An excellent discussion of conventional approaches to reliability modeling is provided by Ebeling (1997), and readers who are not familiar with these approaches are encouraged to consult this text.
Most reliability modeling approaches involve the assumption of a static model, where the system configuration never changes (other than due to the failure/repair of components), and where its properties don’t change with time. This is a convenient assumption, as it allows the use of simple techniques, such as closed form mathematical equations or reliability block diagrams. Markov chains are another conventional reliability approach, and although they introduce an element of dynamism, the system itself (and its properties) cannot change with time. Because of the simplifying assumptions required to use these conventional techniques, they may be inappropriate for some systems.
Some of the difficulties with using these approaches for complex systems are summarized below.
Closed-Form Equations. These methods are heavily dependent on classical models (i.e., they have been primarily developed for use with standard failure distributions like the Poisson and Weibull). Even if failure data can be fitted to a standard distribution, it is difficult to model complex systems with closed form equations. For example, if a system has two Weibull failure modes, they cannot be algebraically combined into a single Weibull failure mode for use with the Weibull reliability equation.
Reliability Block Diagrams. Reliability block diagram models are static and do not account for the highly dynamic nature of many systems. A reliability block diagram model also assumes the system is in steady state, and unless correction factors are used, assumes that all of its components are independent.
Markov Chains. Markov chains enumerate a number of system “states” and the probabilities for transitioning between these states. However, the number of transition probabilities (and the computational effort) required to solve a Markov chain grows exponentially with the number of states. Because of this “state-space explosion”, in many cases a system must be greatly simplified in order to use a Markov chain approach.
Of course, the conventional approaches are appropriate for many systems, particularly when employed by an experienced practitioner. However, in some cases, a more realistic reliability model may be required.