Memory type control charts with inverse-Gaussian response: An application to yarn manufacturing industry

Amin, Muhammad; Mahmood, Tahir; Kinat, Summera

doi:10.1177/0142331220952965

Cited by 21 publications

(16 citation statements)

References 50 publications

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“…The CUSUM parameter

k_{1 false[scriptD false]}

is the reference value, which is often one‐half of the magnitude of the shift, or

k_{1 false[scriptD false]} = \frac{δ}{2} σ = \frac{| μ_{1 [D]} - μ_{0 [D]} |}{2} σ

. Therefore, by following Amin et al, 43

k_{1 false[scriptD false]}

is set here as 0.5. The process is said to be OOC if any plotting statistic

C_{i false[scriptD false]}^{+}

exceeds the decision value

H_{[D]} = h_{[D]} \sqrt{σ_{false[scriptD false]}^{2}}

.…”

Section: Monitoring Schemes Based On Zero‐inflated Modelsmentioning

confidence: 99%

“…The

PR_D_CUSUM

control chart is a model‐based control chart, and its statistic is defined as

M_{i false[scriptD false]}^{+} = \max false[0, {PR}_{i false[scriptD false]} - false(μ_{PR false[scriptD false]} + k_{2 false[scriptD false]} false) + M_{i - 1 false[scriptD false]}^{+} false] .

The starting values of the CUSUM statistic is considered as zero (i.e.,

M_{0 false[scriptD false]}^{+} = 0

) and the parameter

k_{2 false[scriptD false]}

is the reference value, which is often one‐half of the magnitude of the shift or

k_{2 false[scriptD false]} = \frac{δ}{2} σ = \frac{| μ_{1 [D]} - μ_{0 [D]} |}{2} σ

. Therefore, by following Amin, 43

k_{2 false[scriptD false]}

is set as 0.5. For the

PR_D_CUSUM

control chart, decision criteria is obtained as

H_{PR false[scriptD false]} = h_{PR false[scriptD false]} \sqrt{σ_{PR [D]}^{2}}

.…”

Section: Monitoring Schemes Based On Zero‐inflated Modelsmentioning

confidence: 99%

See 1 more Smart Citation

The generalized linear model‐based exponentially weighted moving average and cumulative sum charts for the monitoring of high‐quality processes

Mahmood

Xie

2021

Appl Stoch Models Bus & Ind

Self Cite

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In this industry 4.0 revolution, most of the manufacturing processes are equipped with the digital devices which are continuously recording the data. To monitor the quality of a manufacturing system, variable about number of conforming or nonconforming items is usually used and statistical analysis based on it is further utilized for developing the policies. In this era of sophisticated and modern technology, most of the manufacturing systems are producing near zero‐defect items. Such processes are known as high‐quality processes, and their dataset consists of excess number of zeros. Generally, the zero excess or near zero‐defect dataset is well fitted by the zero‐inflated distributions, and the zero‐inflated Poisson (ZIP) and zero‐inflated Negative Binomial (ZINB) distributions are the most common models. Most of the time, in high‐quality processes, few covariates are also measured along with defect counts. Hence, to model such processes, generalized linear model (GLM) based on ZIP and ZINB distributions are used to fit the data. In monitoring perspective, data‐based control charts are designed to monitor high‐quality datasets while the GLM‐based control charts based on the residuals of the GLM models are used to monitor a change in the mean of the zero excess datasets. In this study, we have developed memory‐type data‐based and GLM‐based control charts (i.e., exponentially weighted moving average and cumulative sum) to monitor the increasing average defect counts in a high‐quality process. Further, the proposed methods are evaluated using run‐length properties and compared with its competitive charts. Furthermore, to highlight the importance of the study, the proposed methods are implemented on a dataset concerning the number of flight delays between Atlanta and Orlando airports.

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“…The CUSUM parameter

k_{1 false[scriptD false]}

is the reference value, which is often one‐half of the magnitude of the shift, or

k_{1 false[scriptD false]} = \frac{δ}{2} σ = \frac{| μ_{1 [D]} - μ_{0 [D]} |}{2} σ

. Therefore, by following Amin et al, 43

k_{1 false[scriptD false]}

is set here as 0.5. The process is said to be OOC if any plotting statistic

C_{i false[scriptD false]}^{+}

exceeds the decision value

H_{[D]} = h_{[D]} \sqrt{σ_{false[scriptD false]}^{2}}

.…”

Section: Monitoring Schemes Based On Zero‐inflated Modelsmentioning

confidence: 99%

“…The

PR_D_CUSUM

control chart is a model‐based control chart, and its statistic is defined as

M_{i false[scriptD false]}^{+} = \max false[0, {PR}_{i false[scriptD false]} - false(μ_{PR false[scriptD false]} + k_{2 false[scriptD false]} false) + M_{i - 1 false[scriptD false]}^{+} false] .

