A control chart using an auxiliary variable and repetitive sampling for monitoring process mean

Lee, Hyeseon; Aslam, Muhammad; Shakeel, Qurat-ul-ain; Lee, Wonji; Jun, Chi‐Hyuck

doi:10.1080/00949655.2014.970553

Cited by 39 publications

(19 citation statements)

References 28 publications

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“…The performance of the proposed CUSUM charts is compared with that of some existing control charts such as the CUSUM chart introduced by Roberts [3], Mean-FIR control chart suggested by Lucas and Crosier [36], robust CUSUM charts based on median, Mid-Range (MR), and Hodges-Lehmann (HL) and Tri-Mean (TM) suggested by Nazir et al [37]. Moreover, the per-formance of the proposed charts is also evaluated in comparison to the auxiliary information based M-type control chart introduced by Riaz [21], the modi cation of M-type charts by using repetitive sampling proposed by Lee et al [20], and the combined Shewhart CUSUM (CSC) charts suggested by Sanusi et al [28]. When n = 5, k = 0:5, xy = 0:75, and ARL 0 = 370, the proposed auxiliary information based CUSUM control charts using E 1 , E 2 , and E 3 considerably outperform the existing CSC control charts for small to Table 10.…”

Section: Comparison Of the Proposed And Existing Control Chartsmentioning

confidence: 99%

“…A similar comparison can be made for various combinations of n, k, and xy . A comparison between the proposed CUSUM charts and M-Type control charts of Riaz [21] and Lee et al [20] is made for n = 20 and xy = 0:50 at ARL 0 = 220. Riaz [21] did not report the ARL performance of his chart; however, Lee et al [20] provided the ARL comparison between their chart and that of Riaz [21].…”

Section: Comparison Of the Proposed And Existing Control Chartsmentioning

confidence: 99%

“…A comparison between the proposed CUSUM charts and M-Type control charts of Riaz [21] and Lee et al [20] is made for n = 20 and xy = 0:50 at ARL 0 = 220. Riaz [21] did not report the ARL performance of his chart; however, Lee et al [20] provided the ARL comparison between their chart and that of Riaz [21]. The suggested charts have shown a better shift detection ability in the process mean than the auxiliary information based M-Type control charts proposed by Riaz [21] and Lee et al [20].…”

Section: Comparison Of the Proposed And Existing Control Chartsmentioning

confidence: 99%

“…Few researchers have presented their ideas in the context of utilizing auxiliary information in control charting structures (see [16{19]). The product-di erence type estimator of the mean was used by Lee et al [20] for process monitoring under repetitive sampling. It is based on inner and outer control limits so that repetitive sampling is allowed when the monitoring statistic lies between the inner and outer limits.…”

Section: Introductionmentioning

confidence: 99%

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On designing CUSUM charts using ratio-type estimators for monitoring the location of normal processes

2018

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A control chart is an important tool in statistical process control that plays a signi cant role in monitoring and identifying variations in production processes. The Shewhart, the cumulative sum (CUSUM), and the Exponentially Weighted Moving Average (EWMA) control charts are commonly used for detecting process shifts. The CUSUM and the EWMA control charts are more sensitive in detecting smaller shifts, whereas the typical Shewhart chart is sensitive to large process shifts. The present study incorporates ratiotype estimators of the population mean based on auxiliary information in the CUSUM charting structure for monitoring the location of the normal processes. These estimators are more e cient than simple mean estimator in the presence of a high correlation between the study and the auxiliary variables. The Average Run Length (ARL), the standard deviation of run length, and the extra quadratic loss are used to measure the performance of the proposed charts. The proposed charts are compared with the existing CUSUM, CUSUM-FIR, and some other auxiliary information-based control charts on the basis of out-of-control ARLs. The comparison reveals the superiority of the suggested charts over the other existing charts. An illustrative example is also provided for the performance evaluation of the proposed charts.

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Section: Comparison Of the Proposed And Existing Control Chartsmentioning

confidence: 99%

Section: Comparison Of the Proposed And Existing Control Chartsmentioning

confidence: 99%

Section: Comparison Of the Proposed And Existing Control Chartsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On designing CUSUM charts using ratio-type estimators for monitoring the location of normal processes

2018

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“…It is complicated to derive the distribution of C w , i , so, we will develop a Monte Carlo simulation algorithm to find the average run lengths of the proposed control chart by following Lee et al. This algorithm is stated as follows: Computation of the proposed EWMA–CUSUM statistic.…”

Section: Proposed Control Chartmentioning

confidence: 99%

A Mixed EWMA–CUSUM Control Chart for Weibull‐Distributed Quality Characteristics

Aslam

2016

Quality & Reliability Eng

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The control charts have been widely used for process monitoring. Shewhart control chart has ability to detect large disturbances in the process. The EWMA and CUSUM charts have ability to detect a small change in the manufacturing process. In this paper, we will design a mixed EWMA-CUSUM control chart for Weibull-distributed quality characteristics. The Weibull distribution is one of the most popular distributions used to model failure mechanism because of flexible selection of shape and scale parameters. A Monte Carlo simulation is developed to assess the average run lengths for incontrol and out-of-control process. The comparison revealed that the proposed mixed chart is more sensitive to detect a small shift in the process.

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On a class of mixed EWMA‐CUSUM median control charts for process monitoring

Hussain

Wang

Ahmad

et al. 2020

Quality & Reliability Eng

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Monitoring of any manufacturing, production, or industrial process can be controlled and improved by removing these special cause of variations using control charts. Shewhart‐type control charts are effective to control a large amount of special variations, whereas, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts detect small and moderate variations efficiently in the process parameters. Monitoring of location parameter can be done with mean control charts under the assumption that the parameters are known or correctly estimated from in‐control samples and data are free from outliers (but in practice data occasionally have outliers). In this study, we have proposed generalized mixed EWMA‐CUSUM median control charts structures for known and unknown parameters based on auxiliary variables for detecting shifts in process location parameter. The proposed charts are compared with the corresponding charts for the mean, based on contaminated and uncontaminated data. Different performance measures are used to evaluate the performance of proposed control charts and revealed through results that the median‐based charts are more sensitive to detect a shift in process location parameter in the presence of outliers. An illustrative example using real data is also shown for practical consideration.

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A control chart using an auxiliary variable and repetitive sampling for monitoring process mean

Cited by 39 publications

References 28 publications

On designing CUSUM charts using ratio-type estimators for monitoring the location of normal processes

On designing CUSUM charts using ratio-type estimators for monitoring the location of normal processes

A Mixed EWMA–CUSUM Control Chart for Weibull‐Distributed Quality Characteristics

On a class of mixed EWMA‐CUSUM median control charts for process monitoring

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