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In recent years, deep learning methods have been widely used in combination with control charts to improve the monitoring efficiency of complete data. However, due to time and cost constraints, data obtained from reliability life tests are often type-I right censored. Traditional control charts become inefficient for monitoring this type of data. Thus, researchers have proposed various control charts with conditional expected values (CEV) or conditional median (CM) to improve efficiency for right-censored data under normal and non-normal conditions. This study combines the exponentially weighted moving average (EWMA) CEV and CM chart with deep learning methods to increase efficiency for gamma type-I right-censored data. A statistical simulation and a real-world case are presented to assess the proposed method, which outperforms the traditional EWMA charts with CEV and CM in various skewness coefficient values and censoring rates for gamma type-I right-censored data.

Control charts are a statistical approach for monitoring cancer data that can assist discover patterns, trends, and unusual deviations in cancer-related data across time. To detect deviations from predicted patterns, control charts are extensively used in quality control and process management. Control charts may be used to track numerous parameters in cancer data, such as incidence rates, death rates, survival time, recovery time, and other related indicators. In this study, CDEC chart is proposed to monitor the cancer patients recovery time censored data. This paper presents a composite dual exponentially weighted moving average Cumulative sum (CDEC) control chart for monitoring cancer patients recovery time censored data. This approach seeks to detect changes in the mean recovery time of cancer patients which usually follows Weibull lifetimes. The results are calculated using type I censored data under known and estimated parameter conditions. We combine the conditional expected value (CEV) and conditional median (CM) approaches, which are extensively used in statistical analysis to determine the central tendency of a dataset, to create an efficient control chart. The suggested chart's performance is assessed using the average run length (ARL), which evaluates how efficiently the chart can detect a change in the process mean. The CDEC chart is compared to existing control charts. A simulation study and a real-world data set related to cancer patients recovery time censored data is used for results illustration. The proposed CDEC control chart is developed for the data monitoring when complete information about the patients are not available. So, instead of doping the patients information we can used the proposed chart to monitor the patients information even if it is censored. The authors conclude that the suggested CDEC chart is more efficient than competitor control charts for monitoring cancer patients recovery time censored data. Overall, this study introduces an efficient new approach for cancer patients recovery time censored data, which might have significant effect on quality control and process improvement across a wide range of healthcare and medical studies.

Control charts with conditional expected value (CEV) can be used with novel statistical techniques to monitor the means of moderately and lowly censored data. In recent years, machine learning and deep learning have been successfully combined with quality technology to solve many process control problems. This paper proposes a residual control chart combining a convolutional neural network (CNN) and support vector regression (SVR) for type-I censored data with the Weibull model. The CEV and exponentially weighted moving average (EWMA) statistics are used to generate training data for the CNN and SVR. The average run length shows that the proposed chart approach outperforms the traditional EWMA CEV chart approach in various shift sizes and censored rates. The proposed chart approach is suitable to be used in detecting small shift size for highly censored data. An illustrative example presents the application of the proposed method in an electronics industry.

Autocorrelation of signals and measurement data makes it difficult to estimate their statistical characteristics. However, the scope of usefulness of autocorrelation functions for statistical description of signal relation is narrowed down to linear processing models. The use of the conditional expected value opens new possibilities in the description of interdependence of stochastic signals for linear and non-linear models. It is described with relatively simple mathematical models with corresponding simple algorithms of their practical implementation. The paper presents a practical model of exponential autocorrelation of measurement data and a theoretical analysis of its impact on the process of conditional averaging of data. Optimization conditions of the process were determined to decrease the variance of a characteristic of the conditional expected value. The obtained theoretical relations were compared with some examples of the experimental results.

This paper explores options to generate Markowitz efficient frontiers, from which a suitable portfolio is recommended to retirees. The risk measures of these options are the standard deviations of asset returns, variance of normalized present values of discounted consumption, shortfall risk, and conditional shortfall risk, or the combinations of them. We report the shortfall risk and conditional shortfall risk for all these efficient portfolios.

ARMA-GARCH models are widely used to model the conditional mean and conditional variance dynamics of returns on risky assets. Empirical results suggest heavy-tailed innovations with positive extreme value index for these models. Hence, one may use extreme value theory to estimate extreme quantiles of residuals. Using weak convergence of the weighted sequential tail empirical process of the residuals, we derive the limiting distribution of extreme conditional Value-at-Risk (CVaR) and conditional expected shortfall (CES) estimates for a wide range of extreme value index estimators. To construct confidence intervals, we propose to use self-normalization. This leads to improved coverage vis-à-vis the normal approximation, while delivering slightly wider confidence intervals. A data-driven choice of the number of upper order statistics in the estimation is suggested and shown to work well in simulations. An application to stock index returns documents the improvements of CVaR and CES forecasts.

In this paper, we propose two new optimal reinsurance models in which both premium budget constraints and the reinsurer’s risk limits are taken into account. To be precise, we assume that the reinsurance premium has an upper bound, and that the admissible ceded loss functions have a pre-specified upper limit. Moreover, we assume that the reinsurance premium principle is calculated by the expected value premium principle. Under the optimality criteria of minimizing the value at risk and conditional value at risk of the insurer’s total risk exposure, we derive the explicit optimal reinsurance treaties, which are layer reinsurance treaties. A new approach is developed to construct the optimal reinsurance treaties. Comparisons with existing studies are also made. Finally, we provide a numerical study based on real data and an example to illustrate the proposed models and results. Our work provides a novel generalization of several known achievements in the literature.

This paper considers the worst-case Conditional Value-at-Risk (CVaR) in the situation where only partial information on the underlying probability distribution is available. The minimization of the worst-case CVaR under mixture distribution uncertainty, box uncertainty, and ellipsoidal uncertainty are investigated. The application of the worst-case CVaR to robust portfolio optimization is proposed, and the corresponding problems are cast as linear programs and second-order cone programs that can be solved efficiently. Market data simulation and Monte Carlo simulation examples are presented to illustrate the proposed approach.

We study preference relations on conditional gambles of a decision maker acting under ambiguity. Dutch book rationality conditions are provided under a linear utility scale, encoding either an optimistic or a pessimistic attitude towards uncertainty. These conditions characterize possibly incomplete preferences representable by totally alternating or monotone conditional functionals. In general, the uniqueness of the representation is not guaranteed, but it can be obtained by adding the hypothesis of existence of a conditional fair price for every conditional gamble. The given rationality conditions have a betting scheme interpretation relying on “penalty fees” for betting on strict preference comparisons.

Large-scale mobile traffic data analysis is important for efficiently planning mobile base station deployment plans and public transportation plans. However, the storage costs of preserving mobile traffic data are becoming much higher as traffic increases enormously population density of target areas. To solve this problem, schemes to generate a large amount of mobile traffic data have been proposed. In the state-of-the-art of the schemes, generative adversarial networks (GANs) are used to transform a large amount of traffic data into a coarse-grained representation and generate the original traffic data from the coarse-grained data. However, the scheme still involves a storage cost, since the coarse-grained data must be preserved in order to generate the original traffic data. In this paper, we propose a scheme to generate the mobile traffic data by using conditional-super-resolution GAN (CSR-GAN) without requiring a coarse-grained process. Through experiments using two real traffic data, we assessed the accuracy and the amount of storage data needed. The results show that the proposed scheme, CSR-GAN, can reduce the storage cost by up to 45% compared to the traditional scheme, and can generate the original mobile traffic data with 94% accuracy. We also conducted experiments by changing the architecture of CSR-GAN, and the results show an optimal relationship between the amount of traffic data and the model size.