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Control Charts are one of the most powerful tools used to detect aberrant behavior in industrial processes. A valid performance measure for a control chart is the average run length (ARL); which is the expected number of runs to get an out of control signal. At the same time, robust estimators are of vital importance in order to estimate population parameters. Median absolute deviation (MAD) and quantiles are such estimators for population standard deviation. In this study, alternative control charts to the Tukey control chart based on the robust estimators are proposed. To monitor the control chart's performance, the ARL values are compare for many symmetric and skewed distributions. The simulation results show that the in-control ARL values of proposed control charts are higher than Tukey's control chart in all cases and more efficient to detect the process mean. However, the out- of- control ARL values for the all control charts are worse when the probability distribution is non-normal. As a result, it is recommended to use control chart based on the estimator Qn for the process monitoring performance when data are from normal or non-normal distribution. An application example using real-life data is provided to illustrate the proposed control charts, which also supported the results of the simulation study to some extent.

In this study, we propose confidence intervals and their bootstrap versions for the difference of variances of two independent population using some robust variance estimators. The proposed confidence intervals are compared with Herbert confidence interval in terms of coverage probability and average width. A simulation study is conducted to evaluate performances of the proposed confidence intervals under different scenarios. The simulation results indicate that the coverage probabilities for the proposed confidence intervals are very close to nominal confidence levels when the difference of population variances is zero. Confidence interval based on binary distance produces the narrowest average widths. Herbert confidence interval have not perform well for skewed distribution populations. Confidence interval based on comedian is generally recommended when the difference of population variances for skewed distributions is not zero. Average widths of bootstrap percentile confidence intervals are smaller, and decreases as sample size and nominal size increases, as expected. Consequently, we recommend bootstrap percentile confidence interval based on binary distances for skewed distributions.