Comparisons of the symmetric and asymmetric control limits for and R charts

Chen, Huifen; Kuo, Wei-Lun

doi:10.1016/j.cie.2010.08.021

Cited by 11 publications

(5 citation statements)

References 9 publications

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“…The results of Kao and Ho demonstrated that for four non‐normal distributions, the performance of range charts is worse than that under normal condition. Meanwhile, numerous papers show that the performance of the control charts with asymmetric control limits is better than those with symmetric control limits when the underlying distributions are skewed . Therefore, the traditional Shewhart control charts can not be applied to the processes whose distributions are heavily skewed.…”

Section: Introductionmentioning

confidence: 99%

“…Meanwhile, numerous papers show that the performance of the control charts with asymmetric control limits is better than those with symmetric control limits when the underlying distributions are skewed. [14][15][16][17][18][19] Therefore, the traditional Shewhart control charts can not be applied to the processes whose distributions are heavily skewed. Thus, it needs to design new control charts for monitoring the changes of these skewed distributions.…”

Section: Introductionmentioning

confidence: 99%

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Control Charts For Monitoring The Weibull Shape Parameter Based On Type‐II Censored Sample

Guo

Wang

2012

Quality & Reliability Eng

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In this paper, a new statistic is proposed to monitor the Weibull shape parameter when the sample is type II censored. The one‐sided and two‐sided average run length‐unbiased control charts are derived based on the new monitoring statistic. The control limits of the proposed control charts depend on the sample size, the failure number and the false alarm rate. Using Monte Carlo simulation, the performance of the proposed control charts is studied and compared with the range‐based charts proposed by Pascual and Li (2012), which is equivalent to the proposed control charts when r = 2. The simulation results show that the proposed control charts perform better than the ones of Pascual and Li (2012). This paper also evaluates the effects of parameter estimation on the proposed control charts. Finally, an example is used to illustrate the proposed control charts. Copyright © 2012 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Control Charts For Monitoring The Weibull Shape Parameter Based On Type‐II Censored Sample

Guo

Wang

2012

Quality & Reliability Eng

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“…Recently, there has been a great deal of work on the control charts with asymmetric control limits which are constructed for the skewed population. The first approach is to derive the exact distributions of sample statistics to construct location and dispersion control charts, some of which include [2,[6][7][8][9]. The advantage of these charts is that it provides a close form of control limits and seems to work adequately when the empirical distribution of the sample statistic is close to the exact distribution.…”

Section: Introductionmentioning

confidence: 99%

Asymmetric Control Limits for Weighted-Variance Mean Control Chart with Different Scale Estimators under Weibull Distributed Process

Zhou

et al. 2022

Mathematics

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Shewhart charts are the most commonly utilised control charts for process monitoring in industries with the assumption that the underlying distribution of the quality characteristic is normal. However, this assumption may not always hold true in practice. In this paper, the weighted-variance mean charts are developed and their population standard deviation is estimated using the three subgroup scale estimators, namely the standard deviation, median absolute deviation and standard deviation of trimmed mean for monitoring Weibull distributed data with different coefficients of skewness. This study aims to compare the out-of-control average run length of these charts with the pre-determined fixed value of the in-control ARL in terms of different scale estimators, coefficients of skewness and sample sizes via extensive simulation studies. The results indicate that as the coefficients of skewness increase, the charts tend to detect the out-of-control signal more rapidly under identical magnitude of shift. Meanwhile, as the size of the shift increases under the same coefficient of skewness, the proposed charts are able to locate the shifts quicker and the similar scenarios arise as a sample size raised from 5 to 10. A real data set from survival analysis domain which, possessing Weibull distribution, was to demonstrate the usefulness and applicability of the proposed chart in practice.

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“…For monitoring a skewed distribution with known parameters and estimated parameters, Chen and Cheng investigated the effect of non‐normality on the control limits of the chart. Chen and Kuo compared the symmetric and asymmetric limits for monitoring skewed distribution. Abbasi and Guillen applied bootstrap methods to construct control limits for the Weibull, Pareto, Burr XII, and Birnbaum‐Saunders distributions.…”

Section: Introductionmentioning

confidence: 99%

EWMA chart with variable sample size and sampling interval for monitoring Pareto data with estimated parameters

Cheng

Wang

2018

Quality & Reliability Eng

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The Pareto distribution has been widely used to model data in numerous areas including actuarial science, climatology, economics, finance, and reliability. The exponential weighted moving average (EWMA) chart with variable sample size and sampling interval (VSSI) is quicker than EWMA chart, EWMA chart with variable sample size (VSS), and EWMA chart with variable sampling interval (VSI) in detecting the mean shifts of a normal process. In this study, we present an EWMA‐VSSI chart to monitor the Pareto data with estimated parameters. The average time to signal (ATS) is computed by using the Markov chain approach. The results indicate that the proposed chart performs better than the other EWMA charts with fixed sample size, VSS, and VSI in terms of ATS. The design parameters of the proposed control charts are given in order to expedite the use of the chart by practitioners. Two examples are used to illustrate the application of the proposed control charts.

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Comparisons of the symmetric and asymmetric control limits for and R charts

Cited by 11 publications

References 9 publications

Control Charts For Monitoring The Weibull Shape Parameter Based On Type‐II Censored Sample

Control Charts For Monitoring The Weibull Shape Parameter Based On Type‐II Censored Sample

Asymmetric Control Limits for Weighted-Variance Mean Control Chart with Different Scale Estimators under Weibull Distributed Process

EWMA chart with variable sample size and sampling interval for monitoring Pareto data with estimated parameters

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