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Re: Plotting a simple line at a weibull

  • To: mathgroup at
  • Subject: [mg125330] Re: Plotting a simple line at a weibull
  • From: Bill Rowe <readnews at>
  • Date: Wed, 7 Mar 2012 05:35:41 -0500 (EST)
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On 3/6/12 at 5:57 AM, tgarza10 at (Tomas Garza) wrote:

>The best I could think of is, by trial and error, to find the right
>position for the horizontal line you want. The idea is to put an
>Epilog in the ProbabilityScalePlot with the appropriate coordinates
>for the end points, for example: ProbabilityScalePlot[{data1, data2,
>data3}, "Weibull",  PlotRange -> Automatic, GridLines -> Automatic,
>GridLinesStyle -> "Classic",  FrameLabel ->
>{{Style["Ausfallwahrscheinlichkeit F(t) in %", Italic,    FontSize
>-> 12],     ""}, {Style["Lebensdauer", Italic, FontSize -> 12],
>""}},  Epilog -> {Thickness[0.005], Line[{{-3.25, 0.025}, {3.6,
>0.025}}]},  Frame -> True] Or maybe you can translate from the scale
>in the graph to the necessary coordinates for Line. Anyway, it looks
>more or less right. -Tomas

No need to use trial and error. What you have to keep in mind is
the x-coordinate for the line will be Log[t] where t is the
value seen on the x-axis. And the y-coordinate will be
Log[-Log[1-CDF]] where CDF is the value of the cumulative
distribution function. This has a particularly simple expression
for the 63rd percentile of a Wiebull. At a characteristic
lifetime the CDF will be 1-1/e. So, the y coordinate becomes
exactly 0 in the transformed coordinate space.

And since the desire is to have the line extend the full width
of the plot picking the starting x coordinate to be Log[t] for
any t smaller than the lowest value seen and the stop coordinate
to be any t greater than the maximum value seen ensures the line
extends the full width of the plot. There is no penalty for
making the x-coordinates smaller/larger than shown since the
PlotRange specification will prevent the line from extending too far.

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