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This paper aims to compare the performances of modified confidence intervals based on robust scale estimators with classical confidence interval for process capability index (Cp) when the process has a non-normal distribution. The estimated coverage probability and the average width of the confidence intervals were obtained by a Monte-Carlo simulation under different scenarios. Simulation results showed that the modified confidence intervals performed well in terms of coverage probability and average width for all cases. Two real-life numerical examples from industry are analyzed to illustrate the performance and the implementation of the classical and modified confidence intervals for the process capability index (Cp) which also supported the results of the simulation study to some extent.

This paper aims to compare the performance of proposed confidence intervals for population coefficient of variation (CV) with the existing confidence intervals, namely, McKay, Miller, and Gulher et al. confidence intervals under both symmetric and skewed distributions. We observed that the proposed augmented-large-sample (AA&K-ALS) confidence interval performed well in terms of coverage probability in all cases. The large-sample (AA&K-LS) and adjusted degrees of freedom (AA&K-ADJ) confidence intervals had much lower coverage probability than the nominal level for skewed distributions. However, the average widths of the AA&K-LS confidence interval are narrower than that of the rest confidence intervals. Two real-life data are analyzed to illustrate the implementation of the several methods .

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.