Probability of more than n machines down any hour?
4
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
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4
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
New contributor
Vance is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
A Poisson distribution describes this situation.
– David G. Stork
Jan 4 at 4:19
1
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 $t$?
– SmileyCraft
Jan 4 at 4:21
@SmileyCraft, the later, the probability that there exists time 0 < t < Y such that more than R machines are down at time t.
– Vance
Jan 4 at 4:27
@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?
– Vance
Jan 4 at 4:36
This is a Poisson distribution with expected number of faults in a given hour of $P N$. That determines all probabilities.
– David G. Stork
Jan 4 at 6:38
|
show 1 more comment
4
4
4
2
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
New contributor
Vance is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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
New contributor
Vance is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 4 at 4:17
VanceVance
212
New contributor
Vance is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Jan 4 at 15:55
Vance
asked Jan 4 at 4:17
VanceVance
212
New contributor
Vance is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 4 at 4:17
VanceVance
212
asked Jan 4 at 4:17
VanceVance
212
212
New contributor
Vance is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Vance is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Vance is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
A Poisson distribution describes this situation.
– David G. Stork
Jan 4 at 4:19
1
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 $t$?
– SmileyCraft
Jan 4 at 4:21
@SmileyCraft, the later, the probability that there exists time 0 < t < Y such that more than R machines are down at time t.
– Vance
Jan 4 at 4:27
@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?
– Vance
Jan 4 at 4:36
This is a Poisson distribution with expected number of faults in a given hour of $P N$. That determines all probabilities.
– David G. Stork
Jan 4 at 6:38
|
show 1 more comment
2
A Poisson distribution describes this situation.
– David G. Stork
Jan 4 at 4:19
1
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 $t$?
– SmileyCraft
Jan 4 at 4:21
@SmileyCraft, the later, the probability that there exists time 0 < t < Y such that more than R machines are down at time t.
– Vance
Jan 4 at 4:27
@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?
– Vance
Jan 4 at 4:36
This is a Poisson distribution with expected number of faults in a given hour of $P N$. That determines all probabilities.
– David G. Stork
Jan 4 at 6:38
2
2
A Poisson distribution describes this situation.
– David G. Stork
Jan 4 at 4:19
A Poisson distribution describes this situation.
– David G. Stork
Jan 4 at 4:19
1
1
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 $t$?
– SmileyCraft
Jan 4 at 4:21
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 $t$?
– SmileyCraft
Jan 4 at 4:21
@SmileyCraft, the later, the probability that there exists time 0 < t < Y such that more than R machines are down at time t.
– Vance
Jan 4 at 4:27
@SmileyCraft, the later, the probability that there exists time 0 < t < Y such that more than R machines are down at time t.
– Vance
Jan 4 at 4:27
@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?– Vance
Jan 4 at 4:36
@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?– Vance
Jan 4 at 4:36
This is a Poisson distribution with expected number of faults in a given hour of $P N$. That determines all probabilities.
– David G. Stork
Jan 4 at 6:38
This is a Poisson distribution with expected number of faults in a given hour of $P N$. That determines all probabilities.
– David G. Stork
Jan 4 at 6:38
|
show 1 more comment
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2
A Poisson distribution describes this situation.
– David G. Stork
Jan 4 at 4:19
1
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 $t$?
– SmileyCraft
Jan 4 at 4:21
@SmileyCraft, the later, the probability that there exists time 0 < t < Y such that more than R machines are down at time t.
– Vance
Jan 4 at 4:27
@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?– Vance
Jan 4 at 4:36
This is a Poisson distribution with expected number of faults in a given hour of $P N$. That determines all probabilities.
– David G. Stork
Jan 4 at 6:38