Assignment 5 Complete Solution

Question 1 (PID 7.23.5)
Recent trends show that the yield of your company’s flagship product is declining. You are uncertain if the supplier of a key raw material is to blame, or if it is due to a change in your process conditions. You begin by investigating the raw material supplier.
The data available has:

• 􀜰 = 24
• 􀜭 = 6 + 1 designation of process outcome
• data set raw‐material‐characterization
• Description: 3 of the 6 measurements are size values for the plastic pellets, while the other 3 are the

outputs from thermogravimetric analysis (TGA), differential scanning calorimetry (DSC) and thermomechanical analysis (TMA), measured in a laboratory. These 6 measurements are thought to adequately characterize the raw material. Also provided is a designation Adequate or Poor that reflects the process engineer’s opinion of the yield from that lot of materials. Import the data, and set the Outcome variable as a secondary identifier for each observation, as shown in the illustration below. The observation’s primary identifier is its batch number.

1. Build a latent variable model for all observations and use auto‐fit to determine the number of components. If your software does not have and auto‐fit features (cross‐validation), then use a Pareto plot of the eigenvalues to decide on the number of components.

2. Interpret component 1, 2 and 3 separately (using the loadings bar plot).
3. Now plot the score plot for components 1 and 2, and colour code the score plot with the Outcome variable. Interpret why observations with Poor outcome are at their locations in the score plot (use a contribution plot).
4. What would be your recommendations to your manager to get more of your batches classified as Adequate rather than Poor?
5. Now build a model only on the observations marked as Adequate in the Outcome variable.
6. Re‐interpret the loadings plot for 􀝌1 and 􀝌2. Is there a substantial difference between this new loadings plot and the previous one?

Assignment 5 Complete Solution

1. Build a latent variable model for all observations and use auto‐fit to determine the number of components. If your software does not have and auto‐fit features (cross‐validation), then use a Pareto plot of the eigenvalues...

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