Phase II monitoring of binary profiles in the presence of within-profile autocorrelation based on Markov Model

Maleki, Mohammad Reza; Amiri, Amirhossein; Taheriyoun, Ali Reza

doi:10.1080/03610918.2016.1249880

Cited by 23 publications

(13 citation statements)

References 30 publications

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“…As noted previously, Maleki et al [28] employed a uni ed methodology for Phase II monitoring of autocorrelated binary pro les concerning the within-pro le autocorrelation. Assume that y i denotes the binary response value at ith; i = 1; :::; n treatment of a sampled pro le.…”

Section: Preliminaries and Assumptionsmentioning

confidence: 99%

“…Using the logistic regression model to express the relationship between binary response variable and explanatory variable(s) leads to misleading results, because this model ignores the within-pro le autocorrelation structure. Considering the rst order autoregressive model, i.e., AR(1), between consecutive response values in each pro le, Maleki et al [28] proposed a stationary state space f0; 1g model for ith treatment as follows:…”

Section: Preliminaries and Assumptionsmentioning

confidence: 99%

“…In the second step, they presented the likelihood function by taking into account the within-pro le autocorrelation. Maleki et al [28] noted that the common approaches in the area of monitoring GLM pro les were proposed under the independency assumption of consecutive response values within each pro le. Hence, they developed an evolutionary algorithm to estimate the regression parameters by maximizing the likelihood function.…”

Section: Preliminaries and Assumptionsmentioning

confidence: 99%

“…They suggested two remedial approaches to account for the e ect of autocorrelation in terms of signal probability criterion. Maleki et al [28] studied Phase II monitoring of autocorrelated binary pro les using a Markov-based model. For this purpose, they introduced a logistic regression model, which took into account the withinpro le autocorrelation.…”

Section: Introductionmentioning

confidence: 99%

“…We assume that the response values within each pro le are autocorrelated and follow rst order autoregressive (AR(1)) model. Note that in Maleki et al [28], only step shifts are taken into account. However, in this paper, not only the step changes but also the linear trends in the vector of model parameter are studied.…”

Section: Introductionmentioning

confidence: 99%

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Identifying the time of step change and drift in Phase II monitoring of autocorrelated logistic regression profiles

2017

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In some pro le monitoring applications, the independency assumption of consecutive binary response values within each pro le is violated. To the best of our knowledge, estimating the time of a change in the parameters of an autocorrelated binary pro le is neglected in the literature. In this paper, two maximum likelihood estimators are proposed to estimate the real time of step changes and drift in Phase II monitoring of binary pro les in the case of within-pro le autocorrelation. Our proposed estimators identify the change point not only in the autocorrelated logistic regression parameters, but also in autocorrelation coe cient. The performance of the proposed estimators to identify the time of change points either in regression parameters or autocorrelation coe cient is evaluated through simulation studies. The results, in terms of the accuracy and precision criteria, show the satisfactory performance of the proposed estimators under both step changes and drift. Moreover, a numerical example is given to illustrate the application of the proposed estimators.

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Section: Preliminaries and Assumptionsmentioning

confidence: 99%

Section: Preliminaries and Assumptionsmentioning

confidence: 99%

Section: Preliminaries and Assumptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Identifying the time of step change and drift in Phase II monitoring of autocorrelated logistic regression profiles

2017

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Deep recurrent neural network‐based residual control chart for autocorrelated processes

Chen

2019

Quality & Reliability Eng

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With the growth of automation in process industries, there is correlation in the process variables. Deep learning has achieved many great successes in image and visual analysis. This paper concentrates on developing a deep recurrent neural network (RNN) model to characterize process variables at vary time lags, and then a residual chart is developed to detect mean shifts in autocorrelated processes. The experiment results indicate that the RNN‐based residual chart outperforms other typical methods (eg, autoregressive [AR]‐based control chart, back propagation network [BPN]‐based residual chart). This paper provides guideline for deep learning technique employed as an effective tool in autocorrelated process control.

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GLM profile monitoring using robust estimators

Moheghi

Noorossana

Ahmadi

2020

Quality & Reliability Eng

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It is well known that performance of control scheme in phase II of statistical process control depends on the estimators utilized in phase I. Sometimes, outliers may be present in the data, which could seriously impact the performance of the estimators. In some practical situations, generalized linear models (GLMs) are used to model a wide class of response variables. This study deals with the robust estimation and monitoring of parameters in GLM profiles in the presence of outliers. In this study, robust estimators are used to estimate the parameters of logistic and Poisson profiles. The results are compared with the maximum likelihood estimators (MLEs). In a numerical example, the profile parameters are estimated by the MLE and robust estimators and the resulting test statistics are monitored by a control scheme. The phase II control charts are determined based on these two types of estimators and compared for different out‐of‐control conditions. The simulation results confirm that robust estimators in most cases lead to better estimates in comparison with the MLE estimator in terms of average run length criterion.

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Phase II monitoring of binary profiles in the presence of within-profile autocorrelation based on Markov Model

Cited by 23 publications

References 30 publications

Identifying the time of step change and drift in Phase II monitoring of autocorrelated logistic regression profiles

Identifying the time of step change and drift in Phase II monitoring of autocorrelated logistic regression profiles

Deep recurrent neural network‐based residual control chart for autocorrelated processes

GLM profile monitoring using robust estimators

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