reliability (no poker content)

[irchans]

pvn,

I wrote a quick simulation for an additional comparison. I don't think my Mathematica code is really readable, but it beats writing a longer c++ program. Here is the code and the results:

<font class="small">Code:</font><hr /><pre>
(* deln computes the differences between elements of the
vector v whose indices differ by n *)
deln[v_List, n_Integer] := Drop[v, n] - Drop[v, -n];

vOverlaps = Table[
(* generate 400 start times in seconds past Jan 1 *)
vStartTimes = Table[ Random[Integer, {0, 365*24*60*60}], {400}] // Sort;

(* count the overlaps where the start times differ
by less than 3600*3 seconds *)
iOverlaps = Count[ Join @@ Table[
deln[vStartTimes, n], {n, 5}],
x_ /; Abs[x] &lt; 3600*3],
{10000}];

(* print the average number of overlaps *)
Print[ Plus @@ vOverlaps /10000. ];
</pre><hr />

I ran the code above twice and got the following results:

first run - ave 54.6250 overlaps/year over 10000 years.
second run - ave 54.6962 overlaps/year over 10000 years.

I think I can use the reasoning in your previous post to generate a number near 54.

As uuDevil pointed out, the expected number of failures in a three hour period is 400/(24*365/3)=0.136986.

We expect to have 400 failure events (averaging three hours each) in a year. During each one of those, the expected number of other machines that will start fail is 399* 3/365/24 = 0.136644. (Except after 9 pm December 31st.)

Now if we multiply 400*0.136644 = 54.6575 we get the expected number of failures. We have not counted any overlaps twice because for each failure start time we only counted overlaps with failures that began after the original start time.