# Converting between mean time between failures and survival probabilities

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,
w/m,
-43 (* not implemented *)
];
Print[totalTime[2, 1, 0, 0], " hours of work required"]

• I think this is a statistics / probability question so maybe more appropriate for stats.stackexchange.com Jun 22 at 18:50
• Thanks for the tip, the math was worked out in stats.stackexchange.com/a/579891/511 2 days ago
• Glad it worked out! Perhaps you could summarize the answer here with a self-answer, including a pointer to the CrossValidated post. 2 days ago