWMA charts, while it is comparable with the SS-DGWMA chart. An automotive industry application is presented in order to implement the Max-DGWMA chart. The goal is to establish statistical control of the manufacturing process of the automobile engine piston rings. The source of the out-of-control signals is interpreted and the efficiency of the proposed chart in detecting shifts faster is evident., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2021 Informa UK Limited, trading as Taylor & Francis Group.)

Control charts are widely used for monitoring quality characteristics of high-yield processes. In such processes where a large number of zero observations exists in count data, the zero-inflated binomial (ZIB) models are more appropriate than the ordinary binomial models. In ZIB models, random shocks occur with probability θ , and upon the occurrence of random shocks, the number of non-conforming items in a sample of size n follows the binomial distribution with proportion p . In the present article, we study in more detail the exponentially weighted moving average control chart based on ZIB distribution (ZIB-EWMA) and we also propose a new control chart based on the double exponentially weighted moving average statistic for monitoring ZIB data (ZIB-DEWMA). The two control charts are studied in detecting upward shifts in θ or p individually, as well as in both parameters simultaneously. Through a simulation study, we compare the performance of the proposed chart with the ZIB-Shewhart, ZIB-EWMA and ZIB-CUSUM charts. Finally, an illustrative example is also presented to display the practical application of the ZIB charts., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2020 Informa UK Limited, trading as Taylor & Francis Group.)