This is just an Excerpt from a larger document, click here to view the entire document.Reliability, Maintainability, and Safety Application of Markov Analysis Methods: the Pros and Cons
Markov methods can be powerful tools in RMS engineering. Markov chains are commonly used to study the dependability of complex systems. Markov analysis provides a means of analyzing the RMS of systems whose components exhibit strong dependencies. Other systems analysis methods (e.g., fault tree analysis) often assume total component independence. Used alone, these methods may lead to optimistic predictions for the system reliability and safety parameters.
The exponential distribution i.e., a constant failure rate, is a common assumption in system analyses based upon Markov methods. Define Event for Which Probability is Desired
Markov methods offer significant advantages over other reliability modeling techniques, some of these advantages are:
Simplistic modeling approach: The models are simple to generate although they do require a more complicated mathematical approach.
Redundancy management techniques: System reconfiguration required by failures is easily incorporated in the model.
Coverage: Covered and uncovered failures of components are mutually exclusive events. These are not easily modeled using classical techniques, but are readily handled by the Markov mathematics.
Complex systems: Many simplifying techniques exist which allow the modeling of complex systems.
Sequenced events: Often the analyst is interested in computing the probability of an event resulting from a sequence of sub-events. While these types of problems do not lend themselves well to classical techniques, they are easily handled using Markov modeling.
The advantage of the Markov process is that it neatly describes both the failure of an item and its subsequent repair. It develops the probability of an item being in a given state, as a function of the sequence through which the item has traveled. The Markov process can thus easily describe degraded states of operation, where the item has either partially failed or is in a degraded state where some functions are performed while others are not. Competing techniques, e.g., FMEA and Fault Tree Analysis (FTA), have a difficult time dealing with degraded states as contrasted with outright failures.
The major drawback of Markov methods is the explosion of the number of states as the size of the system increases. The resulting diagrams for large systems are generally extremely large and complicated, difficult to construct and computationally extensive.
Sometimes, however, a combination approach is best. Markov models may be used to analyze smaller pseudo-systems with strong dependencies requiring accurate evaluation. Then other analysis techniques, such as FTA, may be used to evaluate the total system using simpler probabilistic calculation techniques. Large systems, which exhibit strong component dependencies in isolated and critical parts of the system, may thus be analyzed using a combination of Markov analysis and simpler quantitative models. For example, if a small dynamic portion is solved separately and then combined with the overall static consequences the resulting Markov model can be much smaller.