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I am reading over some process analysis data for some failure analysis tests, and I have come across the following definition of an "estimated cumulative probability": $$F(t) = \frac{i-3/8}{N+1/4},$$ where $i$ is the rank of the failure case (i.e. failure order), and $N$ is the total number of samples.

I had some difficulty in figuring out the who/what/why behind this formula. An internet search brought me to this page, where it seems to be referred to as "White's plotting position." However, a reference is not presented.

Is this relationship familiar to anyone, and if so, could you provide either a reference or a background on this formula. Specifically, why is this a good estimate of cumulative probability, and how those results may be interpreted.

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  • $\begingroup$ For a graphical and intuitive explanation of where this kind of plotting position formula comes from, please see the second half of my class notes at quantdec.com/envstats/notes/class_02/… . $\endgroup$
    – whuber
    Commented Aug 16, 2012 at 18:42

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This is called White’s plotting position, an alternative to the median rank. Check out The Weibull Analysis Handbook, page 21.

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I also found that this has to do with the Weibull distribution for cumulative rank order of failures when the data have more than one censored observation. The StatSoft manual that you cite referenced Dobson (1994) which could be found by properly searching the references for the site.

Dodson, B. (1994). Weibull analysis. Milwaukee, Wisconsin: ASQC.

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