Markov Modeling

Markov modeling is a technique for calculating system reliability as exponential transitions between various states of operability, much like atomic transitions. In addition to the use of constant transition rates, the model depends only on the initial and final states (no memory). 

After the startup transient has passed, i.e., t , this becomes equation 2.5- (3.  

Equation 2.5-43 is a definition of availability. Since 1/p = MTTR (mean time to repair) and 1/A, = MTTF (mean time to failure) A more conventional definition is given by 2.5-44. 

Unavailability = I availability. If p A, it is, asymptotically, found from equation 2.5-43 to be equation 2.5-45, where t -- 1/p is the mean time between repairs. 

While not shown here, if a system has k redundancies of identical subsystems, each with failure q(o 

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A. Mohammad-Djafari M. Nikolova. Eddy current tomography using binary markov model. Signal Processing, 49 119-132, 1996. 

Fig. 10.22 Hidden Markov model used for protein sequence analysis, are match states (corresponding in this...

Mian, K Sjolander and D Haussler 1994. Hidden Markov Models in Computational Biology. Applications to Protein Modelling. Journal of Molecular Biology 235 1501-1531). 

Having built a hidden Markov model for a particular family of proteins, it can then b< used to search a database. A score is computed for each sequence in the database anc those sequences that score significantly more than other sequences of a similar length ar( identified. This was demonstrated for two key families of proteins, globins and kinases ii the original paper [Krogh et al. 1994]. For the kinases, 296 sequences with a Z score abov<... 

Eddy S R 1996. Hidden Markov Models. Current Opinion in Structural Biology 6 361-365. 

Rabiner L R 1989. A Tutorial on Hidden Markov Models and Selected Applications in Spe Recognition. Fhroceedings cf the IEEE TI-lSl-19rB. 

Markov model A mathematical model used in reliabihty analysis. For many safety apphcations, a discrete-state (e.g., working or failed), continuous-time model is used. The failed state may or may not be repairable. 

A Krogh, M Brown, IS Mian, K Sjolander, D Haussler. Hidden Markov models m computational biology Applications to protein modeling. I Mol Biol 235 1501-1531, 1994. 

K Karplus, K Sjolander, C Barrett, M Cline, D Haussler, R Hughey, L Holm, C Sander. Predicting protein structure using hidden Markov models. Proteins Suppl 134-139, 1997. 

TJ Hubbard, J Park. Eold recognition and ab initio structure predictions using hidden Markov models and (I-strand pair potentials. Proteins Struct Eunct Genet 23 398-402, 1995. 

V DiErancesco, J Garnier, PJ Munson. Protein topology recognition from secondary structure sequences Application of the hidden Markov models to the alpha class proteins. J Mol Biol 267 446-463, 1997. 

Accident progression scenarios are developed and modeled as event trees for each of these accident classes. System fault trees are developed to the component level for each branch point, and the plant response to the failure is identified. Generic subtrees are linked to the system fault trees. An example is "loss of clcciric power" which is analyzed in a Markov model that considers the frequencies of lo,sing normal power, the probabilities of failure of emergency power, and the mean times to repair parts of the electric power supply. 

Answer The Markov model was prepared for one diesel having two states working and failed. For two diesels, the probability of both failing at the same time is X = Vi X X, t, where t is... 

Building sequence profiles or Hidden Markov Models to perform more sensitive homology searches. A sequence profile contains information about the variability of every sequence position, improving structure prediction methods (secondary structure prediction). Sequence profile searches have become readily available through the introduction of PsiBLAST [4]... 

A Hidden Markov Model (HMM) is a general probabilistic model for sequences of symbols. In a Markov chain, the probability of each symbol depends only on the preceding one. Hidden Markov models are widely used in bioinformatics, most notably to replace sequence profile in the calculation of sequence alignments. 

Heparin Sulfate Proteoglycans Hepatic Lipase Hepatitis Hepatitis C Heptahelical Domain Heptahelical Receptors HERG-channels Heterologous Desensitization Heterologous Expression System Heterotrimeric G-Proteins Hidden Markov Model High-density Lipoprotein (HDL)... 

HIV/AIDS-induced mortality and morbidity of workers can result in significant economic loss to business, including direct cost due to increased insurance premiums paid by employers, costs due to increased benefits paid by employers, indirect costs due to lost time due to illness, lost and reduced productivity, and other costs, like cost to new training and hiring of staff. Famham and Gorsky (1994) used a Markov model to calculate the expected medical, disability, employee replacement, life insurance, and pension costs to a business firm in the US for an HIV-infected... 

A portion of the database for this polymer is shown in Figure 6. Literature reports that this polymer follows second-order Markov statistics ( 21 ). And, in fact, probabilities that produced simulated spectra comparable to the experimental spectrum could not be obtained with Bernoullian or first-order Markov models. Figure 7 shows the experimental and simulated spectra for these ten pentads using the second-order Markov probabilities Pil/i=0.60, Piv/i=0.35, Pvi/i=0.40, and Pvv/i=0.55 and a linewidth of 14.8 Hz. 

Figure 24.3 Strategic pathway of Bayesian Markov model showing decision points for diagnosis of pancreatic cancer [14]. Bx = biopsy Dx = diagnosis.

Lewis R, Canafax D, Pettit K, et al. Use of Markov model for evaluating the cost-effectiveness of immunosuppressive therapies in renal transplant recipients. Transpl Proc 1996 28 2214-17. 

The Markov 3 order or hi er model can be used to account Bar tire effect of a tertiary norbomene in the polymer drain on the reaction rate and copolymer composition. Higher order models, however, require an inerted number of traction parameters to be determined. For example, in penpmultimate mo l (Markov 3 order model), 16 propa tion rate ranstants should be determined, whraeas 8 rate constants are needed in the penuLtiinate model. In this work, we propose a reduced-order Markov model (ROMM) to effectively reduce the number of reaction parameters. 

Winblad B (1999b). The cost-effectiveness of Donepezil therapy in Swedish patients with Alzheimer s disease a Markov model. Clin Therll, 1320-40. 

Zhang L, Dai S (2007) Application of Markov Model to environmental fate of phenanthrene in Lanzhou Reach of Yellow River. Chemosphere 67 1296—1299... 

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