Investigation of equivalence between the interstate transition rates and state probabilities in the data analysis and applications

Conditions for equivalence of state probabilities obtained from the data on state residence times and those from data on interstate transitions are explored in this paper. The derived conditions are useful in applications under various situations. The situations illustrated in this paper include when data is available only for state residence times but a state transition rate matrix needs to be developed for purposes of application. A situation is also illustrated when data on state residence times and interstate transitions is collected but inaccuracies may exist in the collection or processing of interstate data. Another condition explored is the effect of the probability distribution of state residence times on the reliability indices.