and R control charts based on weighted variance with left-right tail-weighted ratio for skewed distributions

Kao, Shih-Chou

doi:10.1080/03610918.2015.1060331

Cited by 2 publications

(3 citation statements)

References 21 publications

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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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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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“…In this case, it is necessary to test the normality hypothesis, using statistical tests, before the data analysis is started, in order to avoid the consequences of misusing these graphs ( [17].) [11] obtained the X and R control charts in skewed data using Generalized Lambda Distribution (GLD), the percentile matching method and weighted variance method with left and right tail. [12] also obtained some control charts based on weighted bootstrap using some weights for each stratuum in skewed populations.…”

Section: Introductionmentioning

confidence: 99%

“…[12] also obtained some control charts based on weighted bootstrap using some weights for each stratuum in skewed populations. The novelty of this paper with respect to [11] and [12] consists in introducing the application of Extended Generalized Lambda distribution (XGLD) for inividual sampling scheme when the population doesn't necessarily follow the normal distriution.…”

Section: Introductionmentioning

confidence: 99%

The Use of the Extended Generalized Lambda Distribution for Controlling the Statistical Process in Individual Measurements

Noorian

Ahmadabadi

2018

Stat., optim. inf. comput.

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In quality control (QC) of the individual pieces tested, the distribution of the intended variable is not normal in many cases. Therefore, the use of conventional statistical methods to design the control charts (X chart) can lead to misleading and inaccurate results, and hence, it can cause problems to users; because in such a situation it would not be expected that the failure in the production line will be detected in a timely manner. Therefore, in this study, the use of Extended Generalized Lambda distribution (XGLD) has been proposed for approximating the statistical distribution of data and finding a quality control chart based on it. For this purpose, the distribution function of data was firstly estimated by the XGLD, and then, based on this distribution, the control limits were calculated. The research data consists of the tensile strength of 149 aluminum plates categorized into 22 classes. For the goodness of fit test, Chi-square test was utilized and to evaluate the effectiveness of the proposed model, the average run length (ARL) method was used. The results showed that the ARL values in the proposed method are lower than that in the conventional method. Since this is true at all points, it can be concluded that the use of the new method can lead to the faster detection of the systems failure and consequently, the subsequent costs can be reduced. In addition, since the XGLD is a highly flexible distribution and can estimate many conventional (and even unconventional) distributions with high precision, the use of the proposed method instead of using other cases which are based on distributions other than normal, will increase the accuracy of the systems failure detection.

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and R control charts based on weighted variance with left-right tail-weighted ratio for skewed distributions

Cited by 2 publications

References 21 publications

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

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

The Use of the Extended Generalized Lambda Distribution for Controlling the Statistical Process in Individual Measurements

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