The total median in statistical quality control

Figueiredo, Fernanda; Gomes, M. Ivette

doi:10.1002/asmb.545

Cited by 8 publications

(7 citation statements)

References 12 publications

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“…Finally we note that the TMd statistic converges to the median value of the underlying distribution, and thus, for symmetric distributions, it is an unbiased estimator for the process mean value (see Figueiredo & Gomes, 2004). In general, it is not possible to obtain the exact distribution of the TMd statistic, but we easily obtain accurate quantiles by simulation.…”

Section: The Total Median Statisticmentioning

confidence: 96%

“…Note that these probabilities are independent of the underlying distribution F and they depend only on the sample size n. Details to obtain the a i,j,n can be found in Cox and Iguzquiza (2001) and Figueiredo and Gomes (2004). By definition, given in Equation (1), the total median statistic, TMd, is a linear combination of all the possible values of the BMd, where the weights are the previous probabilities a i,j,n , and after simple calculations it can be written as a linear combination of the sample order statistics.…”

Section: The Total Median Statisticmentioning

confidence: 99%

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The total median statistic to monitor contaminated normal data

Figueiredo

Gomes

2016

Quality Technology & Quantitative Management

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Despite the advantages of the use of the normal distribution in Statistical Quality Control, the normality assumption is too restrictive for modelling real data sets, which usually exhibit asymmetry or tails heavier than the normal tails. But even in potential normal situations, there is often a small to moderate percentage of contamination in the data. In this paper, we analyze the efficiency and robustness of the total median statistic in comparison with the sample mean and the sample median to estimate the mean value of symmetric contaminated normal distributions, close to the normal, but with heavier-than-normal tails. We also compare the performance of the total median and the sample mean charts to monitor the mean value of such processes. The simulation results lead us to suggest the use of the total median statistic due to its efficiency and degree of robustness. ARTICLE HISTORY

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Section: The Total Median Statisticmentioning

confidence: 96%

Section: The Total Median Statisticmentioning

confidence: 99%

The total median statistic to monitor contaminated normal data

Figueiredo

Gomes

2016

Quality Technology & Quantitative Management

Self Cite

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“…With a BP of 0.5, the estimate is still bounded even when half of the data is "bad" (Rousseeuw and Croux, 1993). Moreover, its efficiency increases and outperforms ̅ as tails of a distribution become heavier or more skewed, suggesting higher power (Figueiredo and Gomes, 2004).…”

Section: Descriptions Of Robust Estimatorsmentioning

confidence: 98%

Robust Synthetic Control Charting

Rahman¹,

Syed-Yahaya²,

Atta³

2021

IJTech

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The proposal of synthetic charting is based on the normality assumption. This assumption, however, is hard to attain in practice. Therefore, it is important to examine how the chart would response under some types of non-normal data. The focus of this article is to monitor location shifts using a synthetic chart and to validate its performance under the g-and-h distributions. This study shows that the effect of non-normality on the standard synthetic chart is not trivial, especially when the underlying distributions are heavy-tailed. With these types of distribution, Phase II monitoring of location using median-based estimators is advisable. In doing so, the synthetic chart is more robust to departure in the normality assumption with little effect on its out-of-control performance. This paper shows how the synthetic parameters should be attained to reflect the use of the modified one-step M-estimator (MOM) in its Winsorized version, and the median for Phase II. The assessment is based on the average run length and supported by the extra quadratic loss function. Finally, the practical application of the proposed synthetic charts is illustrated using real data.

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“…14 In SPM applications, in which in-control process distribution is assumed to be skewed/long-tailed, 15 robust statistics were found to show good performance for determining CLs in traditional control charts, 16 cumulative sum, and EWMA structures, 17 or in constructing robust control chars. [18][19][20][21] Similarly, for in-control processes assumed to consist of normally distributed data with temporary outliers in Phase I (the view also adopted in the current study), performance of "outlier resistant statistics," such as trimmed mean (TM) and interquartile range (IQR), in estimating of CLs was shown to surprass that of traditional estimators. 22,23 Although asymptotic convergence properties were questioned, 24 incorporation robust statistics into a reweighting scheme was shown to improve monitoring performance, possibly due to desirable finite sample properties of the reweighted robust estimators.…”

Section: Introductionmentioning

confidence: 99%

Revisiting reweighted robust standard deviation estimators for univariate Shewhart S‐charts

Mutlu

Alakent

2018

Quality & Reliability Eng

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Phase I outliers, unless screened during process parameter estimation, are known to deteriorate Phase II performance of process control charts. Reweighting estimators, ie, trimming outlier subgroups and individual observations, were suggested in the literature to improve both the robustness and efficiency of the resulting parameter estimates. In the current study, effects of various reweighted estimators at different trimming levels on the Phase II performance of S‐charts are elucidated using computer simulations including isolated and mixtures of contamination models. Outlier magnitudes in the simulations are held at a moderately low level to mimic industrial practice. Subtleties, such as varying Type I error rate among different trimming levels with respect to quantiles of dispersion estimates, prevent a single method to be revealed as the best performing one under all circumstances, and choice of estimators and trimming levels should depend on the number of subgroups in Phase I and the specifics of the process. Nevertheless, S‐chart using scale M‐estimator with logistic ρ and location M‐estimator at 2% trimming generally stands out in terms of Phase II performance, and high trimming levels are particularly recommended for high number of Phase I subgroups.

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The total median in statistical quality control

Cited by 8 publications

References 12 publications

The total median statistic to monitor contaminated normal data

The total median statistic to monitor contaminated normal data

Robust Synthetic Control Charting

Revisiting reweighted robust standard deviation estimators for univariate Shewhart S‐charts

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