Consider an unreplicated 2^kfactorial, and suppose that one of the treatment combinations is missing. One logical approach to this problem is to estimate the missing value with a number that makes the highest order interaction estimate zero. Apply this technique to the data in Example 14-5, assuming that ab is missing. Compare the results of the analysis of the application of these data with the results in Example 14-5.

Example 14-5

An article in Solid State Technology [€œOrthogonal Design for Process Optimization and Its Application in Plasma Etching€ (May 1987, pp. 127€“132)] describes the application of factorial designs in developing a nitride etch process on a single-wafer plasma etcher. The process uses C2F6 as the reactant gas. It is possible to vary the gas flow, the power applied to the cathode, the pressure in the reactor chamber, and the spacing between the anode and the cathode (gap). Several response variables would usually be of interest in this process, but in this example, we concentrate on etch rate for silicon nitride. We use a single replicate of a 24 design to investigate this process. Because it is unlikely that the three- and fourfactor interactions are significant, we tentatively plan to combine them as an estimate of error. The factor levels used in the design follow:

Design Factor Level Gap (cm) Power (w) 275 325 CF, Flow Pressure (mTorr) 450 550 (SCCM) 125 200 Low (-) 0.80 1.20 High (+)