Multi-state model

More recently, two-state E/B models have been proposed by Chujo and Doi (9.10) for the analysis of polypropylene. Similar E/B models were proposed by Cheng(11) and Asakura, et al(12) for polybutylene. For copolymers, two-state B/B models have been proposed for ethylene-propylene copolymers,(11,13-15) and propylene-butylene copolymers.(11,13) Recently, Cheng(11) generalized these multi-state models and developed computer methodology for the general analysis of such systems. A number of polymer systems were treated. 

Multi-State Models. In studies of copolymerization kinetics and polymer microstructure, the use of reaction probability models can provide a convenient framework whereby the experimental data can be organized and interpreted, and can also give insight on reaction mechanisms. (1.,2) The models, however, only apply to polymers containing one polymer component. For polymers with mixtures of different components, the one-state simple models cannot be used directly. Generally multi-state models(11) are needed, viz. 

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Prowse V (2005) State Dependence in a Multi-State Model of Employment Dynamics. IZA Discussion Paper 1623. IZA, Bonn... 

The Nuclear Magnetic Resonance Model In this section a nuclear magnetic resonance multi state model is fitted to the experimental relaxation data shown in Figures 1 and 2. A fit is not attempted for sample 5 at 100% RH because of the anomolous Ti,T2versus 10VT°K profiles produced by freezing (see Figure 1). 

A multi state model on component as well as system level. 

Figure 2. A multi-state model of an element of the IMS signalling network.

Zahalak, G. I. (2000). The two-state cross-bridge model of muscle is an asymptotic limit of multi-state models, Journal of Theoretical Biology, 204 67-82. 

To tie results of investigations of complex systems inside-dependences together with results coming from assumed their outside-dependencies, the semi-Markov model (Grabski 2002, Kolowrocki 2013, Limnios Oprisan 2005) can be used to describe those systems operation processes. This linking of inside and outside of complex systems dependencies under assumed their structures multi-state models, is the main idea of the systems reliability analysis methodology presented in the paper. 

ABSTRACT This paper presents a holistic treatment to multiple dependent competing degradation processes, by employing the Piecewise-Deterministic Markov Process (PDMP) modeling framework. The proposed method can handle the dependencies between physics-based models, between multi-state models and between these two types of models. A Monte Carlo simulation algorithm is developed to compute the components/systems reliability. A case study on one subsystem of the Residual Heat Removal System (RHRS) of a nuclear power plant is illustrated. 

Based on the available information/data about components degradations and failures, two main types of models are used to represent the degradation processes of components physics-based model and multi-state model. 

We assume that there are N components in the system, K = K, K, . .., K, whose degradation processes are modeled by multi-state models. The component has <4 + 1 states, = 0, 1,. ..,, ranging from perfect functioning state dj to complete failure state O . The component is partially functioning in all generic intermediate states. 

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