Title :
On the False-Positive Rate of Statistical Equipment Comparisons Based on the Kruskal–Wallis H Statistic
Author :
De Vries, Dirk K. ; Chandon, Yves
Author_Institution :
NXP Semicond., Crolles
Abstract :
Using Monte Carlo simulation, we investigate the accuracy of the chi2 approximation used in statistical equipment comparison based on the Kruskal-Wallis H statistic. We show that this approximation is conservative and gives an incorrect false-positive rate on individual steps as well as on the full process flow statistical equipment comparison. Alternative approximations of Wallace are investigated and these are shown to perform significantly better in analysis of datasets typical of semiconductor manufacturing. Wallace approximations also improve the ranking of signals.
Keywords :
Monte Carlo methods; nonparametric statistics; semiconductor device manufacture; semiconductor technology; statistical testing; ANOVA; Kruskal-Wallis H statistical test; Kruskal-Wallis test; Monte Carlo simulation; Wallace approximations; Wilcoxon rank sum test; beta approximation; chi-square approximation; nonparametric tests; semiconductor manufacturing yield; statistical equipment comparisons; Analysis of variance; Data analysis; Manufacturing processes; Performance analysis; Semiconductor device manufacture; Statistical analysis; Statistical distributions; Statistics; Terminology; Testing; ANOVA; Kruskal–Wallis test; Mann–Whitney; Wilcoxon rank sum test; beta approximation; chi-square; commonality analysis; nonparametric tests;
Journal_Title :
Semiconductor Manufacturing, IEEE Transactions on
DOI :
10.1109/TSM.2007.901398