We run a process here where a product is reduced in viscosity to a specification by the addition of rosin. We have a chart that gives a guess of how much should be added based on the starting viscosity result. I am sure that the chart is too conservative.

I have been trying to use Minitab's regression analysis to match up the response (Final Viscosity) with the relevant predictors (Start Viscosity, Rosin). The other possible predictors don't seem to give a low enough p-value, meaning they aren't of particular importance.

The final equation comes out as:

Final Viscosity = 49.5 + (0.401 * Start Viscosity) - (0.179 * Rosin)

This doesn't seem right. If I use an example, say Start Viscosity = 60, Rosin added = 20, then I get Final Viscosity = 70.

If I remove all the cases where Rosin <> 0, then the average viscosity only moves down by 2, in other words, failing an addition of Rosin, the viscosity only drifts down very slightly over time.

Or should I be thinking of it in this way: For every 1 kg of Rosin that I add, the Final Viscosity will be reduced by 0.179?

Final Viscosity = 49.5 + (0.401 * Start Viscosity) - (0.179 * Rosin)

This doesn't seem right. If I use an example, say Start Viscosity = 60, Rosin added = 20, then I get Final Viscosity = 70.The interpretation that each kg of rosin reduces viscosity by 0.179 sounds right. The fit won't be perfect across the whole range. At low initial viscosities, the fit predicts an increase in viscosity, which is not accurate, I expect

I think that excluding the data where you add no rosin would be a good idea. This is nearly half the data and would have a large effect on the resulting regression analysis. Using only the cases where rosin was added, then the equation becomes

Final Viscosity = 50.8 - 0.118 Rosin + 0.307 Start Viscosity

In this case, each kg only drops viscosity by 0.118.

With this equation, then it looks like the target would always right around 85. That seems like a reasonable sort of situation - aiming for a particular value. It might be informative to work backwards from your chart to see how much rosin is suggested for various viscosities.


Two other things I noticed:
* With no rosin, typically the viscosity stayed about the same, or rose slightly. However, there were a few cases with large drops, which made the overall change slightly negative. These large drops seem suspicious. perhaps errors? or problems with the measurement system.
* Rosin was added in some cases where the viscosity was just 73, while in another case, no rosin was added even when the viscosity was 150. This doesn't seem to make sense, unless these were tests to see how the system worked.

Tim F

Actually, the target area is 40 - 60, not 85. This data is based on the first and second tests only, with or without a Rosin addition. I was hoping to get a reasonable equation, then try to determine later on if the same equation could be applied to later tests/additions. Just being cautious here...

Working backwards using this equation I get vastly higher Rosin additions than we've done previously. I understand what the data says, but I'll be taking this in increments, I think.

I've tested the measuring system, it's reasonable without being ideal, but I don't think the company is likely to fork out > $80 000 for a better rheometer. Anyway, I strongly suspect the reason for the unusual results is more to do with sample preparation, so I'll probably need to run some experiments on that.

The reason for the additions being difficult to understand is that the production manager responsible for the material is notorious for tampering with the process, then not being able to understand why everything changes around so wildly. 1970s process control.

You need to run a no intercept model. The intercept would be the final viscosity when both Rosin and Initial Viscosity are equal to zero. Since this value should be zero, fit a no intercept model. When I took the entire data set and fit the no intercept model, you get the following model.

Final Viscosity = 0.903 Start Viscosity - 0.295 Rosin

So for the inital viscosity of 60 and rosin of 20, the final viscosity would be 48.28.

I did not check assumptions fully, but just a quick check shows that for high predicted viscosity, the residuals are off significantly.

Of course the model you really want to fit is

Rosin = Final Viscosity - Viscosity. You really wanto to know given an inital viscosity and an expected final viscosity, how much rosin to add...that is another issue all together.