topic M-charts for failure frequency in Discussions

M-charts for failure frequency

scottrubel0 — Fri, 09 Jun 2023 00:24:03 GMT

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.

Re: M-charts for failure frequency

Mark_Bailey — Tue, 03 Nov 2020 19:16:29 GMT

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).

Re: M-charts for failure frequency

scottrubel0 — Wed, 18 Nov 2020 20:57:21 GMT

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?

Re: M-charts for failure frequency

Mark_Bailey — Thu, 19 Nov 2020 13:34:43 GMT

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