Probability of more than n machines down any hour?
4
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Suppose we have $N$ identical machines, at any given hour, there's a chance $P$ that any given machine went down. A down machine takes $T$ hours to recover. How do I calculate the chances that in a given longer interval $Y$ (assume $Y >> T$), what are the probability that there exists hour $t$, $0 < t < Y$, such that at $t$ there are more than $R$ machines that are down?
probability probability-distributions
asked Jan 4 at 4:17
VanceVance
212
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show 1 more comment
4
$begingroup$
Suppose we have $N$ identical machines, at any given hour, there's a chance $P$ that any given machine went down. A down machine takes $T$ hours to recover. How do I calculate the chances that in a given longer interval $Y$ (assume $Y >> T$), what are the probability that there exists hour $t$, $0 < t < Y$, such that at $t$ there are more than $R$ machines that are down?
probability probability-distributions
asked Jan 4 at 4:17
VanceVance
212
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2
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A Poisson distribution describes this situation.
$endgroup$
– David G. Stork
Jan 4 at 4:19
1
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Do you want to know the probability more than $R$ machines are down at time $Y$ or the probability that there exists time $0<t<Y$ such that more than $R$ machines are down at time $t$?
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– SmileyCraft
Jan 4 at 4:21
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@SmileyCraft, the later, the probability that there exists time 0 < t < Y such that more than R machines are down at time t.
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– Vance
Jan 4 at 4:27
$begingroup$
@DavidG.Stork, how would I apply Poisson distribution to this scenario? I can maybe find the average number of machines going down per year based on theP, and calculate the chances for r <R, but that does not necessarily answer if they are concurrent?
$endgroup$
– Vance
Jan 4 at 4:36
$begingroup$
This is a Poisson distribution with expected number of faults in a given hour of $P N$. That determines all probabilities.
$endgroup$
– David G. Stork
Jan 4 at 6:38
|
show 1 more comment
4
4
4
2
$begingroup$
Suppose we have $N$ identical machines, at any given hour, there's a chance $P$ that any given machine went down. A down machine takes $T$ hours to recover. How do I calculate the chances that in a given longer interval $Y$ (assume $Y >> T$), what are the probability that there exists hour $t$, $0 < t < Y$, such that at $t$ there are more than $R$ machines that are down?
probability probability-distributions
asked Jan 4 at 4:17
VanceVance
212
$endgroup$
Suppose we have $N$ identical machines, at any given hour, there's a chance $P$ that any given machine went down. A down machine takes $T$ hours to recover. How do I calculate the chances that in a given longer interval $Y$ (assume $Y >> T$), what are the probability that there exists hour $t$, $0 < t < Y$, such that at $t$ there are more than $R$ machines that are down?
probability probability-distributions
probability probability-distributions
asked Jan 4 at 4:17
VanceVance
212
asked Jan 4 at 4:17
VanceVance
212
edited Jan 4 at 15:55
Vance
asked Jan 4 at 4:17
VanceVance
212
asked Jan 4 at 4:17
VanceVance
212
asked Jan 4 at 4:17
VanceVance
212
212
2
$begingroup$
A Poisson distribution describes this situation.
$endgroup$
– David G. Stork
Jan 4 at 4:19
1
$begingroup$
Do you want to know the probability more than $R$ machines are down at time $Y$ or the probability that there exists time $0<t<Y$ such that more than $R$ machines are down at time $t$?
$endgroup$
– SmileyCraft
Jan 4 at 4:21
$begingroup$
@SmileyCraft, the later, the probability that there exists time 0 < t < Y such that more than R machines are down at time t.
$endgroup$
– Vance
Jan 4 at 4:27
$begingroup$
@DavidG.Stork, how would I apply Poisson distribution to this scenario? I can maybe find the average number of machines going down per year based on theP, and calculate the chances for r <R, but that does not necessarily answer if they are concurrent?
$endgroup$
– Vance
Jan 4 at 4:36
$begingroup$
This is a Poisson distribution with expected number of faults in a given hour of $P N$. That determines all probabilities.
$endgroup$
– David G. Stork
Jan 4 at 6:38
|
show 1 more comment
2
$begingroup$
A Poisson distribution describes this situation.
