Abstract
This chapter discusses many different problems in reliability theory that require the use of stochastic transition matrices in their analysis. The reason these matrices arise is that, in many stochastic problems, the effect of random occurrences is to cause a transition of the reliability properties from one condition to another. The problems in reliability theory for which transition analyses are useful or necessary are surprisingly varied. For instance, matrix methods are used to describe the degeneration of reliability in a chain of logic elements each with a binary output that has a given probability of being an incorrect function of its inputs. Another nonredundant application is in the analysis of voltage levels in a chain of physical circuits implementing binary logic. These circuits have an input/output voltage characteristic that is a function of random component parameters. Matrix analyses are equally fundamental in the analysis of redundant systems. One such application is the reliability analysis of a chain of restoring organs.
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