The time taken for an engine to reach stable operation was studied using a 2 level factorial experiment with three factors A, B and C. Two replications were carried out and the results are given below. Identify the significant variables and interactions. A B C Replication 1 Replication 2 -1 -1 -1 12 14 1 -1 -1 37 32 -1 1 -1 9 9 1 1 -1 35 42 -1 -1 1 24 28 1 -1 1 26 43 -1 1 1 31 21 1 1 1 38 27
Added by Akhil S.
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We have three factors (A, B, C) each at two levels (-1 and 1), and two replications for each combination of factor levels. Here's how the data looks in a table: | A | B | C | Replication 1 | Replication 2 | |---|---|---|---------------|---------------| | -1| -1| Show more…
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Seven factors are varied at two levels in an experiment involving only 16 trials. A $\frac{1}{8}$ fraction of a $2^{7}$ factorial experiment is used, with the defining contrasts being $A C D, B E F,$ and $C E G .$ The data are as follows: $$ \begin{array}{cc|lc} \text { Treat. } & & \text { Treat. } & \\ \text { Comb. } & \text { Response } & \text { Comb. } & \text { Response } \\ \hline(1) & 31.6 & a c g & 31.1 \\ a d & 28.7 & c d g & 32.0 \\ a b c e & 33.1 & \text { beg } & 32.8 \\ \text { cdef } & 33.6 & \text { adefg } & 35.3 \\ \text { acef } & 33.7 & \text { efg } & 32.4 \\ \text { bcde } & 34.2 & \text { abdeg } & 35.3 \\ \text { abdf } & 32.5 & \text { bcdf } g & 35.6 \\ \text { bf } & 27.8 & \text { abcfg } & 35.1 \end{array} $$ Perform an analysis of variance on all seven main effects, assuming that interactions are negligible. Use a 0.05 level of significance.
$2^{k}$ Factorial Experiments and Fractions
Analysis of Fractional Factorial Experiments
A factorial experiment involving two levels of factor A and three levels of factor $\mathrm{B}$ resulted in the following data. Test for any significant main effects and any interaction. Use $\alpha=.05$.
A manufacturing company designed a factorial experiment to determine whether the number of defective parts produced by two machines differed and if the number of defective parts produced also depended on whether the raw material needed by each machine was loaded manually or by an automatic feed system. The following data give the numbers of defective parts produced. Use $\alpha=.05$ to test for any significant effect due to machine, loading system, and interaction. $$ \begin{aligned} &\text { Loading System }\\ &\begin{array}{cc} \text { Manual } & \text { Automatic } \\ 30 & 30 \\ 34 & 26 \\ 20 & 24 \\ 22 & 28 \end{array} \end{aligned} $$
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