Markov Chain Modelling for Reliability Estimation of Engineering Systems at Different Scales - Some Considerations

TL;DR

This paper explores how Markov Chain models, enhanced by recent developments in Monte Carlo, Bayesian theory, and quantum physics, can be applied to reliability estimation across different scales of engineering systems.

Contribution

It presents a conceptual framework integrating quantum physics insights into Markov Chain modeling for multi-scale reliability analysis.

Findings

Quantum physics aids interpretation of transition probabilities.

Markov Chain models can be scaled from nano to macro systems.

Careful density selection is crucial in computations.

Abstract

The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic evolution of system and in system reliability estimation. The recent developments in Markov Chain Monte Carlo and the possible integration of Bayesian theory within Markov Chain theory have enhanced its application possibilities. However, the application possibility can be furthered to range over wider scales of application (perhaps from nano- to macro-) by considering the developments in Physics (in particular Quantum Physics). This paper tries to present the results of quantum physics that would help in interpretation of transition probability matrix. However, care has to be taken in the choice of densities in computing the transition probability matrix. The paper is based on available literature, and the aim is only to make an attempt to show how Markov Chain can be used to model systems at various scales.