Problem #1.
The data correspond to yields (in tons per hectare) of a pasture with 3 levels of nitrogen fertilizers, the design was randomized, applied in 5 plots per treatment (blocks).
You want to know if the performance was different in the treatments.
Check the hypothesis with = 0.01%
Nitrogen Levels
1
2
3
Plot 1
14.823
25.151
32.605
Plot 2
14.676
25.401
32.46
Plot 3
14.72
25.131
32.256
Plot 4
14.514
25.031
32.669
Plot 5
15.065
25.277
32.111
Problem #2.
A product development engineer wants to maximize the tensile strength of a new synthetic fiber that will be used to make shirts. From experience, it appears that strength (or strength) is influenced by the% cotton present in the fiber.
It is also suspected that high cotton values negatively affect other quality qualities that are desired (for example: that the fiber can receive a permanent press treatment).
Faced with this situation, the engineer decides to take five samples for different levels of cotton and measure the strength of the fibers thus produced.
Cotton %
Observations (strengths of the 25 manufactured fibers)
Total
Average
15%
7
7
15
11
9
49
9.8
20%
12
17
12
18
18
77
15.4
25%
14
18
18
19
19
88
17.6
30%
19
25
22
19
23
108
21.6
35%
7
10
11
15
11
54
10.8
Total sum of the 25 Strength values obtained
376
15.04
Problem # 3 Full factorial example
Data Source
This example uses data from a NIST high performance ceramics experiment
This data set was taken from an experiment that was performed a few years ago at NIST by Said Jahanmir of the Ceramics Division in the Material Science and Engineering Laboratory. The original analysis was performed primarily by Lisa Gill of the Statistical Engineering Division. Do the DOE set up and analysis and find the significant factors affecting your response.
The original data set was part of a high performance ceramics experiment with the goal of characterizing the effect of grinding parameters on sintered reaction-bonded silicon nitride, reaction bonded silicone nitride, and sintered silicon nitride.
Description of Experiment: Response and Factors
Response and factor variables
Purpose: To determine the effect of machining factors on ceramic strength
Response variable = mean (over 15 repetitions) of the ceramic strength
Number of observations = 32 (a complete 25 factorial design)
Response Variable Y = Mean (over 15 reps) of Ceramic Strength
Factor 1 = Table Speed (2 levels: slow (.025 m/s) and fast (.125 m/s))
Factor 2 = Down Feed Rate (2 levels: slow (.05 mm) and fast (.125 mm))
Factor 3 = Wheel Grit (2 levels: 140/170 and 80/100)
Factor 4 = Direction (2 levels: longitudinal and transverse)
Factor 5 = Batch (2 levels: 1 and 2)
The data
The design matrix, with measured ceramic strength responses, appears below. The actual randomized run order is given in the last column.
speed rate grit direction batch strength order
1 -1 -1 -1 -1 -1 680.45 17
2 1 -1 -1 -1 -1 722.48 30
3 -1 1 -1 -1 -1 702.14 14
4 1 1 -1 -1 -1 666.93 8
5 -1 -1 1 -1 -1 703.67 32
6 1 -1 1 -1 -1 642.14 20
7 -1 1 1 -1 -1 692.98 26
8 1 1 1 -1 -1 669.26 24
9 -1 -1 -1 1 -1 491.58 10
10 1 -1 -1 1 -1 475.52 16
11 -1 1 -1 1 -1 478.76 27
12 1 1 -1 1 -1 568.23 18
13 -1 -1 1 1 -1 444.72 3
14 1 -1 1 1 -1 410.37 19
15 -1 1 1 1 -1 428.51 31
16 1 1 1 1 -1 491.47 15
17 -1 -1 -1 -1 1 607.34 12
18 1 -1 -1 -1 1 620.80 1
19 -1 1 -1 -1 1 610.55 4
20 1 1 -1 -1 1 638.04 23
21 -1 -1 1 -1 1 585.19 2
22 1 -1 1 -1 1 586.17 28
23 -1 1 1 -1 1 601.67 11
24 1 1 1 -1 1 608.31 9
25 -1 -1 -1 1 1 442.90 25
26 1 -1 -1 1 1 434.41 21
27 -1 1 -1 1 1 417.66 6
28 1 1 -1 1 1 510.84 7
29 -1 -1 1 1 1 392.11 5
30 1 -1 1 1 1 343.22 13
31 -1 1 1 1 1 385.52 22
32 1 1 1 1 1 446.73 29
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Problem #4.
Replicate the DOE in the following website. Write a 3-line report with your conclusions