M-charts for failure frequency

[#1]

We have a production process with very low (ppm-ish) fail rates that we would like to monitor for fails.  Rather than monitoring ppm fail rates, it is a stronger test to monitor the number of fails (or time) between them, under the assumption that they follow a binomial distribution. In an M chart (this is what we call it) you then calculate a Z score every time there is a fail and chart as usual.  It's not clear that JMP has this capability, but maybe it exists under a different name.  Can anyone comment?  We are using JMP 15.2 Pro.

[#2]

Click the Shewhart Variables button in the control panel on the left side of Control Chart Builder and select Rare Event. You can make a G-chart (negative binomial distribution model) or a T-chart (Weibull distribution model).

[#3]

Thanks Mark.  Unfortunately that doesn't seem to quite be what I need.  I can pre-process my data to convert from PPFPPPPPFPPF, etc. into counts of # of passes between each fail, and that has a negative binomial distribution.  The strategy you recommend seems to calculate limits based on the percentile points of the observed distributions.  However for a control chart I need to put in control limits based on a maximum allowed success (=Fail) probability (e.g., 1 ppm), rather than what is observed in the sample.  Our general methodology is to map the binomial percentile to a z score using the inverse normal CDF, so that a value of -3 is a good lower limit; using that approach my data set averages around z = -4.7.  The lower limit on the JMP chart is 0 however, which is essentially z = -INF.  Do you have any recommendations?

[#4]

You can right-click on the chart and select Limits > Set Control Limits. You can now enter your pre-determined limits this way.