With lecture 37 we start the Analyze phase of six sigma. In this lecture, we will discuss the introduction of analyze phase, how to create and interpret multivariate studies in respect of positional and temporal variation as well as correlation and regression. Do you recognize this illustration, we had discussed this in one of the lectures of measure face and measure face. We identified the various output characteristics, CD cues and input Characteristics ctps let us have an illustration of what we are going to do in the Analyze phase. As I have told in measure phase, we identify cdp's. Now, in the Analyze phase, we will try to analyze the variation of cdp's and identify two or three root causes.

Let us learn the various tools for identifying the root causes. multivariate study is one of the tools to identify the root cause of variations It is a graphical method to understand the multiple sources of variation in a process by multivariate studies, we study the various sources of variations such as positional variation, cyclical variation, tempo variation, etc. Let me illustrate it for your better understanding. Suppose, we have a manufacturing process that produces cylindrical components for an OEM. Let us take one output from the process and measure its quality characteristics I have taken one cylindrical block and measured the diameter in three different positions from the top from the middle and from the bottom positions, prospectively I don't have to say that these measurements vary at each position, it is obvious to you by now. Now, the positional variation is the variation within different positions of same product.

Further, I have taken two more blocks and taken measurements as you know the measurements vary at different positions as well as the measurements vary from product to product also. Now, the cyclical variation is the variation and measurements among different parts of our shift. Now, if I take the measurements for over a period of time for several number of blocks, it is also going to give me a lot of radiation and the temporal variation is the variation among different parts over a period of time and shifts. Let us learn multi very study in detail By taking an example I have taken one cylindrical block and find out the measurements from top, middle and bottom positions, prospectively the result of measurements are as tabulated. You can see the variations in the measurement at different positions, the positional variation. Similarly, the measurement for part two, Part three and part four respectively in the table by looking at the table could we comment any Think about positional are cyclical variation.

Difficult, isn't it? Let us have a graphical study using multivariate as you can see four columns for four parts and at each column the space for showing d, m and b that are top, middle and bottom respectively. Now, at the left hand side of the graph, plot the measurement scales now plot the individual measurement in part one, the top position measurement Was 0.993 middle position measurement was 0.994 and bottom position measurement was 0.992. Similarly, we can plot all other measurements to what can we commence now, by seeing this graph, we can see the variation between different positions are less the measurement are more clustered and this is the same for all the parts. What about the cyclical variation the variation between Between the parts this variation is significant there are more variations from one part to the other. We can analyze from this graph that the cyclical variation is more significant than the positional variation.

Now, the Six Sigma team could arrange a brainstorming to find out the reason for cyclical variations. Now, let us learn about another major tool in Six Sigma the correlation coefficient and the regression analysis Do you remember this graph that we had discussed in measure phase as part of graphical representation of data? Yes, this is the same scatterplot that we have used to identify the relationship between two variables. During scatterplot we would be able to identify a correlation if it exists, that was fine. But, but could we be able to define the degree of correlation or could we develop a mathematical model based on the correlation Let us review this as I have just Told scatter diagram does not convey the degree of correlation. The correlation studies help you for this purpose by determining whether there exists correlation and measuring the degree of relationships.

Call Pearson's correlation is the most popular method used for this purpose. The correlation coefficient is indicated by R. When we get r is equals to plus one It means a perfect positive correlation. if r is equals to minus one It means Perfect negative correlation where r is equals to zero, it implies no correlation. calculation for correlation are tedious. We can easily find out the correlation by using Excel select a column and type equals to coral, open the bracket, add a one comma added to close the bracket for everyone and era to select the respective columns, where we have stored the set of data. Let us move a step ahead with correlation regression equation provides a mathematical model for the correlation After identifying the relation between two variables, we can use regression equation to predict one variable if other variable is known regression analysis is finding the equation of regression line regression equation is nothing, but the equation of a straight line represented as y is equals to a plus b x, where b is calculated as summation of x y minus n into x bar into y bar divided by summation of x square minus and x bar square.

Do you scale calculation? It was just to give you awareness. This calculation could be easily done with Minitab. Let us see how this is the same file that was used for scatterplot example, double click on the file, then click Start regression fitted line plot fitted line plot window opens now Type in response y box as defect rate, you can also double click instead in the predictor, x box type, soldier temperature. Now click OK Minitab gives the graphical view of fitted plot line and its equation. Now, what you see at the top is the equation that can be used to predict the defect rate for a known value of soldier temperature.

That's all for this lecture. Let us move to another important lecture for hypothesis testing. Thank you