This paper combines time varying failure rates and Markov chain analysis to obtain a hybrid reliability and availability analysis. However, combining these techniques can, depending on the size of the system, result in solutions of the Markov chain differential matrix equations that are intractable. This paper identifies solutions that are tractable, These form the analytical baseline for the reliability and availability analysis of systems with time varying failure rates. Tractable solutions were found for the 1-component 2-state and the 2-component 4-state configurations. Time varying failure rates were characterized by a general polynomial expression. Constant, linear, and Weibull failure rate functions are special cases of this polynomial. The general polynomial failure rate provides flexibility in modeling the time varying failure rates that occur in practice.
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