On autoregressive model selection for the exponentially weighted moving average control chart of residuals in monitoring the mean of autocorrelated processes

Li, Yaping; Pan, Ershun; Yan, Xin

doi:10.1002/qre.2701

Cited by 17 publications

(4 citation statements)

References 39 publications

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“…When there is autocorrelation effect in Phase II, the LMM approach, as well as the proposed statistics by Noorossana, Amiri and Soleimani [45], Soleimani, Noorossana and Amiri [46] and Ahmadi, Yeganeh and Shadman [47] can be utilized to remove the autocorrelation effect; note that this is similar to the Phase I analysis for the T 2 control chart. On the other hand, several researchers, such as Sheu and Lu [53] and Li, et al [54], studied the robustness of EWMA control charts with the effect of autocorrelation in the Phase II analysis so that the MEWMA approach [42] can be directly employed with autocorrelated data. More discussions on the latter are presented in Appendix A.…”

Section: Phase II Analysismentioning

confidence: 99%

Data-Driven Surveillance of Internet Usage Using a Polynomial Profile Monitoring Scheme

Netshiozwi,

Yeganeh,

Shongwe

et al. 2023

Mathematics

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Control charts, which are one of the major tools in the Statistical Process Control (SPC) domain, are used to monitor a process over time and improve the final quality of a product through variation reduction and defect prevention. As a novel development of control charts, referred to as profile monitoring, the study variable is not defined as a quality characteristic; it is a functional relationship between some explanatory and response variables which are monitored in such a way that the major aim is to check the stability of this model (profile) over time. Most of the previous works in the area of profile monitoring have focused on the development of different theories and assumptions, but very little attention has been paid to the practical application in real-life scenarios in this field of study. To address this knowledge gap, this paper proposes a monitoring framework based on the idea of profile monitoring as a data-driven method to monitor the internet usage of a telecom company. By definition of a polynomial model between the hours of each day and the internet usage within each hour, we propose a framework with three monitoring goals: (i) detection of unnatural patterns, (ii) identifying the impact of policies such as providing discounts and, (iii) investigation of general social behaviour variations in the internet usage. The results shows that shifts of different magnitudes can occur in each goal. With the aim of different charting statistics such as Hoteling T2 and MEWMA, the proposed framework can be properly implemented as a monitoring scheme under different shift magnitudes. The results indicate that the MEWMA scheme can perform well in small shifts and has faster detection ability as compared to the Hoteling T2 scheme.

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Section: Phase II Analysismentioning

confidence: 99%

Data-Driven Surveillance of Internet Usage Using a Polynomial Profile Monitoring Scheme

Netshiozwi,

Yeganeh,

Shongwe

et al. 2023

Mathematics

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“…In general, the values of the weight λ = 0 . 05 , 0 . 1 , 0 . 2 are typical choices in detecting small shifts in processes. 45–47 Also, λ = 0 . 4 has been recommended to ensure the weights match those given by a Shewhart control chart with the Western Electric rules. 48 Moreover, when λ = 1 , the EWMA control chart is actually a Shewhart one.…”

Section: Case Studymentioning

confidence: 99%

An MEWMA-based segmental multivariate hidden Markov model for degradation assessment and prediction

Zio

Pan

2021

Proceedings of the Institution of Mechanical Engineers, Part O:

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Degradation is an unavoidable phenomenon in industrial systems. Hidden Markov models (HMMs) have been used for degradation modeling. In particular, segmental HMMs have been developed to model the explicit relationship between degradation signals and hidden states. However, existing segmental HMMs deal only with univariate cases, whereas in real systems, signals from various sensors are collected simultaneously, which makes it necessary to adapt the segmental HMMs to deal with multivariate processes. Also, to make full use of the information from the sensors, it is important to differentiate stable signals from deteriorating ones, but there is no good way for this, especially in multivariate processes. In this paper, the multivariate exponentially weighted moving average (MEWMA) control chart is employed to identify deteriorating multivariate signals. Specifically, the MEWMA statistic is used as a comprehensive indicator for differentiating multivariate observations. Likelihood Maximization is used to estimate the model parameters. To avoid underflow, the forward and backward probabilities are normalized. In order to assess degradation, joint probabilities are defined and derived. Further, the occurrence probability of each degradation state at the current time, as well as in the future, is derived. The Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dataset of NASA is employed for comparative analysis. In terms of degradation assessment and prediction, the proposed model performs very well in general. By sensitivity analysis, we show that in order to improve further the performance of the method, the weight of the chart should be set relatively small, whereas the method is not sensitive to the change of the in-control average run length (ARL).

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“…Chen and Yu [20] proposed a deep learning approach for monitoring autocorrelated observations. Li et al [21] used the EWMA control chart to monitor the residual of the p-th order autoregressive model. Keshavarz et al [22] modified the accelerated failure time regression model to account for the autocorrelated data.…”

Section: Introductionmentioning

confidence: 99%

Constructing a Sensitive Control Chart to Monitor Process Mean using Optimal Filter: Time-Frequency Analysis Approach

2023

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Control charts are one of the critical tools for process monitoring. Test statistics are computed as a function of sample means in control charts for monitoring the process mean. In this study, these functions are modeled by filters. These filters have essential properties in both time and frequency domains. In previous studies, only their properties in the time domain have been considered. Thus, the resulting filters have sub-optimal performance. This study investigates the optimal design of these filters for monitoring the process mean. The behavior of these filters is analyzed not only in the time domain but also in the frequency domain. Properties such as stability are considered in designing this filter. An optimization model is designed and solved using a Genetic Algorithm to minimize the Average Run Length. The proposed optimal filter is compared with other control charts using simulation studies. Results showed the high speed of the proposed filter in detecting shifts in the process mean. The proposed optimal filter is also used to monitor the oil price of the OPEC basket. The results showed that shifts were detected at the right time using the proposed optimal filter.

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On autoregressive model selection for the exponentially weighted moving average control chart of residuals in monitoring the mean of autocorrelated processes

Cited by 17 publications

References 39 publications

Data-Driven Surveillance of Internet Usage Using a Polynomial Profile Monitoring Scheme

Data-Driven Surveillance of Internet Usage Using a Polynomial Profile Monitoring Scheme

An MEWMA-based segmental multivariate hidden Markov model for degradation assessment and prediction

Constructing a Sensitive Control Chart to Monitor Process Mean using Optimal Filter: Time-Frequency Analysis Approach

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