This is more of a math question, but I'm hoping some math wizard can help me map these concepts to functions in Mathematica's reliability API.

$f$ of my machines will experience a failure in the first 24 hours of operation. (ie, $f\approx 0.2$ from AWS spot instance interruption rate)

It takes $s$ seconds to replace this machine, during which time, all work is stopped on all machines.

I need to perform total of $w$ machine-hours of work, by using $m$ machines simultaneously.

How would I write a function that takes $w$, $m$, $s$, $f$ and returns expected time to complete the work?

totalTime[w_, m_, s_, f_] := If[f == 0,
   -43 (* not implemented *)
Print[totalTime[2, 1, 0, 0], " hours of work required"]
  • $\begingroup$ I think this is a statistics / probability question so maybe more appropriate for stats.stackexchange.com $\endgroup$
    – MarcoB
    Jun 22 at 18:50
  • $\begingroup$ Thanks for the tip, the math was worked out in stats.stackexchange.com/a/579891/511 $\endgroup$ 2 days ago
  • 1
    $\begingroup$ Glad it worked out! Perhaps you could summarize the answer here with a self-answer, including a pointer to the CrossValidated post. $\endgroup$
    – MarcoB
    2 days ago


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