Is there any way to change the y axis of a run chart (or any control chart) to logarithmic? For some data distributions, it would be helpful, but it doesn't appear to be possible.
It doesn't appear as though you can scale the y axis on a control or run chart as you suggest. What I did was use the Fit Y by X platform, placing the process factor on the y axis, and your 'Label' on the x axis. You may have to modify the x axis with Value Ordering? Then from the report hot spot, select Flexible -> Fit Each Value. This will connect all the points with a straight line between each point. Then modify the y axis scaling as one would normally to Log. If you've got control limits, you could manually add those as reference lines...cumbersome. But doable.
Here's what it looks like:
Control charts are very powerful WITHOUT transforming the data. Transformations are virtually always useless for gaining knowledge about your process. I suggest you Google Donald Wheeler's articles on the subject.