On the canonical representation of homogeneous markov processes modelling failure - time distributions
Abstract This paper deals with the use of Multistate Homogeneous Markov Models (MHMM) to represent failure-time distributions in reliability analysis, with particular emphasis on MHMM's representable by acyclic transition graphs (Triangular MHMM's). It is shown that a generic TMHMM can be transformed into an equivalent minimum-parameter form (canonical form). This result is used to characterize the class of distributions representable by TMHMM's. It is shown that, although not all distributions which are linear combinations of exponential terms can be exactly represented by a TMHMM, such models can nevertheless be used to approximate as closely as desired any reasonable failure-time distribution.