**Re: Regression for MTBF (Medical Device: Repairs vs Install Base) with Reliability Da**

not sure what the relationship between the install base and the count of repairs will tell you without **first** looking at the time series.

statistical inference and model building do rely on the homogeneity of the underlying process and with the shift in failure rates at point 12 you do not have a homogenous process so any interpretation of the regression plot alone will be misleading as the shift is confounded with (or coincident with) a particular point in time when the install was increasing. for example, if the defect rate is constant, then an increase in the install base will result in a an increase in the number of repairs and we would expect that there would be a linear relationship between install base and repairs. Now, let's say that at point 12 there was a new defect introduced with a new batch of one of the system components. IF this were the case imagine what the defect rate would have been in points 1-11 if those instruments had the 'new defect rate': it would be higher. so the curve in the regression plot is NOT due to the install base as much as it is due to the 'new defect' introduced in point 12.

There are of course other complications that could shape the regression curve. another example is if the repaired units are returned to the install base their defect rate will change and now you have a mix of instruments that will have different failure rates. this is why we often do a 'vintage' time series to pull this apart...

fancy statistics can be very seductive, but I've found that the simple stuff - plot your data in it's rawest forms in time series and ask yourself questions about that first - is a far more productive approach. there are so many nuances about processes that can get hidden by the 'blind' application of statistical tools. If you first understand the nature of your data and the process it represents you will not be blind when you select a more sophisticated statistical tool. I tell my students to imagine what would happen if they were to pick up a chainsaw to cut down a tree but they were blindfolded. :mg:

As for which chart to use, you need to try both and determine which one fits your need best. *I* have found that the p chart works reasonably well with field repair/return/warranty data especially when the install base is growing substantially as it modifies the control limits based on the install base size and this type of data is reasonable modeled by the binomial. the I, MR chart doesn't do that. I have attached a new file that shows both charts for your data; the upward shift at point 12 is still clear in I, MR chart...