Question

1. In Orthogonal Design for Process Optimization and Its Applications in Plasma Etching, G.Z. Yin and D.W. Jille describes an experiment to determine the effect of Hexafluoroethane C2F6 flowrate on the uniformity of the etch on a Silicon wafer used in integrated circuit manufacturing. Three flowrates are used in the experiment, and the resulting uniformity (in percent) for six replicates is shown below (SCCM: Standard Cubic Centimeters per Minute).

Hexafluoroethane Rate	Observations
(SCCM)
125	2.7	4.6	2.6	3	3.2	3.8
160	4.9	4.6	5	4.2	3.6	4.2
200	4.6	3.4	2.9	3.5	4.1	5.1

1. Write down the Null and Alternative hypotheses to test if at least one flowrate causes a different uniformity than the other uniformities. Define all the terms used.

2. What is the calculated Ftest statistic? What are the critical F value and the rejection region of H0 at α=5% ?

1. c. Test the hypotheses using the test statistic / critical value method (use your answers to (b), and (c)). Clearly interpret the test result in the context of the problem.
2. d. What is the P value for the test? Test the hypotheses using the P value. Do you get the same answer as (d)? If your answer is different, clearly interpret it.

Answer 1

Result:

Write down the Null and Alternative hypotheses to test if at least one flowrate causes a different uniformity than the other uniformities. Define all the terms used.

The three groups ( group 1 , group 2 and group 3) are flow rates with 125, 160 and 200.

µis the population mean.

Ho: µ₁= µ₂= µ₃

H₁: At least one of the mean is different from the others

What is the calculated Ftest statistic? What are the critical F value and the rejection region of H0 at α=5% ?

calculated Ftest statistic = 3.5856

critical F value = 3.68

Reject Ho if calculated F value > 3.68

c. Test the hypotheses using the test statistic / critical value method (use your answers to (b), and (c)). Clearly interpret the test result in the context of the problem.

calculated Ftest statistic 3.5856   < critical F value 3.68, Fail to reject Ho.

There is not sufficient evidence to conclude that at least one flowrate causes a different uniformity than the other uniformities.

d. What is the P value for the test? Test the hypotheses using the P value. Do you get the same answer as (d)? If your answer is different, clearly interpret it.

P value =0.0534 which is > 0.05 level of significance. Ho is not rejected. We get the same answer as above.

Excel calculations:

ANOVA: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Rate125	6	19.9	3.316666667	0.5777
Rate160	6	26.5	4.416666667	0.2737
Rate200	6	23.6	3.933333333	0.6747
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	3.6478	2	1.8239	3.5856	0.0534	3.6823
Within Groups	7.6300	15	0.5087
Total	11.2778	17
			Level of significance	0.05