Statistics Modeling Question

I am trying to model the amount of time it will take to produce a
component-ized product. It has been a few years since I left college,
and I'm trying to get my head back around this stuff... here's
something analogous to what I'm trying to do...

A widget is produced by producing widget-part-a, widget-part-b, widget-
part-c, and widget-part-d.

widget-part-a historically takes:
- >= 0 hrs at 0 probability
- 0-8 hrs at .05 probability
- 8-16 hrs at .35 probability
- 16-24 hrs at .25 probability
- 24-32 hrs at .16 probability
- 32-40 hrs at .10 probability
- 40-48 hrs at .05 probability
- 48-56 hrs at .03 probability
- 56-64 hrs at .01 probability

widget-part-b historically follows the same distribution, but cannot
be started until halfway through the process of widget-part-a

widget-part-c takes half the time and can be started in parallel with
widget-part-a (and can be run in parallel with widget-part-b if there
is overlap)

widget-part-d follows same distribution as widget-part-c but cannot be
started until widget-part-c completes.

I want to know how long until the entire widget is complete. I can
reason that there is 0 probability until the last of the 4 widgets is
complete, but I am not sure where to go from there.

I should note that I am just trying to get an approximation. We are
reviewing our estimation techniques, and I am trying to introduce some
statistics (currently the technique treats estimation as
deterministic).

Any help would be much appreciated. I was pretty strong in stats, but
having been out of school for a few years, I need a nudge to wrap my
head around this again.

Thanks!
.

Relevant Pages

  • Re: Statistics Modeling Question
    ... 8-16 hrs at .35 probability ... widget-part-b historically follows the same distribution, ... be started until halfway through the process of widget-part-a ...
    (sci.stat.math)
  • Re: Statistics Modeling Question
    ... and I'm trying to get my head back around this stuff... ... 8-16 hrs at .35 probability ... be started until halfway through the process of widget-part-a ...
    (sci.stat.math)
  • Re: Statistics Modeling Question
    ... and I'm trying to get my head back around this stuff... ... 8-16 hrs at .35 probability ... be started until halfway through the process of widget-part-a ...
    (sci.stat.math)
  • Re: Statistics Modeling Question
    ... and I'm trying to get my head back around this stuff... ... 8-16 hrs at .35 probability ... If you use some physical indication, and if you see that indication nine hours into the production of an A widget, does that guarantee that the A widget will need exactly nine more hours to complete? ...
    (sci.stat.math)
  • Re: Statistics Modeling Question
    ... and I'm trying to get my head back around this stuff... ... part-c, and widget-part-d. ... 8-16 hrs at .35 probability ...
    (sci.stat.math)