On the False-Positive Rate of Statistical Equipment Comparisons Based on the Kruskal-Wallis H Statistic

• Published in: IEEE transactions on semiconductor manufacturing Vol. 20; no. 3; pp. 286 - 292
• Main Authors: de Vries, D.K., Chandon, Y.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Analysis of variance; ANOVA; Applied sciences; Approximation; beta approximation; chi-square; commonality analysis; Computer simulation; Data analysis; Electronics; Exact sciences and technology; Kruskal-Wallis test; Mann-Whitney; Manufacturing processes; Mathematical analysis; Microelectronic fabrication (materials and surfaces technology); Monte Carlo methods; nonparametric tests; Performance analysis; Ranking; Semiconductor device manufacture; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Semiconductors; Statistical analysis; Statistical distributions; Statistics; Terminology; Testing; Wilcoxon rank sum test; beta approximation; Monte Carlo method; Microelectronic fabrication; chi-square; commonality analysis; ANOVA; Mann-Whitney; non- parametric tests; Numerical simulation; Kruskal-Wallis test; Wilcoxon rank sum test; Comparative study
• ISSN: 0894-6507; 1558-2345
• DOI: 10.1109/TSM.2007.901398

Using Monte Carlo simulation, we investigate the accuracy of the chi 2 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.