Group runs revised m -of- k runs rule control chart

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In this paper, we propose and study nonparametric exponentially weighted moving average (EWMA) control charts based on the sign statistic, which are suitable for detecting changes in process dispersion. The sign statistic is defined by using appropriate deciles of the in‐control process distribution. The statistical performances of the proposed charts are determined through Monte Carlo simulation. Practical guidelines are provided for the statistical designs of these charts. We evaluate the statistical performances of the proposed charts by comparing them with that of the deciles‐based CUSUM sign chart and the EWMA lnS2 chart. The comparisons show that the proposed charts are viable nonparametric methods for monitoring the process dispersion. Finally, we provide an illustrative example to demonstrate the implementation of the proposed charts in practice.

“…First, the zero‐state performance is used to design a control chart by fixing its in‐control zero‐state ARL value. Moreover, according to Knoth 41 (see also Chong et al 42 …”

Section: Measures Of Statistical Performance and Designs Of The Ewma ...mentioning

confidence: 99%

Section: Measures Of Statistical Performance and Designs Of The Ewma ...mentioning

confidence: 99%

Deciles‐based EWMA‐type sign charts for process dispersion

Godase

Rakitzis

Mahadik

et al. 2022

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“…This is because the computation time increases greatly as the size of the Markov chain transition probability matrix increases exponentially with

L_{1}^{'}

and

L_{2}^{'}

. It is interesting to note that this problem also happens for other GR‐type charts, see, for example, Chong et al From Table (Table ), for the same n and δ values, the value of ANOS 1, m (ssANOS 1, m ) generally decreases with an increase in m , except for some cases in Table when δ is large. This is due to the fact that the larger the number of phase I samples taken, the closer is the performance of the Case‐U SSMGR

\overset{X}{true}

chart to the corresponding Case‐K chart, ie, the ANOS 1, m (or ssANOS 1, m ) value decreases to indicate a better performance.…”

Section: Performance Analysis Of the Case‐u Ssmgr Truex¯ Chartmentioning

confidence: 99%

Optimal design of the side‐sensitive modified group runs (SSMGR) chart when process parameters are estimated

Chong

Khoo

Teoh

et al. 2018

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A side‐sensitive modified group runs (SSMGR) trueX¯ chart is commonly examined under the assumption of known process parameters (denoted as Case‐K). However, in practical situations, the process parameters are seldom known, and it is essential to estimate them from in‐control (IC) phase I samples. From the study of the minimum amount of phase I samples, m that is required by the SSMGR trueX¯ chart when the process parameters are estimated (represented as Case‐U), to achieve practically the same performance as that of the Case‐K, it was found that a huge number of IC phase I samples are needed. Due to time and cost factors, accumulating a substantial amount of IC phase I samples is difficult. To circumvent this problem, we study the optimal designs of the Case‐U SSMGR trueX¯ chart, based on both the zero and steady states' average number of observations to signal (ANOS) and expected ANOS (EANOS). Tables containing optimal charting parameters are provided to ease the implementation of the Case‐U SSMGR trueX¯ chart. By using these optimal parameters specifically designed for the Case‐U SSMGR trueX¯ chart, we can obtain similar zero and steady states' ANOS and EANOS performances to that of the Case‐K. The use of the optimal Case‐U SSMGR trueX¯ chart is demonstrated with real data taken from a hard‐bake process in a manufacturing company.

“…In terms of the effectiveness of the charts in detecting process mean shifts, Gadre et al 19 showed that the SSMGR

\overset{X}{true}

chart outperforms the Shewhart

\overset{X}{true}

, synthetic

\overset{X}{true}

, GR

\overset{X}{true}

, MGR

\overset{X}{true}

, and SSGR

\overset{X}{true}

charts. More recent extensions on the GR type charts include You et al, 20 Khoo et al, 21 Chong et al, 22 Saha et al, 23 Chong et al, 24 Mim et al, 25 and Gadre and Kakade 26 …”

Section: Introductionmentioning

confidence: 99%

Side‐sensitive modified group runs charts with and without measurement errors for monitoring the coefficient of variation

Saha

Khoo

Castagliola

et al. 2020

Self Cite

The coefficient of variation (CV) is used in process monitoring when the process mean and standard deviation are proportional to each other. In this work, a side‐sensitive modified group runs CV (SSMGR CV) chart is proposed for monitoring the process CV. The run length performance of the SSMGR CV chart is compared to those of the existing CV charts in terms of the average and standard deviation of the run length criteria. The SSMGR CV chart is found to outperform the existing CV charts. In addition, the run length performance of the SSMGR CV chart is also evaluated in the presence of measurement errors, as these errors are not only unavoidable in practice but they also affect the sensitivity of a control chart in detecting an out‐of‐control situation. The results obtained show that the accuracy and precision errors affect the performance of the SSMGR CV chart in detecting an out‐of‐control situation.