Multi-state reliability systems under discrete time semi-Markovian hypothesis

We consider repairable Multi-state reliability systems with m components, the lifetimes and the repair times of which are s-independent. The ℓ-th component can be either in the complete failure state 0, in the perfect state dℓ, or in one of the degradation states {1,2,⋯d ℓ-1}. The sojourn time in any of these states is a random variable following a discrete distribution. Thus, the time behavior of each component is described by a discrete-time semi-Markov chain, and the time behavior of the whole system is described by the vector of paired processes of the semiMarkov chain and the corresponding backward recurrence time process. Using recently obtained results concerning the discrete-time semi-Markov chains, we derive basic reliability measures. Finally, we present some numerical results of our proposed approach in specific reliability systems, namely series, parallel, k-out-of-n:F, and consecutive-k-out-of-n:F systems. © 2010 IEEE

Bayesian Estimation for the GreenLab Plant Growth Model with Deterministic Organogenesis

Plant growth modeling has attracted a lot of attention due to its potential applications. Many scientific disciplines are involved, and a lot of research effort and intensive computer methods were needed to understand better the complex mechanisms underlying plant evolution. Among the numerous challenges, one can cite mathematical modeling, parameterization, estimation and prediction. One of the most promising models that have been proposed in the literature is the GreenLab functional–structural plant growth model. In this study, we focus only on one of its versions, named GreenLab-1, particularly adapted to a certain class of plants with known organogenesis, such as sugar beet, maize, rapeseed and other crop plants. The parameters of the model are related to plant functioning, and the vector of observations consists of organ masses measured only once at a given observation time. Previous efforts for parameter estimation in GreenLab-1 include Kalman-type filters, stochastic variants of EM and/or ECM algorithms, and hybrid sequential importance sampling algorithms with Bayesian estimation only for the functional parameters of the model. In this paper, the first purely Bayesian approach for parameter estimation of the GreenLab-1 model is proposed. This approach has much more flexibility in handling complex structures, thus providing a useful tool for analyzing such types of models. In order to sample from the posterior distribution an MCMC algorithm is used and its implementation issues are also discussed. The performance of this method is illustrated on a simulated and a real dataset from the sugar beet plant, and a comparison is made with the MLE approach. © 2021, International Biometric Society

Bayesian Estimation for the GreenLab Plant Growth Model with Deterministic Organogenesis

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