scholarly journals One-sided 4-out-of-5 Run Rules Charts for the Multivariate Coefficient of Variation in the Finite Horizon Process

2021 ◽  
Vol 20 ◽  
pp. 455-460
Author(s):  
Khai Wah Khaw ◽  
Xin Ying Chew ◽  
Ming Ha Lee ◽  
Wai Chung Yeong ◽  
Sajal Saha
Keyword(s):  
Process Monitoring ◽  
Coefficient Of Variation ◽  
Flexible Manufacturing ◽  
Average Run Length ◽  
Past Research ◽  
Finite Horizon ◽  
Run Length ◽  
Multivariate Coefficient Of Variation ◽  
Run Rules ◽  
Made In

Quality improvement has been receiving great attention in industries. In recent years, the finite horizon process is commonly encountered in industries due to flexible manufacturing production. Past research works on finite horizon process monitoring are still limited. Because of this, one-sided 4-out-of-5 run rules charts are proposed to monitor the multivariate coefficient of variation in a finite horizon process. The performance measures of the proposed charts are derived using the Markov-chain approach. The proposed schemes can serve as a framework for practitioners who wish to perform process monitoring easily and efficiently. Numerical comparisons between the proposed and existing charts have been made, in terms of the truncated average run length and the expected truncated average run length criteria. The findings reveal that the proposed charts outperform the existing charts for detecting small and moderate process shifts in the finite horizon process.

One-sided control charts for monitoring the multivariate coefficient of variation in short production runs

2018 ◽  
Vol 41 (6) ◽  
pp. 1712-1728 ◽  
Author(s):  
Mahfuza Khatun ◽  
Michael BC Khoo ◽  
Ming Ha Lee ◽  
Philippe Castagliola
Keyword(s):  
Covariance Matrix ◽  
Process Monitoring ◽  
Coefficient Of Variation ◽  
Control Charts ◽  
Finite Horizon ◽  
New Method ◽  
The Mean ◽  
Multivariate Coefficient Of Variation ◽  
Study Process ◽  
Mean Vector

In production, it is common to deal with short production runs, where flexibility is required in the built-up of parts to produce numerous variants of manufactured goods. Monitoring the multivariate coefficient of variation (MCV) is an effective method to monitor the relative multivariate variability compared with the mean. Monitoring the relative multivariate variability is important when practitioners are not interested in the changes in the mean vector or the covariance matrix. Monitoring the univariate coefficient of variation in short production runs has already been successfully executed. In this paper, the statistical performance of one-sided charts for monitoring the MCV of a multivariate process with finite horizon is investigated. Prior to this work, no attempt has been made to study process monitoring of MCV in short production runs. Investigations are made when the exact shift size can be specified and when there is a random shift size. It is found that the proposed upward chart detects an increasing shift in the MCV quicker than its downward counterpart detects a decreasing shift, for the same shift size (from the nominal value). An example is presented to illustrate the implementation of the new method.

scholarly journals An Optimal Adaptive Variable Sample Size Scheme for the Multivariate Coefficient of Variation

2021 ◽  
Vol 9 (3) ◽  
pp. 681-693
Author(s):  
KHAI WAH KHAW ◽  
XINYING CHEW ◽  
MING HA LEE ◽  
WAI CHUNG YEONG
Keyword(s):  
Sample Size ◽  
Process Monitoring ◽  
Coefficient Of Variation ◽  
Markov Chain Model ◽  
Average Run Length ◽  
Industrial Process ◽  
Salient Feature ◽  
Numerical Comparison ◽  
Chain Model ◽  
Run Length

Development of an efficient process monitoring system has always received great attention. Previous studies revealed that the coefficient of variation (CV) is important in ensuring process quality, especially for monitoring a process where its process mean and variance are highly correlated. The fact that almost all industrial process monitoring involves a minimum of two or more related quality characteristics being monitored simultaneously, this paper incorporates the salient feature of the adaptive sample size VSS scheme into the standard multivariate CV (MCV) chart, called the VSS MCV chart. A Markov chain model is developed for the derivation of the chart’s performance measures, i.e the average run length (ARL), the standard deviation of the run length (SDRL), the average sample size (ASS), the average number of observations to signal (ANOS) and the expected average run length (EARL). The numerical comparison shows that the proposed chart prevails over the existing standard MCV chart for detecting small and moderate upward and downward MCV shifts.

scholarly journals Evaluating the Steady-state Performance of the Synthetic Coefficient of Variation Chart

2021 ◽  
Vol 29 (3) ◽  
Author(s):  
Ming Hui Chew ◽  
Wai Chung Yeong ◽  
Muzalwana Abdul Talib ◽  
Sok Li Lim ◽  
Khai Wah Khaw
Keyword(s):  
Steady State ◽  
Process Monitoring ◽  
Coefficient Of Variation ◽  
Average Run Length ◽  
Small Sample ◽  
State Condition ◽  
Steady State Condition ◽  
Actual Application ◽  
Small Sample Sizes ◽  
State Assumption

The synthetic coefficient of variation (CV) chart is attractive to practitioners as it allows for a second point to fall outside the control limits before deciding whether the process is out-of-control. The existing synthetic CV chart is designed with a head-start feature, which shows an advantage under the zero-state assumption where shifts happen immediately after process monitoring has started. However, this assumption may not be valid as shifts may happen quite some time after process monitoring has started. This is called the steady-state condition. This paper evaluates the performance of the chart under the steady-state condition. It is shown that the steady-state out-of-control average run length (ARL1) is substantially larger than the zero-state ARL1, hence larger number of samples are needed to detect the out-of-control condition. From the comparison with other CV charts, the steady-state synthetic CV chart does not show better performance, especially for small sample sizes and shift sizes. Hence, the synthetic CV chart is not recommended to be adopted under the steady-state condition, and its good performance is only applicable under the zero-state assumption. The results of this paper enable practitioners to be aware that the performance of the synthetic CV chart may be inferior under actual application (when shifts do not happen at the beginning of process monitoring) compared to its zero-state performance.

