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A resolution III design in the five two-level factors could be obtained, and the number of treatment combinations reduced, by using a one-quarter fractional factorial in the two-level factors. The number of treatment combinations would now be reduced to 3 x 25'2 = 24. In this design, each of the three operators would have been running an independent replicate of a one-quarter fractional factorial in the five two-level factors. However, replicates were not needed to estimate the effects arising from the two-level factors (see the sample size discussion in the Data Collection Plan), nor were all eight values (from the 25"2 fractional factorial hidden replicates) needed for estimation of operator effects.

2. For the duration of the study, these values were treated as though they were known values subject to no variability. After choosing the levels for the standard specimens, the remainder of the experimental design was extremely simple as can be seen from Appendix A: five measurements per standard were taken every day for ten days. This statement is by no means an apology since simplicity was an important consideration in selecting an appropriate design for the gauge study. This was to assure that all tests would be conducted as specified, with no mistakes introduced by the operator during the tedious repetition of measurements.

1996. Montgomery, Douglas C. Design and Analysis of Experiments, fourth edition. , 1997. , and Graybill, Franklin A. Confidence Intervals on Variance Components. , 1992. This page intentionally left blank CHAPTER 2 PROMETRIX RS35e GAUGE STUDY IN FIVE TWO-LEVEL FACTORS AND ONE THREE-LEVEL FACTOR James Buckner, Barry L. Chin, and Jon Henri T he total measurement precision (variability) of a Prometrix RS35e automatic four- point prober tool was determined for two responses: wafer-to-wafer and within-wafer sheet resistance uniformity.

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Probability, random variables, stochastic processes: solution manual by Papoulis A., Pillai S.U.

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