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Equipment Availability
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Scott Diamond
Mar 29, 2012, 4:14:02 PM3/29/12
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I’m trying to work out equipment availability. For example suppose you
have a fleet of 10 cars with some failure rate (assume constant
failure rate). I’d like to calculate what the probability is of having
8 cars which are running. I’m trying to work up to this and thought
I’d start with an example with dice. The problem can be stated pretty
simply. Suppose you have 7 dice, what is the chance that at 3 or more
of them come up with the number 6?
I’m of course more interested in the general case of M dice and N of
them with the number 6 and then relate this back to my original
question for equipment availability for my car fleet.
I can work out some simple examples but the general question of M dice
eludes me. Can anyone point me to a reference or anyone have the
ability to answer this question? I would be interested in hiring some
consulting time if anyone could answer and work with me on the more
general question for the car fleet.
Thank you, Scott
have a fleet of 10 cars with some failure rate (assume constant
failure rate). I’d like to calculate what the probability is of having
8 cars which are running. I’m trying to work up to this and thought
I’d start with an example with dice. The problem can be stated pretty
simply. Suppose you have 7 dice, what is the chance that at 3 or more
of them come up with the number 6?
I’m of course more interested in the general case of M dice and N of
them with the number 6 and then relate this back to my original
question for equipment availability for my car fleet.
I can work out some simple examples but the general question of M dice
eludes me. Can anyone point me to a reference or anyone have the
ability to answer this question? I would be interested in hiring some
consulting time if anyone could answer and work with me on the more
general question for the car fleet.
Thank you, Scott
danh...@yahoo.com
Mar 30, 2012, 9:58:23 AM3/30/12
to
On Mar 29, 4:14 pm, Scott Diamond <scott.diamond.m...@gmail.com>
wrote:
This is a standard problem; look up the binomial distribution. For the
car availability model, you also need to describe the down times. It
turns out that the steady-state probability of having k cars available
is binomial and that only the mean up- and down-times matter. Look up
machine-repair model and Engset model in a book on queueing theory.
Some survey books on operations research will have them too; the
Encyclopedia of OR and Management Science edited by Gass and Harris
has them.
wrote:
car availability model, you also need to describe the down times. It
turns out that the steady-state probability of having k cars available
is binomial and that only the mean up- and down-times matter. Look up
machine-repair model and Engset model in a book on queueing theory.
Some survey books on operations research will have them too; the
Encyclopedia of OR and Management Science edited by Gass and Harris
has them.
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