Reliability theory systems applications

Natvig, B. 2010. Multistate Systems Reliability Theory with Applications. WiXey Seri. Chichester Wiley 1st Edition. 

If we need to be able to deal with all types of uncertainty, can mathematics as a formal language help us It is the purpose of this chapter to review briefly and qualitatively the basic ideas of mathematics, in particular logic and set theory, on which probability theory depends. The nature of probability and its application in reliability theory as applied to structural design, and the problems of applying it to estimate system uncertainty are then discussed. It is not intended to cover the techniques associated with the theories, only the ideas behind them. Many texts are available on all the subjects touched here, to which reference will have to be made if techniques for handling the ideas are required. The purpose of the following discussion is to attempt to clarify the basis on which we work... 

Rausand, M. Hoyland, A. 2004. System reliability theory models, statistical methods, and applications. Hoboken, N.J., Wiley-Interscience. 

Most of the reliability theory literature focuses on binary systems, i.e., systems with only two states functioning or failed. See e.g., (Barlow Proschan, 1981). In many real life applications, however, systems have more than two states. A typical example is a network flow system where the state of the system may be defined as the flow capacity of the system. Depending on the number of functioning links in the system, this capacity varies between full capacity and zero capacity, but with several intermediate states as well. 

Lundteigen, M.A. Rausand, M. 2009. Architectural constraints in lEC 61508 Do they have the intended effect Reliability Engineering and System Safety 94 520-525 Rausand, M. Hoyland, A. (2 ed.) 2004. System reliability theory models, statistical methods, and applications. New York Wiley... 

Rausand, M., Hoyland, A. (2004). System Reliability Theory — Models, Statistical Methods, and Applications Second Edition, Wiley series. 

Kolowrocki, K. 2007a. Reliability modelling of complex systems — Part 1. International Journal of Gnedenko e-Forum Reliability Theory Application", Vol. 2, No 3-4, 116-127. 

Rausant, Marvin, Reliability of Safety-Critical Systems Theory and Applications, John Wiley Sons, Inc., New York, 2014. 

M. Rausand, Reliability of SafetyeCritical Systems Theory and Applications, J. Wiley. 

El-Damoese, M A. Temraz N.S., 2011. Availability and Reliability Measures for Multi-State System by Using Markov Reward Model. Reliability Theory Applications, 6(3) 68-85. 

Rausand, M. and Hoyland, A. 2004. System Reliability Theory. Models, Statistical Method, and Applications. 2nd edition. Wiley. 

Moghaddass, R. and Zuo, M.J. 2011. A parameter estimation method for a multi-state deteriorating system with incomplete information. Proceedings of the Seventh International Conference on Mathematical Methods in Reliability Theory, Methods, and Applications (MMR 201 l) pp. 34-42. 

Jodejko-Pietruczuk, A., Nowakowski, T, Werbinska-Wojciechowska, S. (2013b). Block inspection pohqr model with imperfect inspections formulti-unit systems. Reliability Theory Applications 8(3) 75 6. 

Talavera, A. et al., 2013. Application of Dempster-Shafer theory for the quantification and propagation of the uncertainty caused by the use of AIS data. Reliability Engineering System Safety, 111, pp. 95-105. 

Ceccoli C, Mazzotti C, Savoia M (1999) Non-linear seismic analysis of base-isolated RC frame structures. Earthq Eng Struct Dyn 28(6) 633-653 Ching J, Au SK, Beck JL (2005) Reliability estimation for dynamical systems subject to stochastic excitation using subset simulation with splitting. Comput Method Appl Mech Eng 194(12-16) 1557-1579 Chopra AK (2001) Dynamics of structures theory and applications to earthquake engineering. Prentice Hall, Englewood Cliffs, Upper Saddle River, NJ 07458. USA... 

Routine Application of Complex Theories. Technical people in the coatings and many other industries tend to shy away from theoretical approaches in their work. There are many legitimate and practical reasons for this, such as complexity of real systems, lack of comprehensive theories, inability to understand theories and the mathematics involved, and time consuming to apply theories. In many cases, it is easier, quicker and more reliable to use the experimental approach. On the other hand, if pertinent theories are computerized and the computer programs contain the required physical properties data, it becomes risk free and easy, to apply theories. We have found that computerization of theories does encourage more people to use them, thus improving both productivity and quality of technical efforts. 

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