Question 9.10: The thickness of the silicon dioxide layer on a semiconducto...

The thickness of the silicon dioxide layer on a semiconductor wafer is crucial to its performance. In the article “Virgin Versus Recycled Wafers for Furnace Qualification: Is the Expense Justified?” (V. Czitrom and J. Reece, Statistical Case Studies for Process Improvement, SIAM-ASA, 1997:87- 103), oxide layer thicknesses were measured for three types of wafers: virgin wafers, wafers recycled in-house, and wafers recycled by an external supplier. In addition, several furnace locations were used to grow the oxide layer. A two-way ANOVA for three runs at one wafer site for the three types of wafers at three furnace locations was performed. The data are presented in the following table, followed by the results (from MINITAB).

\begin{array}{cllll}\hline \text{Furnace Location}& \text{Wafer Type}& Oxide& Layer& Thickness\\\hline 1 & \text{Virgin}& 90.1 & 90.7 & 89.4 \\1 & \text{In-house}& 90.4 & 38.8 & 90.6 \\1 & \text{External}& 92.6 & 90.0 & 93.3 \\2 & \text{Virgin}& 91.9 & 88.6 & 89.7 \\2 & \text{In-house}& 90.3 & 91.9 & 91.5 \\2 & \text{External}& 88.3 & 88.2 & 89.4 \\3 & \text{Virgin}& 88.1 & 90.2 & 86.6 \\3 & \text{In-house}& 91.0 & 90.4 & 90.2 \\3 & \text{External}& 91.5 & 89.8 & 89.8 \\\hline\end{array}

Since recycled wafers are cheaper, the company hopes that there is no difference in the oxide layer thickness among the three types of chips. If possible, determine whether the data are consistent with the hypothesis of no difference. If not possible, explain why not.