|
5.
Process Improvement
5.6. Case Studies 5.6.3. Catapult Case Study
|
|||
| Effects Estimation |
Although the effect estimates were given on the
dex mean interaction plot on the previous
page, they can also be estimated quantitatively.
Fractional factorial designs with 2 levels can be fit using the Yates technique, which is described in Box, Hunter, and Hunter. The Yates technique utilizes the special structure of these designs to simplify the computation and presentation of the fit. Note that the center points are not included in the Yates analysis for estimating the effects. |
||
| Dataplot Output |
Dataplot generated the following output for the Yates analysis.
(NOTE--DATA MUST BE IN STANDARD ORDER)
NUMBER OF OBSERVATIONS = 16
NUMBER OF FACTORS = 4
NO REPLICATION CASE
PSEUDO-REPLICATION STAND. DEV. = 0.23333400726E+02
PSEUDO-DEGREES OF FREEDOM = 5
(THE PSEUDO-REP. STAND. DEV. ASSUMES ALL
3, 4, 5, ...-TERM INTERACTIONS ARE NOT REAL,
BUT MANIFESTATIONS OF RANDOM ERROR)
STANDARD DEVIATION OF A COEF. = 0.11666700363E+02
(BASED ON PSEUDO-REP. ST. DEV.)
GRAND MEAN = 0.55296875000E+02
GRAND STANDARD DEVIATION = 0.37568069458E+02
99% CONFIDENCE LIMITS (+-) = 0.47041816711E+02
95% CONFIDENCE LIMITS (+-) = 0.29990217209E+02
99.5% POINT OF T DISTRIBUTION = 0.40321440697E+01
97.5% POINT OF T DISTRIBUTION = 0.25705826283E+01
IDENTIFIER EFFECT T VALUE RESSD: RESSD:
MEAN + MEAN +
TERM CUM TERMS
----------------------------------------------------------
MEAN 55.29688 37.56807 37.56807
4 40.28125 3.5* 32.38174 32.38174
3 35.90625 3.1* 33.82029 27.06551
1 26.96875 2.3 36.11603 23.47657
1234 24.09375 2.1 36.69212 19.75246
2 -22.15625 -1.9 37.03936 15.25831
34 15.21875 1.3 38.02627 12.47985
14 9.40625 0.8 38.56024 11.44448
13 9.28125 0.8 38.56889 10.02313
23 -6.34375 -0.5 38.73853 9.50675
123 6.28125 0.5 38.74143 8.76873
124 5.65625 0.5 38.76894 8.00750
12 -5.53125 -0.5 38.77409 6.68584
134 5.34375 0.5 38.78160 3.15269
24 -2.21875 -0.2 38.86856 0.43301
234 0.21875 0.0 38.88647 0.00000
|
||
| Interpretation |
In fitting 2-level factorial designs, Dataplot takes advantage
of the special structure of these designs in computing the fit
and printing the results. Specifically, the main effects and
interaction effects are printed in sorted order from most
significant to least significant. It also prints the t-value
for the term and the residual standard deviation obtained by
fitting the model with that term and the mean (the column
labeled RESSD MEAN + TERM) and for the model with that term, the
mean, and all other terms that are more statistically significant
(the column labeled RESSD MEAN + CUM TERMS).
For the t distribution with 5 degrees of freedom, the critical values for significance levels of 0.01, 0.05, and 0.10 are 4.032, 2.571, and 2.015 respectively. In this case, no factors are statistically significant at the 0.01 level, factors 4 (Arm Length) and 3 (Number of Bands) are statistically significant at the 0.05 level, and factor 1 (Band Height) and the interaction of factors 1, 2, 3, and 4 are statisically significant at the 0.10 level. The remaining factors (including interaction terms) are not statistically significant even at the 0.10 level. |
||
