Probability of more than n machines down any hour?
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 chances that there exists $0 < t < Y$ such that at time $t$, there are more than $R$ machines that are down?
probability probability-distributions
edited 3 hours ago
Sauhard Sharma
71714
asked 5 hours ago
Vance
112
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.
|
show 1 more comment
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 chances that there exists $0 < t < Y$ such that at time $t$, there are more than $R$ machines that are down?
probability probability-distributions
edited 3 hours ago
Sauhard Sharma
71714
asked 5 hours ago
Vance
112
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
5 hours ago
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
5 hours ago
@SmileyCraft, the later, the probability that there exists time 0 < t < Y such that more than R machines are down at time t.
– Vance
5 hours ago
@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
5 hours ago
This is a Poisson distribution with expected number of faults in a given hour of $P N$. That determines all probabilities.
– David G. Stork
3 hours ago
|
show 1 more comment
2
2
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 chances that there exists $0 < t < Y$ such that at time $t$, there are more than $R$ machines that are down?
probability probability-distributions
edited 3 hours ago
Sauhard Sharma
71714
asked 5 hours ago
Vance
112
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 chances that there exists $0 < t < Y$ such that at time $t$, there are more than $R$ machines that are down?
probability probability-distributions
probability probability-distributions
edited 3 hours ago
Sauhard Sharma
71714
asked 5 hours ago
Vance
112
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 3 hours ago
Sauhard Sharma
71714
asked 5 hours ago
Vance
112
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 3 hours ago
Sauhard Sharma
71714
edited 3 hours ago
Sauhard Sharma
71714
edited 3 hours ago
Sauhard Sharma
71714
71714
asked 5 hours ago
Vance
112
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 5 hours ago
Vance
112
asked 5 hours ago
Vance
112
112
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
5 hours ago
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
5 hours ago
@SmileyCraft, the later, the probability that there exists time 0 < t < Y such that more than R machines are down at time t.
– Vance
5 hours ago
@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
5 hours ago
This is a Poisson distribution with expected number of faults in a given hour of $P N$. That determines all probabilities.
– David G. Stork
3 hours ago
|
show 1 more comment
2
A Poisson distribution describes this situation.
– David G. Stork
5 hours ago
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
5 hours ago
@SmileyCraft, the later, the probability that there exists time 0 < t < Y such that more than R machines are down at time t.
– Vance
5 hours ago
@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
5 hours ago
This is a Poisson distribution with expected number of faults in a given hour of $P N$. That determines all probabilities.
– David G. Stork
3 hours ago
2
2
A Poisson distribution describes this situation.
– David G. Stork
5 hours ago
A Poisson distribution describes this situation.
– David G. Stork
5 hours ago
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
5 hours ago
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
5 hours ago
@SmileyCraft, the later, the probability that there exists time 0 < t < Y such that more than R machines are down at time t.
– Vance
5 hours ago
@SmileyCraft, the later, the probability that there exists time 0 < t < Y such that more than R machines are down at time t.
– Vance
5 hours ago
@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
5 hours ago
@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
5 hours ago
This is a Poisson distribution with expected number of faults in a given hour of $P N$. That determines all probabilities.
– David G. Stork
3 hours ago
This is a Poisson distribution with expected number of faults in a given hour of $P N$. That determines all probabilities.
– David G. Stork
3 hours ago
|
show 1 more comment
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Vance is a new contributor. Be nice, and check out our Code of Conduct.
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3061320%2fprobability-of-more-than-n-machines-down-any-hour%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Vance is a new contributor. Be nice, and check out our Code of Conduct.
draft saved
draft discarded
Vance is a new contributor. Be nice, and check out our Code of Conduct.
Vance is a new contributor. Be nice, and check out our Code of Conduct.
Vance is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3061320%2fprobability-of-more-than-n-machines-down-any-hour%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
2
A Poisson distribution describes this situation.
– David G. Stork
5 hours ago
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
5 hours ago
@SmileyCraft, the later, the probability that there exists time 0 < t < Y such that more than R machines are down at time t.
– Vance
5 hours ago
@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
5 hours ago
This is a Poisson distribution with expected number of faults in a given hour of $P N$. That determines all probabilities.
– David G. Stork
3 hours ago