The starting values of the CUSUM statistic is considered as zero (i.e.,

M_{0 false[scriptD false]}^{+} = 0

) and the parameter

k_{2 false[scriptD false]}

is the reference value, which is often one‐half of the magnitude of the shift or

k_{2 false[scriptD false]} = \frac{δ}{2} σ = \frac{| μ_{1 [D]} - μ_{0 [D]} |}{2} σ

. Therefore, by following Amin, 43

k_{2 false[scriptD false]}

is set as 0.5. For the

PR_D_CUSUM

control chart, decision criteria is obtained as

H_{PR false[scriptD false]} = h_{PR false[scriptD false]} \sqrt{σ_{PR [D]}^{2}}

.…”

Section: Monitoring Schemes Based On Zero‐inflated Modelsmentioning

confidence: 99%

The generalized linear model‐based exponentially weighted moving average and cumulative sum charts for the monitoring of high‐quality processes

Mahmood

Xie

2021

Appl Stoch Models Bus & Ind

Self Cite

View full text Add to dashboard Cite

show abstract

“…It is expected to have the lowest EQL for the best chart. For the details on these and some other useful measures, one may be seen in studies [37][38][39][40] and the references therein. The computational algorithm for the proposed MPVC is outlined as:…”

Section: F I G U R E 1 Arl Curves Of the Proposed Charts And Their Counterpartsmentioning

confidence: 99%

On the multivariate progressive control chart for effective monitoring of covariance matrix

Ajadi

Hung

Riaz

et al. 2021

Quality & Reliability Eng

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With the development of modern acquisition techniques, data with several correlated quality characteristics are increasingly accessible. Thus, multivariate control charts can be employed to detect changes in the process. This study proposes two multivariate control charts for monitoring process variability (MPVC) using a progressive approach. First, when the process parameters are known, the performance of the MPVC charts is compared with some multivariate dispersion schemes. The results showed that the proposed MPVC charts outperform their counterparts irrespective of the shifts in the process dispersion. The effects of the Phase I estimated covariance matrix on the efficiency of the MPVC charts were also evaluated. The performances of the proposed methods and their counterparts are evaluated by calculating some useful run length properties. An application of the proposed chart is also considered for the monitoring of a carbon fiber tubing process. K E Y W O R D Sdispersion monitoring, estimation effects, multivariate control chart, phase I, progressive setup INTRODUCTIONMany manufacturing processes have multiple correlated quality characteristics; multivariate control chart is very effective in monitoring such processes. 1 For example, monitoring multivariate quality variables like the diameter and length of the manufacturing process of a dowel pin. Hotelling 2 introduced a 2 -control chart; this chart is very efficient at detecting large shifts in the process mean vector, which is also mentioned by Mahmood et al. 3 Two multivariate cumulative sum (MCUSUM) charts were proposed by Healy, 4 where the first chart monitors the process mean vector, and the other monitors the covariance matrix. Crosier 5 also proposed a multivariate CUSUM chart. Pignatiello Jr and Runger 6 introduced another multivariate CUSUM control charts for detecting shifts in the process mean vector. Lowry et al 7 provided a Multivariate exponentially weighted moving average (EWMA) chart for detecting small and intermediate shifts in the process parameter. This chart is a direct extension of the univariate EWMA control chart by Roberts. 8 The multivariate CUSUM and EWMA control charts are very efficient in detecting small and moderate shifts in the process parameters. Ajadi and Riaz 9 proposed two multivariate charts which combine the effects of MEWMA and MCUSUM charts. Their proposed charts are more effective in detecting only small shifts in the proposed than the MEWMA and MCUSUM charts. Next, multivariate dispersion charts are employed to detecting changes in the covariance matrices. For example, Alt 10 proposed generalized variance chart (GVC), |S|. The determinant of the sample covariance matrix was employed as the summary statistics. Chen et al 11 worked on a Max-MEWMA chart in monitoring the mean vector and covariance matrix 2724

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“…Diverse literature on other control charting schemes formed on GLM is given in. [30][31][32][33][34][35] In previous studies, various control charts based on GLM are derived from residuals determined by generalized linear modelling. Jearkpaporn et al 36 and Amiri et al 37 proposed a charting structure to observe deviance residuals calculated from the GLM.…”

Section: Introductionmentioning

confidence: 99%

Efficient GLM‐based control charts for Poisson processes

Mahmood

Iqbal²,

Amin

2021

Quality & Reliability Eng

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The control charts are essential instruments that can impart crucial insights to quality controllers for maintaining the productivity of manufacturing processes. The conventional charting designs are based on a single study variable without exerting auxiliary information. Control charts derived from simple linear regression, generally with normality assumption, are one straightforward way of overcoming this difficulty. But, for a count distributed process, the generalized linear model (GLM) based strategy yields better outcomes. Hence, this study presents GLM-based progressive mean (PM) and double progressive mean (DPM) charting structures by employing the standardized residuals of the Poisson regression model. The functioning of the suggested and existing schemes (i.e., SR-EWMA) is investigated in the matter of run length distributions. The comparative analysis demonstrated that PM structures based on standardized residuals (i.e., SR-PM and SR-DPM) outperform the existing counterpart (i.e., SR-EWMA). Specifically, the SR-DPM chart is found to be more productive in identifying increasing alterations in the process mean. Finally, a case study about a 3D manufacturing procedure is presented to accentuate the significance of the suggested methods.

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Memory type control charts with inverse-Gaussian response: An application to yarn manufacturing industry

Cited by 21 publications

References 50 publications

The generalized linear model‐based exponentially weighted moving average and cumulative sum charts for the monitoring of high‐quality processes

The generalized linear model‐based exponentially weighted moving average and cumulative sum charts for the monitoring of high‐quality processes

On the multivariate progressive control chart for effective monitoring of covariance matrix

Efficient GLM‐based control charts for Poisson processes

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