This paper aims to modify Shewhart, the weighted variance and skewness correction methods in industrial statistical process control. The robust and asymmetric control limits of range chart are constructed to use in contaminated and skewed distributed process. The way of construction of control limits is simple and corresponds to three methods in which sample range estimator is replaced with the robust interquartile range. These three modified methods are evaluated in terms of their type I risks and average run length by using simulation study. The performance of the proposed range charts is assessed when the Phases I and II data are uncontaminated and contaminated. The Weibull, gamma and lognormal distributions are chosen since they can represent a wide variety of shapes from nearly symmetric to highly skewed.

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<p>In this study, robust Brown-Forsythe and robust Modified Brown-Forsythe ANOVA tests are proposed to take into consideration heteroscedastic and non-normality data sets with outliers. The non-normal data is assumed to be a two parameters Weibull distribution. Robust proposed tests are obtained by using robust mean and variance estimators based on median=MAD and median=Qn methods instead of maximum likelihood. The behaviors of the robust proposed and classical ANOVA tests are examined by simulation study. The results shows that the proposed robust tests have good performance especially in the presence of heteroscedasticity and contamination.</p>

In this paper the control limits of \(\bar{X}\) and \(R\) control charts for skewed distributions are obtained by considering the classic, the weighted variance (\(\mathit{WV}\)), the weighted standard deviations (\(\mathit{WSD}\)) and the skewness correction (\(\mathit{SC}\)) methods. These methods are compared by using Monte Carlo simulation. Type I risk probabilities of these control charts are compared with respect to different subgroup sizes for skewed distributions which are Weibull, gamma and lognormal. Simulation results show that Type I risk of \(\mathit{SC}\) method is less than that of other methods. When the distribution is approximately symmetric, then the Type I risks of Shewhart, \(\mathit{WV}\) , \(\mathit{WSD}\), and \(\mathit{SC}\) \(\bar{X}\) charts are comparable, while the \(\mathit{SC}\) \(R\) chart has a noticeable smaller Type I risk.

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