Engineering Statistics Handbook Episode 4 Part 15 docx

3. Production Process Characterization 3.4. Data Analysis for PPC 3.4.2.Exploring Relationships The first analysis of our data is exploration Once we have a data file created in the desired format, checked the data integrity, and have estimated the summary statistics on the response variables, the next step is to start exploring the data and to try to understand the underlying structure. The most useful tools will be various forms of the basic scatter plot and box plot. These techniques will allow pairwise explorations for examining relationships between any pair of response variables, any pair of explanatory and response variables, or a response variable as a function of any two explanatory variables. Beyond three dimensions we are pretty much limited by our human frailties at visualization. Graph everything that makes sense In this exploratory phase, the key is to graph everything that makes sense to graph. These pictures will not only reveal any additional quality problems with the data but will also reveal influential data points and will guide the subsequent modeling activities. Graph responses, then explanatory versus response, then conditional plots The order that generally proves most effective for data analysis is to first graph all of the responses against each other in a pairwise fashion. Then we graph responses against the explanatory variables. This will give an indication of the main factors that have an effect on response variables. Finally, we graph response variables, conditioned on the levels of explanatory factors. This is what reveals interactions between explanatory variables. We will use nested boxplots and block plots to visualize interactions. 3.4.2. Exploring Relationships http://www.itl.nist.gov/div898/handbook/ppc/section4/ppc42.htm [5/1/2006 10:17:39 AM] 3.4.2.1. Response Correlations http://www.itl.nist.gov/div898/handbook/ppc/section4/ppc421.htm (2 of 2) [5/1/2006 10:17:40 AM] The second graph is a box plot of the number of large particles added for each cassette type. 3.4.2.2. Exploring Main Effects http://www.itl.nist.gov/div898/handbook/ppc/section4/ppc422.htm (2 of 9) [5/1/2006 10:17:50 AM] We conclude from these two box plots that cassette does not appear to be an important factor for small or large particles. There is a difference between slots for small particles, one slot is different for large particles We next generate box plots of small and large particles for the slot variable. First, the box plot for small particles. 3.4.2.2. Exploring Main Effects http://www.itl.nist.gov/div898/handbook/ppc/section4/ppc422.htm (3 of 9) [5/1/2006 10:17:50 AM] Next, the box plot for large particles. 3.4.2.2. Exploring Main Effects http://www.itl.nist.gov/div898/handbook/ppc/section4/ppc422.htm (4 of 9) [5/1/2006 10:17:50 AM] We conclude that there is a difference between slots for small particles. We also conclude that one slot appears to be different for large particles. Load lock may have a slight effect for small and large particles We next generate box plots of small and large particles for the load lock variable. First, the box plot for small particles. 3.4.2.2. Exploring Main Effects http://www.itl.nist.gov/div898/handbook/ppc/section4/ppc422.htm (5 of 9) [5/1/2006 10:17:50 AM] Next, the box plot for large particles. 3.4.2.2. Exploring Main Effects http://www.itl.nist.gov/div898/handbook/ppc/section4/ppc422.htm (6 of 9) [5/1/2006 10:17:50 AM] We conclude that there may be a slight effect for load lock for small and large particles. For small particles, temperature has a strong effect on both location and spread. For large particles, there may be a slight temperature effect but this may just be due to the outliers We next generate box plots of small and large particles for the temperature variable. First, the box plot for small particles. 3.4.2.2. Exploring Main Effects http://www.itl.nist.gov/div898/handbook/ppc/section4/ppc422.htm (7 of 9) [5/1/2006 10:17:50 AM] Next, the box plot for large particles. 3.4.2.2. Exploring Main Effects http://www.itl.nist.gov/div898/handbook/ppc/section4/ppc422.htm (8 of 9) [5/1/2006 10:17:50 AM] ' We conclude that temperature has a strong effect on both location and spread for small particles. We conclude that there might be a small temperature effect for large particles, but this may just be due to outliers. 3.4.2.2. Exploring Main Effects http://www.itl.nist.gov/div898/handbook/ppc/section4/ppc422.htm (9 of 9) [5/1/2006 10:17:50 AM] [...]...3 .4. 2.3 Exploring First Order Interactions We conclude from this plot that for small particles, the load lock effect is not as strong for high temperature as it is for low temperature The same may be true for large particles but not as strongly The following is the box plot of large particles for load lock nested within temperature http://www.itl.nist.gov/div898 /handbook/ ppc/section4/ppc423.htm... http://www.itl.nist.gov/div898 /handbook/ ppc/section4/ppc423.htm (2 of 3) [5/1/2006 10:17:53 AM] 3 .4. 2.3 Exploring First Order Interactions We conclude from this plot that for large particles, the load lock effect may not be as strong for high temperature as it is for low temperature However, this effect is not as strong as it is for small particles http://www.itl.nist.gov/div898 /handbook/ ppc/section4/ppc423.htm (3 of 3) [5/1/2006 10:17:53 AM] . Effects http://www.itl.nist.gov/div898 /handbook/ ppc/section4/ppc422.htm (3 of 9) [5/1/2006 10:17:50 AM] Next, the box plot for large particles. 3 .4. 2.2. Exploring Main Effects http://www.itl.nist.gov/div898 /handbook/ ppc/section4/ppc422.htm. Effects http://www.itl.nist.gov/div898 /handbook/ ppc/section4/ppc422.htm (5 of 9) [5/1/2006 10:17:50 AM] Next, the box plot for large particles. 3 .4. 2.2. Exploring Main Effects http://www.itl.nist.gov/div898 /handbook/ ppc/section4/ppc422.htm. small particles. 3 .4. 2.2. Exploring Main Effects http://www.itl.nist.gov/div898 /handbook/ ppc/section4/ppc422.htm (7 of 9) [5/1/2006 10:17:50 AM] Next, the box plot for large particles. 3 .4. 2.2.