Two different plasma etchers in a semiconductor factory have the same mean etch rate

Chapter 7, Problem 7-32

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Two different plasma etchers in a semiconductor factory have the same mean etch rate . However, machine 1 is newer than machine 2 and consequently has smaller variability in etch rate. We know that the variance of etch rate for machine 1 is and for machine 2 it is . Suppose that we have independent observations on etch rate from machine 1 and independent observations on etch rate from machine 2. (a) Show that 1 11 2 2 is an unbiased estimator of for any value of between 0 and 1. (b) Find the standard error of the point estimate of in part (a). X X n2 n1 2 2 a2 1 2 1 2 . S2 p 1n1 12 S2 1 1n2 12 S2 2 n1 n2 2 2 1 2 2 2 X1 X2 (c) What value of would minimize the standard error of the point estimate of ? (d) Suppose that and . What value of would you select to minimize the standard error of the point estimate of ? How bad would it be to arbitrarily choose in this case? 7-