$endgroup$
– David G. Stork
Jan 4 at 4:19
1
$begingroup$
Do you want to know the probability more than $R$ machines are down at time $Y$ or the probability that there exists time $0<t<Y$ such that more than $R$ machines are down at time $t$?
$endgroup$
– SmileyCraft
Jan 4 at 4:21
$begingroup$
@SmileyCraft, the later, the probability that there exists time 0 < t < Y such that more than R machines are down at time t.
$endgroup$
– Vance
Jan 4 at 4:27
$begingroup$
@DavidG.Stork, how would I apply Poisson distribution to this scenario? I can maybe find the average number of machines going down per year based on theP, and calculate the chances for r <R, but that does not necessarily answer if they are concurrent?
$endgroup$
– Vance
Jan 4 at 4:36
$begingroup$
This is a Poisson distribution with expected number of faults in a given hour of $P N$. That determines all probabilities.
$endgroup$
– David G. Stork
Jan 4 at 6:38
2
2
$begingroup$
A Poisson distribution describes this situation.
$endgroup$
– David G. Stork
Jan 4 at 4:19
$begingroup$
A Poisson distribution describes this situation.
$endgroup$
– David G. Stork
Jan 4 at 4:19
1
1
$begingroup$
Do you want to know the probability more than $R$ machines are down at time $Y$ or the probability that there exists time $0<t<Y$ such that more than $R$ machines are down at time $t$?
$endgroup$
– SmileyCraft
Jan 4 at 4:21
$begingroup$
Do you want to know the probability more than $R$ machines are down at time $Y$ or the probability that there exists time $0<t<Y$ such that more than $R$ machines are down at time $t$?
$endgroup$
– SmileyCraft
Jan 4 at 4:21
$begingroup$
@SmileyCraft, the later, the probability that there exists time 0 < t < Y such that more than R machines are down at time t.
$endgroup$
– Vance
Jan 4 at 4:27
$begingroup$
@SmileyCraft, the later, the probability that there exists time 0 < t < Y such that more than R machines are down at time t.
$endgroup$
– Vance
Jan 4 at 4:27
$begingroup$
@DavidG.Stork, how would I apply Poisson distribution to this scenario? I can maybe find the average number of machines going down per year based on the
P, and calculate the chances for r < R, but that does not necessarily answer if they are concurrent?$endgroup$
– Vance
Jan 4 at 4:36
$begingroup$
@DavidG.Stork, how would I apply Poisson distribution to this scenario? I can maybe find the average number of machines going down per year based on the
P, and calculate the chances for r < R, but that does not necessarily answer if they are concurrent?$endgroup$
– Vance
Jan 4 at 4:36
$begingroup$
This is a Poisson distribution with expected number of faults in a given hour of $P N$. That determines all probabilities.
$endgroup$
– David G. Stork
Jan 4 at 6:38
$begingroup$
This is a Poisson distribution with expected number of faults in a given hour of $P N$. That determines all probabilities.
$endgroup$
– David G. Stork
Jan 4 at 6:38
|
show 1 more comment
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2
$begingroup$
A Poisson distribution describes this situation.
$endgroup$
– David G. Stork
Jan 4 at 4:19
1
$begingroup$
Do you want to know the probability more than $R$ machines are down at time $Y$ or the probability that there exists time $0<t<Y$ such that more than $R$ machines are down at time $t$?
$endgroup$
– SmileyCraft
Jan 4 at 4:21
$begingroup$
@SmileyCraft, the later, the probability that there exists time 0 < t < Y such that more than R machines are down at time t.
$endgroup$
– Vance
Jan 4 at 4:27
$begingroup$
@DavidG.Stork, how would I apply Poisson distribution to this scenario? I can maybe find the average number of machines going down per year based on the
P, and calculate the chances for r <R, but that does not necessarily answer if they are concurrent?$endgroup$
– Vance
Jan 4 at 4:36
$begingroup$
This is a Poisson distribution with expected number of faults in a given hour of $P N$. That determines all probabilities.
$endgroup$
– David G. Stork
Jan 4 at 6:38