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The usual practice in Statistical Process Monitoring (SPM) techniques assumes that the data distribution is known and the related parameters are accurately estimated. In practice, the underlying distribution and its parameters are rarely known, and control charts need to be constructed with parameters being estimated. Such issues have recently received an increasing attention in evaluating the properties of both parametric and nonparametric charts. However, the same study is seldom conducted for the control charts based on the data‐driven tools. In this paper, we investigated the in‐control performance of a nonparametric control chart based on the Support Vector Data Description (SVDD) theory. More specifically, we discuss the conditional effect of the training Phase‐I samples on the Phase‐II efficiency when different distributions are considered. Simulation results show that the conditional performance of the SVDD‐based chart can be strongly affected by the Phase‐I samples. It this situation, adjusted control limits with a specific number of available training sample is suggested. [ABSTRACT FROM AUTHOR]

Several scholarly works intrinsically assume that the frequency and magnitude of events are two independent variables. However, in many practical situations, it is necessary to consider the dependence between these two characteristics of events. In this paper, two Smith–Adelfang–Tubbs (SAT) models, namely, the four‐ and the five‐parameter bivariate Gamma distributions (BGD) with a particular dependency parameter, are first reviewed. Then, a synthetic multivariate exponentially weighted moving average (synthetic MEWMA, or SMEWMA) type scheme is proposed to monitor the individual BGD observations (subgroups of size one) generated from those two specific SAT models. The Monte‐Carlo simulation method is developed to evaluate the run length (RL$\mathrm{RL}$) properties of the recommended SMEWMA BGD scheme in both the zero‐state and the steady‐state cases. Furthermore, we discuss the average run length (ARL) of the proposed SMEWMA BGD scheme with different design parameters, and then compare both the zero‐state and the steady‐state out‐of‐control ARL performances of the recommended SMEWMA BGD scheme with those of the classic MEWMA chart, the paired individual Gamma chart, and the MCUSUM chart. Simulation results suggest that the overall performance of the recommended SMEWMA BGD scheme is superior to the other comparative schemes. Finally, the implementation of the proposed SMEWMA BGD scheme is illustrated with a natural flood event dataset. [ABSTRACT FROM AUTHOR]

Exponentially distributed data are commonly encountered in high‐quality processes. Control charts dedicated to the univariate exponential distribution have been extensively studied by many researchers. In this paper, we investigate a multivariate cumulative sum (MCUSUM) control chart for monitoring Gumbel's bivariate exponential (GBE) data. Some tables are provided to determine the optimal design parameters of the proposed MCUSUM GBE chart. Furthermore, both zero‐state and steady‐state properties of the proposed MCUSUM GBE chart for the raw and the transformed GBE data are compared with the multivariate exponentially weighted moving average (MEWMA) chart and the paired individual cumulative sum (CUSUM) chart. The results show that the proposed MCUSUM GBE chart outperforms the other two types of control charts for most shift domains. In addition, an extension to Gumbel's multivariate exponential (GME) distribution is also investigated. Finally, an illustrative example is provided in order to explain how the proposed MCUSUM GBE chart can be implemented in practice. [ABSTRACT FROM AUTHOR]