Design of Experiment! Explained with an example.

Hello friends! Hope you are doing good. Today we will discuss about Design of experiment (DOE), it is an important part of Six Sigma. Let us understand concept of DOE with simple example. 

 Benefits of DOE.

• Efficiency Enhancement.
• Resource Optimization
• Optimal Process Setting
• Robust Decision Making
• Quality Improvement

Tea Preparation

 Suppose we want to prepare milk tea, and there is a list of ingredients and other necessary items for making the tea. The ultimate outcome of this process is the Taste of the tea, although there are other outcomes such as the color of the tea, etc. The Critical to Quality (CTQ) of tea preparation is the taste (Y-Response). Factors that influence the taste of tea are referred to as X factors. Any variable that can be considered for a trial is known as a factor.

We need to identify the factors (X) that affect the taste (Y) of the tea.

1. Milk –   Quality, Quantity
2. Tea powder – Brand, Quantity
3. Sugar – Quality
4. Temperature
5. Water
6. Boiling Time
7. Mixing Ratio
8. Masala

We have done a trail and result is listed below. Taste rating is given in scale of (1-10).

10 – Good

 1 –    Bad

Factor	Level 1	Level 2
Quantity of Tea Powder (X1)	1Tea Spoon (L1)	2Tea Spoon(L2)
Boiling Time (X2)	5 Mins (L1)	10 Mins(L2)

So here we can see 2 factors of 2 level each. 

No of Experiment = 4.

Experiment No	Quantity of Teaspoon	Boiling Time	Taste of Tea
1	1T	5 Mins	8
2	1T	10 Mins	3
3	2T	5 Mins	7
4	2T	10 Mins	2

The idea behind this example is to identify factors and their levels. In this case, the number of factors is 2, and the number of levels is also 2. Therefore, the total number of experiments is calculated as L^F, where L is the level and F is the factor, using the formula Level to the power of Factor.

For conducting experiments, at least 2 levels are required. Here’s another example: Number of factors – 4, Number of levels – 2. So, the total number of experiments is calculated as 2^4 = 16.

In a more general case: Number of factors – K, Number of levels – 2. So, the total number of experiments is calculated as 2^K.

Secondly, now question arises why do we do repeat test?

The Answer is to estimate the error of testing.

Basic principles of experiments 

• Replication
• Randomization (to avoid the systematic Bias).

Now take the average of taste (Y ) when 1T =  (8+3)/2 = 5.5

 Take the average of taste (Y ) when 2T =  (7+2)/2 = 4.5

Now take the average of taste (Y ) when 5 mins =  (8+7)/2 = 7.5

 Take the average of taste (Y ) when 10 mins =  (3+2)/2 = 2.5

Now draw the graph the Main effects plot in Minitab.

Path –

Stat > DOE> Factorial >Create factorial Design > General Full Factorial design.

^{Go to the Design tab and create Factors and level. Select number of replicates.}

The Go to the factors tab and fill up the level values against each factor.

Then Click ok.

Now the column C7 needs to filled up as per experiment data. (Taste of tea)

Then draw main effects plot.

Path

Stat> ANOVA> Main Effects Plot . then fill up the Response and factors.

Then click ok. we can get the graph of main Effect plot.

Conclusion – Optimum factor level combination

Quantity of Tea powder – 1T ( Tea Spoon)

Boiling Time – 5 Min