Design of Experiment! Explained with a solved example.

Hi readers! Today, we are discussing Design of Experiments (DOE), a crucial component of Six Sigma. This is the second article about Design of Experiments (DOE). The link to the initial content on DOE is available here. https://readandgain.com/2024/02/04/design-of-experiment-explained-with-an-example/#google_vignette

Steps for DOE.

• Identify the problem.
• Select factor and level.
• Design the experiment as per plan.
• Conduct the experiment as per plan.
• Collect Data
• ANOVA
• Main effect plot
• Identify significant factors.
• Identify the best level.
• Predict expected result.
• Trail implementation/ confirmatory trail 

Let us understand with an example. 

Oil pick up (OPU) is a measure of the amount of oil observed by the fiber at the finishing stage of fiber manufacturing. An experiment was carried out to achieve target OPU at 0.28 with minimum variation. A 2^3 experiment was with data are given below. Analyze the data and draw conclusion.

Exp No.	Evaporation residue (A)	pH (B)	Temp (0C)  (C)	OPU
				1	2
1	1.0	7.5	60	0.15	0.16
2	1.0	7.5	65	0.17	0.20
3	1.0	8.0	60	0.24	0.23
4	1.0	8.0	65	0.19	0.22
5	2.0	7.5	60	0.27	0.25
6	2.0	7.5	65	0.33	0.27
7	2.0	8.0	60	0.29	0.31
8	2.0	8.0	65	0.36	0.30

In the above example, we can see that there are three factors, each with two levels.

• Select factor and level.  Here is three factors and 2 factors. No of Experiment – 2^3.
• Design the experiment as per plan.  
• Path – Open Minitab
• Stat > DOE> Factorial >Create factorial Design > General Full Factorial design.

Next, navigate to the Design tab, where you should input the three factors – Evaporation Residue, pH, and Temperature. Set the factors to level 2 and specify the number of replicates as 2. 

Next, go to the ‘Factors’ section and input different values for each factor.

Next, navigate to the ‘Option’ tab and uncheck the ‘Randomize Runs’ option

Afterward, click ‘OK,’ and you will receive the design summary.

Now we got 16 design different plan.

• Then Conduct the experiment as per plan.

In this case, input the results (OPU) into the Minitab data sheet, as illustrated in the picture below.”.

• Collect Data
• ANOVA
• Main effect plot

Let do the ANOVA Test.

Path – Stat >DOE>Factorial> Analyze factorial design >Terms> Ok

In conclusion, the p-values for the factors Evaporation Residue and pH are both less than 0.05, indicating a significant effect on OPU.

Main effect plot

Path

Stat > DOE >Factorial >Factorial plot ,then select main effect.

Now, let’s analyze the graph above. Since the p-value for temperature is greater than 0.05, it suggests that temperature is not influencing OPU. Therefore, for practicality and cost-effectiveness, we will opt for 60°C, considering it as a suitable choice over 65°C.

In question it is given an experiment was carried out to achieve target OPU at 0.28 with minimum variation.

Path for Prediction

Path – Stat >DOE>Factorial>Predict then we put Evaporation –  2 and pH – 8  and then we got the prediction result. As mentioned below.