Reliability Theory - Science topic

Dear Sanchit Saran Agarwal , Here is the answer

A Bayesian network, Bayes network, belief network, Bayes(ian) model or probabilistic directed acyclic graphical model is a probabilistic graphical model (a type of statistical model) that represents a set of random variables and their conditional dependencies via a directed acyclic graph (DAG). For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases.

An example of a Markov random field. Each edge represents dependency. In this example: A depends on B and D. B depends on A and D. D depends on A, B, and E. E depends on D and C. C depends on E.

In the domain of physics and probability, a Markov random field (often abbreviated as MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described by an undirected graph. In other words, a random field is said to be Markov random field if it satisfies Markov properties.

A Markov network or MRF is similar to a Bayesian network in its representation of dependencies; the differences being that Bayesian networks are directed and acyclic, whereas Markov networks are undirected and may be cyclic. Thus, a Markov network can represent certain dependencies that a Bayesian network cannot (such as cyclic dependencies); on the other hand, it can't represent certain dependencies that a Bayesian network can (such as induced dependencies). The underlying graph of a Markov random field may be finite or infinite.

This would be of great help with only 13 pages http://www.cs.cmu.edu/~epxing/Class/10708-07/Slides/lecture3-BN&MRF.pdf

You might read my book, 'Landscape Appreciation: Theories since the cultural turn', out last December.

Dear Marcello Fera

I know maybe it is difullcut :) but generally its possible.

Thanks for your answer anyway.

Best.

Dear Parag,

The formula Availability=Uptime/(Uptime+Downtime) is the most general, and therfore will ALWAYS be correct.

The expression MTBF/(MTBF+MTTR) holds only if ALL MTBF & MTTR assumptions are in effect, and these assumptions are another, extensive discussion which is beyond our scope.

From the prctical point of view, Uptime is the interval during which a system is available WHEN WE NEED IT, and Downtime is the complementary period of time.

Downtime can result from faulty system, maintenance (both preventive and corrective), inspection/calibration, and sometimes also power-up and set-up etc.

A major contributor to Downtime is logistic times, during which a system is unavailable due to a missing part, an unavailable technician etc.

Best,

Alon Sneor

Dear Parag Sen,

your problem concerns the relationship between Poisson distribution and exponential distribution - namely:

For example, see Wikipedia:

If for every t > 0 the number of arrivals in the time interval [0, t] follows the Poisson distribution with mean value λt, then the sequence of inter-arrival times are independent and identically distributed exponential random variables having mean 1/λ.

In general, the exponential distribution describes the distribution of time intervals between every two subsequent Poisson events.

The answer to your question can be found at the following addresses:

Best regards

Anatol Badach

Dear Prof. Naderpour.

Thank you very much. I appreciate your reply.

Best wishes,

Hamzeh

I would add another risk of error (or inaccuracy) when comparing the results of different reliability tests.

Depending on how we test item reliability / test plan / - if the reliability information is collected while all items are be damaged - the result will be one.

If the reliability information is collected until then, when a certain number of items are be damaged, the result will be different.

If the reliability information is collected for a certain duration of work - the result will be third. Etc.

This makes it difficult to compare the reliability data and makes the results debatable

The modeling of standby systems is typically done with state-based thinking. You need to distinguish three system states, assuming that the backup unit is a warm spare:

You can now create something like a Markow chain and model the different state transition rates based on your given input. You will end up with probabilities for being in some of the states, expressible as reliability function, but no longer with an overall failure rate or repair rate for the whole system. As the other authors pointed out, it doesn't make sense in most cases. Talking in 'rates' assumes an exponential distribution of failure and repair times - but your standby system does not fail in a 'memoryless' fashion. The failure probability of the overall system at any given point in time depends on the question if and how long the primary unit already failed . There is some in-build dependency in your system behavior, so you can not seriously talk in failure and repair rates about it.

Shooman discussed a simplified example of your case in his book (978-0-471-29342-2) and showed how to derive a reliability function for the resulting system. May this is good enough for your purpose. You can also read papers by K. Trivedi, who investigated a lot of similar cases in the past. Dynamic fault trees have a spare gate for exactly such cases, so any reasonable reliability analysis tool will give you a reliability function for the resulting system. 

 Hi Xin,

There is no one-cut off point for all these parameters. if you tell me what topic you are working on, then i can advise. However, have a look at the following article

Hope this helps

I know about the "Marlowe–Crowne Social Desirability Scale"  as a common tool to multiple studies since 1982.

If it is for indigenous population, I see those (see the attach).

Thanks,

Alejandro Martínez S.

If you have the record of incidents in function of time, you could use the Exponentiated Weibull distribution.

Over 0.6 for reliability is no problem in social science.

and reliability can be improved because you have 10 itmens.

In literary studies it is possible to work with more than one analylist and to look for interrater agreement. It would be arbitrary to make some generalizations depending on one researcher's analyses and conclusions. Interrater agreement, through statistical analyses, gives a score of how much homogeneity, or consensus, there is in the ratings given by judges. But be careful about the refining the tools given to human judges.

If we consider the reserved systems, I think this might be useful.

The concept of single particle nonlocality is discussed in the following papers:

S. M. Tan, D. F. Walls, and M. J. Collett, Phys. Rev. Lett. 66, 252 (1991).

L. Hardy, Phys. Rev. Lett. 73, 2279 (1994).

J.Dunningham and V.Vedral, Phys. Rev. Lett. 99, 180404 (2007)

Thank you very much, it was great

Hi,

no I would still propose the same way: Pairwise comparisons of each method with the gold-standard.

Just some minor modifications(*):

- Instead of using the averages as x-coordinates you can use the values of the gold-standrad then.

- the variance of the differences is a measure for the precision of the new method. Still I would provide quantile- or predcion -ranges.

- if the differences do not scatter around zero, the average difference is the bias of the new method.

- bias (constant or dependent on the reaction time) can be modeled by regression and the estimated regression curve can be used to correct the bias of the new method.

- the residuals of this regression are a measure of the precision of the new method (this is the same as the "bias-corrected differences"; after bias-correction the differences will scatter around zero; again I would provide quantile- or prediction ranges of the corrected differences/residuals)

- it might be the the precision depends on the values. This is difficult to tackle. If you have a lot of values per method you may estimate the variance depending on the value with a running-window approach and then probably use a regression to model a functional relationship to variance versus values.

You can finally compare all the new methods with regard to bias (size, constancy or trend) and precision. Since the bias can be corrected (knowing a gold standard), the main criterion will likely be the precision.

(*) When I write "variance" i mean variability, measured by any means (not strictly the variance as the average squared difference). It may be for instance the median absolute deviation, or some quantile range or prediction range - or some other measure of variability. You should select the measure that is most suited for your specific problem.