Fitting Non-Normal Curves to Data

04/16/2008:

I have a column of 300 numbers that I would like to do a histogram, Johnson bounded curve fit, but the chart that is generated is a normal curve and the program states the selected region could not be fit into a Johnson curve fit What do I have to do to make it fit? I reduced the number of rows to 100 and it worked, but I need all the data if possible.
Thanks,
Wendell W.
Manufacturing Engineer

As I expected, the data is out of control. When you are dealing with n=1 (individuals) data, you need to use some other chart than the Individual-X chart to establish the control of the process, since you need to assume a distribution for the Individual-X chart and you cannot fit a curve until you have established the process is in control (see also: http://www.qualityamerica.com/knowledgecente/knowctrDefining_Control_Limits.asp and associated links).
I used a Moving Average chart with subgroup size 1 and moving size 3. The process was out of control in this scenario, but I noticed groups 205-300 were in control. That is not a lot of data to fit a curve (you would like 300 observations), but it is enough to make it interesting. When I plotted those groups by themselves on the Moving Average chart, they were in control:

Based on this chart, I then plotted all the groups 1-300 on the Ind-X chart and let the software fit the control limits based on groups 205-300 (in the Control Limits tab), specifying a Johnson distribution in the Analysis tab:

This confirms the process out of control, as evidenced on the Moving Average chart.
The key point is that you cannot expect to fit a single distribution to an out of control process: if the process is out of control, then (by definition) there is more than one statistical distribution present in the data.