Welcome to lecture 41. This is our first lecture of the last section the Six Sigma improve and control. We will be discussing about the basics of Design of Experiments do II as well as as well as interpreting the main effects and interaction plot. Let me give you an overview of d o e and this slide. In the process many inputs x play a major role in variation of the end results once we could identify the root causes of Critical Access, we would like to know that which level of x gives us the optimum result in why how do we come to know about this conducting experiments is one way to understand this. For example, temperature of the cooling water has been identified as one of the root causes in some project.

Now, the team would be interested to know which is the best temperature range for optimum performance. Say, for example, 40 degrees centigrade or 50 degrees centigrade or 60 degrees centigrade etc design of experiment do II is a systematic approach in which all parameters of critical axes are varied over a specified range and statistically analyze levels of different variable for optimum output. There are some basic d o e terminologies that a six sigma greenbelt should be aware of, such as independent and dependent variables, factor and levels response Treatment error repetition replication let us discuss them one by one in order to make you understand about dependent and independent variables. Let me take you back to this illustration. Do you remember this picture? It was discussed in the third lecture of this course, we had discussed that the quality of output depends upon the quality of inputs.

What does that mean? It means, here the quality parameters are the dependent variable The input parameters are independent variables. dependent variables are the output characteristics and is often denoted as y. Similarly, the input characteristics are known as independent variables and often denoted as x. Now, let's move forward with other terminologies of d o e response response is the output of the process being investigated, represented by y in the equation as y is equals true f of x The objective of the d o e is to figure out how various X's combined to affect y factors. The excess are called factors whose values are purposely controlled during experiments.

Levels, levels are different values of x that we control. Usually, we take two to three levels for one variable, our x Treatment Treatment is the specific setting or combination of Factor levels for an experimental unit error error is the variation that occurs in the response variable. Beyond that accounted for by the factors. replication. replication occurs when the entire experiment is performed more than once for a given set of independent variables repetition. Repetition is the measurement of a response variable more than once, under similar conditions let us take an example online retail store has conducted a d o e to identify the effects of the factors on sales turnover.

Here are the factors that affect the sales are namely a price in dollars the d o e was conducted with two levels of price in low level at $10 and high level at $20. b promotion expenses in dollars. The low and high levels of d o e were 5000 and $10,000 respectively. See Quality percentage d o e was conducted in two quality levels at average and best respectively. Now, the result of sales at each level of these three factors are shown on screen we have six set of responses. Now, with these responses, we have to find out which factor is more significant to our output.

That is the sales turnover. Could you interpret anything from this table? Difficult, isn't it? That is learn The main effect and interaction plot for lean more for more learning main effects plot is nothing but the graphical representation of the effect of factor levels on the response or the output. There are three columns for three factors namely price, promotion quality. Similarly, at the bottom of column, there are different levels of factors.

See, for price there are two levels 10 and $20 respectively. At the left side of the graph, we have measures of response the sales turnover. Now, let us plot the responses for each level. At price $10 the sales were $7.5 million and at price 20 the sales were $4 million. Similarly, we plot the other main effects. What do you analyze from this graph?

We can say when price decreases, the sales increases and vice versa. for promotion and quality increases the sales increases However, which is a significant factor here, let us find out how what is main effect of price it is a 10 minus a 20 which is 7.5 minus four that is $3.5 million. Similarly, we get the main effect for other two factors A, B and C as three and three respectively. That means, the price factor gives the highest mean effect batters $3.5 million hence We can conclude that price is the significant factor. There is one more concept in d o e called the interaction between the factors. By interaction plot, we try to analyze the interaction between the factors if any and its effect on response interaction plot are drawn similar to main plot.

If there is any interaction the lines cross each other, which needs to be identified further. For interaction plot, we take the responses of two factors in mind Graph. Let us see the interaction plot for the factors, price and promotion on sales. Then quality and promotion on sales and price and quality on sales. How do we interpret the interaction plot? If any of the lines crosses each other, it indicates the interaction of these factors to jointly affect the output or the responses That's all with this lecture.

Let us move to the important and final phases of Six Sigma control. next lecture is about statistical process control based on the A sq. B okay five