Determining if points out of control - non normal distribution I am trying to create a process in which I can identify if a process is out of control.
My idea was to do something similar to 6 sigma, where when a point is outside of the mean by +-3 sigma, then its considered out of control.
However, my process is not normal which is throwing me off.
The process involves counting the number of times that a certain event happens on a day (60%+ of the time the count is 0).
So the process looks like an exponential distribution and I want to draw conclusions from the model  However:
 1) its not continuous, but discrete  - I dont think this is an issue 
 2) the data is not from arrival times or something else but rather a count - I dont think this is an issue.
So, I can fit the data to an exponential model and obtain a lambda, but now what?
Questions:
1) In general, if the data fits a given distribution (assuming all assumptions are met) does it matter that the data is unconventional for that distribution in regards for using the model to draw conclusions?
2) How do I use this model to actually determine if new points are out of control?  Is it even appropriate?  Should I be looking elsewhere?  Thanks.
 A: If you have a discrete exponential distribution you can look at the poisson distribution or geometric distribution for example. As you say you can estimate $\lambda $ from the data but also the variance (=$\sigma^2$). For the poisson distribution the variance is also simply estimated by $\lambda$.
Then if a data point falls outside this mean $\pm 3 \sigma$ it is out of control.
As for your first question: I believe that the data you're describing could fit both a geometric and a poisson distribution but the terminology of events makes me inclined to believe you're really looking at a poission distribution with low $\lambda $. My intuition tells me you want the distribution -and model of your data- to fit the explanation you have but I can't say for sure that using a different, fitting distribution is or isn't allowed.
A: Based upon your description of your data, it looks like a "rare events" control chart is what you are asking for.  Because your data is discrete, the chart type would be a G control chart.
To construct this chart, you make a table of your time-stamped events (simply ignore the 60% of the time when nothing happens), and then calculate the time between events.  Each of these times is then designated $g_1, g_2, \dots, g_i, \dots, g_k$.
The centerline of your chart is drawn as $\overline{g}$ where $\overline{g}=\frac{\sum g_i}{k}$ and the control limits are drawn at $UCL_g=\overline{g}+ 3 \sqrt{\overline{g}\left(\overline{g}+1\right)}$ and $LCL_g=\max \left\{ \overline{g}- 3 \sqrt{\overline{g}\left(\overline{g}+1\right)},0\right\}$.  Your observations, $g_i$ are then plotted in relation to these control limits.
