Mean time particle failure vs Defect Count

As a CVD process engineer one has to accustomed oneself with the habit of looking at trend which is been supported by the SPC system. The Western electric rule is one of the most common method to identify certain drift in the process. This trend is always vivid from process with normal distribution for instance a thickness of the thinfilm measurement.

A thickness measurement trend is easy to look for since it has a certain causality characteristic whereby changes in the trend might be attributed to a chamber maintenance that is taking place. You can see a thickness measurement gradually increases after a certain number of wafers processing which is caused by the seasoning layers that the equipment actually sees and eventually changes the chamber impedance characteristic.

But now, how do one actually sees a trend in a Defect count of particle failure in our SPC trend. I have been thinking of this problem for sometime whereby finding a way to see 'trend' in random distribution. One of the problem that I see is that the count failure sometimes does not lead to any significant information since a failure of 20 counts might just be the same to a 15 counts failure since the number of particles drop is also a random number as the particle might fall 15 this time and would drop more count in the next failure event.

Hence after thinking for sometime I deduce that the best method of capturing a particle trend is by implementing a binomial distribution method. A pass and failure might be the best way of anticipating a failure trend. Thats how I came about with the concept of mean time particle failure. The mean time particle failure actually captures the frequency of the failure itself. The hypothesis is that as the failure of the equipment becomes imminent hence the frequency failure itself regardless of the defect count. After developing the algorithm and testing this method on our particle SPC, i was able to see a trend in some of the equipment as it nears a catastrophic failure or as the system actually nears a certain Preventive maintenance wafer count. There are further work that can be done on the system such as by developing a trend chart between this failure and maybe we can see some different slope magnitude between those failures. A bigger slope might indicate a faster equipment failure.