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

The study proposed the average and range control charts by considering the generalized lambda distribution, the percentile-based method, and the weighted variance with left-right tail-weighted ratio for skewed populations. When the underlying distribution is Weibull, Burr, gamma, lognormal, or inverse Gaussian, the proposed control charts have Type I risks, which are closer to 0.27% of the normal distribution, and they do not rapidly vary with sample sizes and the shape of a distribution. Type II risks of the proposed control charts are closer to those of the exact charts than to those of the skewness correction and weighted variance charts.