How to monitor a response that depends on unit size

Question

Hello,

I want to monitor a process dealing with the porosity of units. We measure a single porosity value for each unit (we have validated that a single measurement is okay, there are daily checks for the tool used to measure porosity). I want to start trending the process performance and identify excursions when they happen. The issue I am facing is that the porosity values are dependant on the size of the sample. Based on the last couple weeks of data, I have a 90%RsqAdjusted model that explains the unit porosity performance based on the unit size (basic model, can be improved with additional terms/factors). Going with the premise that this 2 week performance is a true representation of my system performance, how do I setup a control chart based on porosity + the unit dimensions? Since all sizes are made to order, there is no regularity in the size of units being processed, so I cannot count on sampling a speciifc size to act as a process predictor. I will run this analysis using JMP. I am lost as to what sort of control chart setup I should use for this situation where the response has a varying target based on various known factors. Thinking forward - I know that porosity variation is also size dependent. How do I leverage this in the control charts (for eg, i the last 2 weeks, porosity on large units had a range of 0.05, whereas porosity on small units had a range of only 0.01)?

Mark_Bailey · Answer

Yes, many of the short run SPC techniques transform the measurement into a relative measure, such as a deviation. There are other transformations that work, depending on the original measurment and the other assumptions.

Obviously, short run SPC assumes that the measure after transformation, such as deviation, has the same mean and variance so that all of the measures can be collected into the same control chart. That assumption is usually the over-riding aspect of choosing the appropriate transform.

unknown · Answer

Thanks, I will read up on this. Would this be along the lines of monitoring the deviation of incoming values from the model predicted values for that speciific size? If so, how difficult is it to incorporate the size-dependent 3sigma variation from the model?

Mark_Bailey · Answer

I forgot to add that using the option to treat each different size as a phase will work computationally but I don't know if the limits that you get this way are that good. I again suggest that you learn more about the short run techniques to use your data most efficiently.