1. IE-432 Design Of Industrial Experiments
Lab Tutorials
Maria Arshad

2. Design Of Experiments
The (statistical) design of experiments (DOE) is an efficient procedure for planning experiments so that the data obtained can be analyzed to yield valid and objective conclusions. DOE begins with determining the objectives of an experiment and selecting the process factors for the study.

3. DOE
DOE is a formal mathematical method for systematically planning and conducting scientific studies that change experimental variables together in order to determine their effect of a given response.
DOE makes controlled changes to input variables in order to gain maximum amounts of information on cause and effect relationships with a minimum sample size.

4. DOE
DOE is more efficient that a standard approach of changing “one variable at a time” in order to observe the variable’s impact on a given response.
DOE generates information on the effect various factors have on a response variable and in some cases may be able to determine optimal settings for those factors.

5. DOE
DOE encourages “brainstorming” activities associated with discussing key factors that may affect a given response and allows the experimenter to identify the “key” factors for future studies.
DOE is readily supported by numerous statistical software packages available on the market, like Minitab, Design Expert.
We will use Design Expert V for solving the problems.

6. Design Expert

7. BASIC STEPS IN DOE Four elements associated with DOE:
1. The design of the experiment,
2. The collection of the data,
3. The statistical analysis of the data, and
4. The conclusions reached and recommendations made as a result of the experiment.

8. Special Terminology : Design of Experiments
Response variable
Measured output value
Factors
Input variables that can be changed
Levels
Specific values of factors (inputs)
Continuous or discrete
Replication
Completely re-run experiment with same input levels
Used to determine impact of measurement error
Interaction
Effect of one input factor depends on level of another input factor

9. Problem Statement
An experiment is conducted by an Agricultural engineer to test the effect of soil type and nutrient on the yield of Strawberry plants. He uses 3 types of soil and 4 types of nutrients for the experiment. Design a suitable experiment and check if there is any effect of soil type and nutrient on the yield of strawberry.

10. Steps involved in the Experiment
State the hypotheses (Your objectives are made clear here)
Identify the response variable, factors, levels and ranges
Design the experiment
Conduct the experiment
Do the appropriate statistical Analysis – Two-Way ANOVA
Get the ANOVA table or other results, and draw meaningful conclusions
Comment on the results, give your recommendations

11. One Factor Experiment SOIL TYPE Experiments 1 2 3 Row Mean 84.9 89.1
SOIL TYPE
Experiments 1 2 3
Row Mean
84.9
89.1
85.3
86.42
75.4
79.4
84.7
79.8
70.3
76.7
78.2
75.05 4
73.2
81.1
77.2
77.17
Column Mean
75.9
81.6
81.3
79.61

12. Analysis via Microsoft Excel
Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
Column 1 4
303.68
75.92
Column 2
326.28
81.57
Column 3
325.36
81.34
ANOVA
Source of Variation SS df MS F
P-value
F crit
Between Groups 2
Within Groups 9
Total 11

13. Analysis via Design Expert

14. Two Factor Experiment SOIL TYPE NUTRIENT 1 2 3 Row Mean A 84.85 89.13
85.28
86.42 B
75.35
79.4
84.65
79.8 C
70.3
76.65
78.2
75.05 D
73.18
81.1
77.23
77.17
Column Mean
75.92
81.57
81.34
79.61

15. Analysis via Microsoft Excel
Anova: Two-Factor Without Replication
SUMMARY
Count
Sum
Average
Variance
Row 1 3
259.26
86.42
5.5543
Row 2
239.4
79.8
Row 3
225.15
75.05
Row 4
231.51
77.17
Column 1 4
303.68
75.92
Column 2
326.28
81.57
Column 3
325.36
81.34
ANOVA
Source of Variation SS df MS F
P-value
F crit
Rows
Columns 2
Error 6
Total 11

16. Using DesignEx to Analyze a design
The following are a few notes on the facilities that are available under each tab.
Effects
Half-Normal and Normal plots for highlighting active factors .
ANOVA
Analysis of variance: This can sometimes be used as alternative way of highlighting active factors.

17. Using DesignEx to Analyze a design
Diagnostics
Residual plots Design Expert offers the usual range of residual plots for checking assumptions such as Normality and constant variance.

18. Using DesignEx to Analyze a design
Model Graphs Design Expert offers a wide range of different plots to show how the response varies with changes in the controls. Available plots are . .
One Factor Main effects plot showing the average effect of shifting a single control, while holding the other controls constant.
Interaction Plot showing how the effect of changing one control varies with changes in a second control