Six Sigma - Two way ANOVA An engineer suspects that the cutting speed and the fe
ID: 3229431 • Letter: S
Question
Six Sigma - Two way ANOVA
An engineer suspects that the cutting speed and the feed rate influence the surface finish of a metal part. For the study the engineer collected 4 cutting speeds and 3 feed rates and conducted a 2 factor experiment to obtain the data in Table 4 with 3 replications.
Conduct ANOVA at = 0.05 to test for the significance of all possible effects.
Table 4 Feed Rate Cutting Speed 0.1 0.2 0.3 100 54, 60, 65 79, 68, 80 99, 88, 94 200 98, 89, 94 98, 106, 90 100, 98, 108 300 109, 98, 89 100, 108, 94 99, 82, 102 400 112, 100, 82 94, 104, 108 98, 116, 106Explanation / Answer
applying two way ANOVA on above:
as p value is lower then 0.05 in cutting speed , feed and interaction, it has siginificance of of all possible effects.
Cutting Speed 100 Count 3 3 3 9 Sum 179 227 281 687 Average 59.66667 75.66667 93.66667 76.33333 Variance 30.33333 44.33333 30.33333 243.25 Cutting Speed 200 Count 3 3 3 9 Sum 281 294 306 881 Average 93.66667 98 102 97.88889 Variance 20.33333 64 28 41.11111 Cutting Speed 300 Count 3 3 3 9 Sum 287 302 283 872 Average 95.66667 100.6667 94.33333 96.88889 Variance 34.33333 49.33333 116.3333 58.36111 Cutting Speed 400 Count 3 3 3 9 Sum 294 306 320 920 Average 98 102 106.6667 102.2222 Variance 228 52 81.33333 104.4444 Total Count 12 12 12 Sum 1041 1129 1190 Average 86.75 94.08333 99.16667 Variance 326.2045 163.7197 78.69697 ANOVA Source of Variation SS df MS F P-value F crit Cutting speed 3612.667 3 1204.222 18.55822 1.91E-06 3.008787 feed 935.1667 2 467.5833 7.205908 0.00354 3.402826 Interaction 1084.833 6 180.8056 2.786387 0.033539 2.508189 Within 1557.333 24 64.88889 Total 7190 35