Life distribution: The failure rate/probability plot does not match with the table

[#1]

Hello,

I am new to the JMP life distribution plot.

I think it is a basic understanding issue.

The below is the test table I made.

According to the description: https://www.jmp.com/support/help/en/18.1/index.shtml#page/jmp/event-plot.shtml#ww1386833

I think it meas there are total 100 samples.

And exactly at 4 readings: 50, 100, 150 and 200, there are 25 new failures happened.

So the failure rate I expected will be:

50, 25%

100, 50%,

150, 75%

200,100%.

Then I lauch the life distribution with setting as below:

However, the dots in the Weibull plot are very different from the failure rate I expected.

For example, the first read point at time 50 has failure rate as ~13%.

I don't understand why.

Could you help me with this?

Thank you very much for your help!

I am using JMP17

[#2]

For large N the estimated percent is 

rank/ ( N + 1)

For N=4 you would get 0.2, 0.4, 0.6 and 0.8.
(instead of the 0.25, 0.5, 0.75, 1 which you expected)

For small N the estimated percent is "corrected". There are several approaches for the correction.
I have seen an overview in Wikipedia - I will try to find it ...

[#3]

It's kind of surprising that "N" is just 4 - because of 4 rows?
And not 100 - because of Freq = 25+25+25+25.

So, users should not be lazy, an use multiple lines instead of aggregating results via Freq : )

the same input, using 100 rows:

[#4]

Hi Hogi,

Thank you for your reply.

I think you meant the probability is an estimate instead of a measured value, so the it won't be the same as the actual failure rate in the test.

Is that correct?

In that case, I wonder if there is a document explains the thoughts and math behind it? I tried the JMP document but had no luck.

And if I want to do the plot as my acual failure rate, is there a way to do it in JMP?

Thank you.

[#5 · Accepted solution]

Sorry, my first guess was wrong.

I just checked the probability values in Life Distribution for tables with different numbers of rows. *) 
Seems that life distribution uses Hazen (Midpoint) plotting positions - independent of the number of data points:

prob = (rank - 0.5) / N

aka "Weibull" is what you get when you use the right click "new formula column" menu in the data table:

Here is an overview of different plotting positions which are available in MatPlotLib (via the "postype" argument)
from: https://matplotlib.org/mpl-probscale/tutorial/closer_look_at_plot_pos.html 

seg = current report () ["Compare Distributions",FrameBox(1)] << find seg (Marker Seg( 1 ));
data= seg <<Get Y Values;

col = current data table() << new column ("prob");
col << set values(data)

 *)  get Y positions from a Marker Seg

[#6]

Thank you Hogi.

I will read into it.