MathsGee Q&A - Recent questions tagged failure
https://mathsgee.com/tag/failure
Powered by Question2AnswerWhat is South Africa’s competitive advantage as far as re-industrialisation is concerned?
https://mathsgee.com/58164/africas-competitive-advantage-industrialisation-concerned
What is South Africa’s competitive advantage as far as re-industrialisation is concerned?Economics & Financehttps://mathsgee.com/58164/africas-competitive-advantage-industrialisation-concernedSat, 19 Aug 2023 06:52:52 +0000Is it accurate to state that "As far as capital is concerned, it is now through statistics that dead generations, or at least past events, weigh on the brains of the living"?
https://mathsgee.com/51070/accurate-capital-concerned-through-statistics-generations
Is it accurate to state that "As far as capital is concerned, it is now through statistics that dead generations, or at least past events, weigh on the brains of the living"?Data Science & Statisticshttps://mathsgee.com/51070/accurate-capital-concerned-through-statistics-generationsSun, 05 Feb 2023 13:09:43 +0000How does the use of a distributed network in a blockchain prevent single points of failure?
https://mathsgee.com/48150/distributed-network-blockchain-prevent-single-points-failure
How does the use of a distributed network in a blockchain prevent single points of failure?Blockchain & Cryptohttps://mathsgee.com/48150/distributed-network-blockchain-prevent-single-points-failureThu, 15 Dec 2022 01:00:57 +0000If the spare part of a cement mixer has the Weibull failure-time distribution with the parameters \(\alpha=\) \(0.001\) per hour and \(\beta=0.65\), find the probability that it will not operate successfully for at least 1,000 hours.
https://mathsgee.com/43726/distribution-parameters-probability-operate-successfully
If the spare part of a cement mixer has the Weibull failure-time distribution with the parameters \(\alpha=\) \(0.001\) per hour and \(\beta=0.65\), find the probability that it will not operate successfully for at least 1,000 hours.Data Science & Statisticshttps://mathsgee.com/43726/distribution-parameters-probability-operate-successfullyFri, 12 Aug 2022 04:40:04 +0000A transistor has a constant failure rate of \(0.005\) per ten thousand hours.
https://mathsgee.com/43724/transistor-has-constant-failure-rate-005-per-thousand-hours
A transistor has a constant failure rate of \(0.005\) per ten thousand hours.<br />
<br />
(a) What is the probability that it will perform satisfactorily for at least 75,000 hours?<br />
<br />
(b) What is the 20,000-hour reliability of a chip consisting of 6 such transistors connected in series?Data Science & Statisticshttps://mathsgee.com/43724/transistor-has-constant-failure-rate-005-per-thousand-hoursFri, 12 Aug 2022 04:37:52 +0000For a given product, suppose the probability of an initial failure (a failure prior to time \(t=\alpha\) ) is \(\theta_{1}\), the probability of a wear-out failure (a failure beyond time \(t=\beta\) ) is \(\theta_{2}\), and that for the interval
https://mathsgee.com/43723/probability-initial-probability-failure-failure-interval
For a given product, suppose the probability of an initial failure (a failure prior to time \(t=\alpha\) ) is \(\theta_{1}\), the probability of a wear-out failure (a failure beyond time \(t=\beta\) ) is \(\theta_{2}\), and that for the interval \(\alpha \leq t \leq \beta\) the failure-time density is given by<br />
\[<br />
f(t)=\frac{1-\theta_{1}-\theta_{2}}{\beta-\alpha}<br />
\]<br />
(a) Find an expression for \(F(t)\) for the interval \(\alpha \leq t \leq \beta\)<br />
(b) Show that for the interval \(\alpha \leq t \leq \beta\), the failure rate is given by<br />
\[<br />
Z(t)=\frac{1-\theta_{1}-\theta_{2}}{(\beta-\alpha)\left(1-\theta_{1}\right)-\left(1-\theta_{1}-\theta_{2}\right)(t-\alpha)}<br />
\]<br />
(c) Suppose that the failure of a digital television set is considered to be an initial failure if it occurs during the first 100 hours of usage and a wear-out failure if it occurs after 15,000 hours. Assuming that the model given in this exercise holds and that \(\theta_{1}\) and \(\theta_{2}\) equal \(0.05\) and \(0.75\), respectively, sketch the graph of the failure-rate function from \(t=100\) to \(t=15,000\) hours.Data Science & Statisticshttps://mathsgee.com/43723/probability-initial-probability-failure-failure-intervalFri, 12 Aug 2022 04:36:44 +0000In some reliability problems we are concerned only with initial failures, treating a component as if (for all practical purposes) it never fails, once it has survived past a certain time \(t=\alpha\).
https://mathsgee.com/43722/reliability-concerned-failures-treating-component-practical
In some reliability problems we are concerned only with initial failures, treating a component as if (for all practical purposes) it never fails, once it has survived past a certain time \(t=\alpha\). In a problem like this, it may be reasonable to use the failure rate<br />
\[<br />
Z(t)= \begin{cases}\beta\left(1-\frac{t}{\alpha}\right) & \text { for } 0<t<\alpha \\ 0 & \text { elsewhere }\end{cases}<br />
\]<br />
(a) Find expressions for \(f(t)\) and \(F(t)\).<br />
(b) Show that the probability of an initial failure is given by<br />
\[<br />
1-e^{-\alpha \beta / 2}<br />
\]Data Science & Statisticshttps://mathsgee.com/43722/reliability-concerned-failures-treating-component-practicalFri, 12 Aug 2022 04:35:18 +0000Is electric shock an example of failure of a capacitor?
https://mathsgee.com/18762/is-electric-shock-an-example-of-failure-of-a-capacitor
Is electric shock an example of failure of a capacitor?General Knowledgehttps://mathsgee.com/18762/is-electric-shock-an-example-of-failure-of-a-capacitorSat, 05 Sep 2020 05:38:57 +0000When should one give up on mathematics?
https://mathsgee.com/855/when-should-one-give-up-on-mathematics
When should one give up on mathematics?Mathematicshttps://mathsgee.com/855/when-should-one-give-up-on-mathematicsWed, 08 May 2019 05:44:53 +0000SHould one treat failure as an exception or as a regular occurrence to be dealt with?
https://mathsgee.com/847/should-treat-failure-exception-regular-occurrence-dealt-with
SHould one treat failure as an exception or as a regular occurrence to be dealt with?Mathematicshttps://mathsgee.com/847/should-treat-failure-exception-regular-occurrence-dealt-withThu, 02 May 2019 21:44:28 +0000