scholarly journals Optimal designs of the side sensitive synthetic chart for the coefficient of variation based on the median run length and expected median run length

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0255366
Author(s):  
Waie Chung Yeong ◽  
Ping Yin Lee ◽  
Sok Li Lim ◽  
Peh Sang Ng ◽  
Khai Wah Khaw
Keyword(s):  
Optimal Design ◽  
Coefficient Of Variation ◽  
Average Run Length ◽  
Length Distribution ◽  
Median Number ◽  
False Alarms ◽  
Actual Performance ◽  
Run Length ◽  
Run Length Distribution ◽  
Synthetic Chart

The side sensitive synthetic chart was proposed to improve the performance of the synthetic chart to monitor shifts in the coefficient of variation (γ), by incorporating the side sensitivity feature where successive non-conforming samples must fall on the same side of the control limits. The existing side sensitive synthetic- γ chart is only evaluated in terms of the average run length (ARL) and expected average run length (EARL). However, the run length distribution is skewed to the right, hence the actual performance of the chart may be frequently different from what is shown by the ARL and EARL. This paper evaluates the entire run length distribution by studying the percentiles of the run length distribution. It is shown that false alarms frequently happen much earlier than the in-control ARL (ARL0), and small shifts are often detected earlier compared to the ARL1. Subsequently, this paper proposes an alternative design based on the median run length (MRL) and expected median run length (EMRL). The optimal design based on the MRL shows smaller out-of-control MRL (MRL1), which shows a quicker detection of the out-of-control condition, compared to the existing design, while the results from the optimal design based on the EMRL is similar to that of the existing designs. Comparisons with the synthetic-γ chart without side sensitivity shows that side sensitivity reduces the median number of samples required to detect a shift and reduces the variability in the run length. Finally, the proposed designs are implemented on an actual industrial example.

DESIGN OF THE SYNTHETIC MULTIVARIATE COEFFICIENT OF VARIATION CHART BASED ON THE MEDIAN RUN LENGTH

2020 ◽  
Vol 9 (9) ◽  
pp. 7397-7406
Author(s):  
Ming Ha Lee ◽  
Victor Y. C. Lim ◽  
Xin Ying Chew ◽  
Man F. Lau ◽  
Sebastian Yakub ◽  
...  
Keyword(s):  
Coefficient Of Variation ◽  
Run Length ◽  
Multivariate Coefficient Of Variation

An Optimal Design of the Synthetic Coefficient of Variation Chart Based on the Median Run Length

2020 ◽  
pp. 2150018
Author(s):  
Wai Chung Yeong ◽  
Sok Li Lim ◽  
Michael Boon Chong Khoo ◽  
Khai Wah Khaw ◽  
Peh Sang Ng
Keyword(s):  
Coefficient Of Variation ◽  
Average Run Length ◽  
Moving Average ◽  
Small Sample ◽  
False Alarms ◽  
Small Shift ◽  
Run Length ◽  
Ewma Chart ◽  
Synthetic Chart ◽  
Run Lengths

The synthetic coefficient of variation (CV) chart is currently evaluated based only on the average run length (ARL), but this paper evaluates the chart based on different percentiles of the run length, which shows that false alarms frequently happen earlier than that shown by the in-control ARL (ARL[Formula: see text], and for small sample sizes and shift sizes, the out-of-control condition is frequently detected before what is shown by the out-of-control ARL (ARL[Formula: see text]. Furthermore, the run lengths show large variations. Hence, the chart’s performance could not be interpreted only in terms of the ARL. This paper proposes the median run length (MRL)-based design for the synthetic CV chart, which is not available in the literature. The MRL-based design shows larger MRL0 and ARL0, smaller MRL1 and ARL1, and less variation in the out-of-control run lengths compared to existing ARL-based designs. However, the in-control run lengths show more variation. Comparisons show that the synthetic chart outperforms the VSS and Shewhart charts, while comparison with the Exponentially Weighted Moving Average (EWMA) chart shows that although it outperforms the synthetic chart based on the ARL for small shift sizes, the synthetic chart shows better performance in terms of the MRL. The MRL-based synthetic chart is then implemented on an industrial example.

scholarly journals Treating Measurement Errors in the Run Rule Schemes Integrated with Shewhart X ¯ Chart

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
TingTing Shan ◽  
WeiDong Huang
Keyword(s):  
Quality Control ◽  
Measurement Errors ◽  
Average Run Length ◽  
Error Model ◽  
Quality Characteristic ◽  
Control Applications ◽  
Run Length ◽  
Negative Effect ◽  
Characteristic Two ◽  
Run Rules

In modern quality control applications, there often exist significant measurement errors because observations are measured quickly in time order. As a result, the errors influence the power of a control chart to detect a given change in the process parameter(s) of a quality characteristic. In this paper, by using a covariate error model, the properties of the Shewhart X ¯ chart integrated with run rules are investigated when errors exist in the measurement of quality characteristic. Two metrics, the average run length and 95% quantile of the run length, are adopted to evaluate the chart’s performance for different mean shifts and sample sizes. Numerous simulations are conducted, and the results indicate that the errors in the measurement significantly affect the performance of the run rule X ¯ chart, especially when the errors are large. To reduce this negative effect on the run rule X ¯ chart, measuring more times of each item in each subgroup and increasing the coefficient in the covariate error model are shown to be good choices for practitioners.

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