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In this paper, we propose an optimal fractional-order accumulative Grey Markov model with variable parameters (FOGMKM (1,1)) to predict the annual total energy consumption in China and improve the accuracy of energy consumption forecasting. The new model is built upon the traditional Grey model and utilized matrix perturbation theory to study the natural and response characteristics of a system when the structural parameters change slightly. The particle swarm optimization algorithm (PSO) is used to determine the number of optimal fractional order and nonlinear parameters. An experiment is conducted to validate the high prediction accuracy of the FOGMKM (1,1) model, with mean absolute percentage error (MAPE) and root mean square error (RMSE) values of 0.51% and 1886.6, respectively, and corresponding fitting values of 0.92% and 6108.8. These results demonstrate the superior fitting performance of the FOGMKM (1,1) model when compared to other six competitive models, including GM (1,1), ARIMA, Linear, FAONGBM (1,1), FGM (1,1) and FOGM (1,1). Our study provides a scientific basis and technical references for further research in the finance as well as energy fields and can serve well for energy market benchmark research. [ABSTRACT FROM AUTHOR]

Among adaptive charts, the variable parameters chart shows the best performance as it varies all charting parameters. The existing variable parameters chart is designed by assuming that process parameters are known. However, process parameters are rarely known but are usually estimated based on Phase-I data. Hence, the variable parameters ... chart with estimated parameters is proposed. Formulae to evaluate various performance measures are derived through Markov chains. This paper shows that adopting the optimal charting parameters by incorrectly assuming that process parameters are known results in a large deterioration on the actual performance, especially for small shifts, a small number of subgroups, and small sample sizes. Subsequently, this paper proposes algorithms to obtain the optimal charting parameters for estimated parameters that show better performance, especially for small shift sizes, number of subgroups, and sample sizes. Finally, from an illustrative example, the proposed variable parameters ... chart is able to detect more out-of-control samples. [ABSTRACT FROM AUTHOR]

In this paper, a new variable parameters chart for the process mean with a statistic that integrates information from the study and auxiliary variables is proposed. The proposed variable parameters chart with auxiliary information (AI) (abbreviated as VP-AI) is optimally designed to minimize the out-of-control steady-state (i) average time to signal (ATS1) and (ii) expected average time to signal (EATS1) values when the mean shift sizes are known and unknown, respectively. The Markov chain approach is adopted to derive the formulae of the performance measures ATS1, standard deviation of the time to signal (SDTS1) and EATS1. The VP-AI chart significantly outperforms the standard VP chart; thus, justifying the incorporation of auxiliary information to enhance the ability of the VP chart. The VP-AI chart is also compared with the Shewhart AI, synthetic AI, exponentially weighted moving average (EWMA) AI, run sum AI and variable sample size and sampling interval (VSSI) AI charts. The VP-AI chart significantly outperforms the Shewhart AI, synthetic AI and VSSI AI charts for all levels of shifts. Meanwhile, the VP-AI chart outperforms the EWMA AI and run sum AI charts for most shifts. The VP-AI chart is found to be more robust than the EWMA-AI chart when the correlation coefficient is misspecified or the bivariate normality assumption is violated as long as the size of the shift is moderate or large. A real application which monitors spring elasticity is used to illustrate the VP-AI chart's implementation. [ABSTRACT FROM AUTHOR]

Evaluating the effect of measurement errors on either adaptive or simultaneous control charts has been a topic of interest for the researchers in the recent years. Nevertheless, the effect of measurement errors on both adaptive and simultaneous monitoring control charts has not been considered yet. In this paper, through extensive numerical studies, we evaluate the effect of measurement errors on an adaptive (variable parameters) simultaneous multivariate control chart for the mean vector and the variance‐covariance matrix of p quality characteristics assumed to follow a multivariate normal distribution. In order to do so, (a) we use eight performance measures computed using a Markov chain model, (b) we consider the effects of multiple measurements as well as the error model's parameters, and (c) we also consider the overall performance of this adaptive simultaneous chart including the chart parameters values optimization, which have never been considered so far for this scheme. At last, a real case is presented in order to illustrate the proposed scheme. [ABSTRACT FROM AUTHOR]

An efficient process monitoring system is important for achieving sustainable manufacturing. The control charting technique is one of the most effective techniques to monitor process quality. In certain processes where the process mean and variance are not independent of one another, the coefficient of variation (CV), which measures the ratio of the standard deviation to the mean, should be monitored. In line with industrial settings, where at least two or more variables are monitored simultaneously in most processes, this paper proposes a variable parameter (VP) chart to monitor the multivariate CV (MCV). Formulae and algorithms to optimize the various performance measures are discussed. The proposed VP MCV chart is designed based on a Markov chain approach. The performance comparison shows that the proposed VP MCV chart prevails over the existing MCV charts, in terms of the average time to signal (ATS), standard deviation of the time of signal (SDTS), and expected average time to signal (EATS) criteria. An example is presented to illustrate the implementation of the proposed VP MCV chart. [ABSTRACT FROM AUTHOR]

The variable parameters (VP) [ABSTRACT FROM AUTHOR]