Applications and extensions of the chains-of-rare-events model

The chains-of-rare-events model (ChRE) is extended. The ChRE was originally introduced in order to analyze occurrences which can be produced with simple, double, triple, etc., multiplicity. In the original ChRE, each occurrence of multiplicity (i) is independently distributed according to a Poisson law with parameter λ_i ; and a simple relation for these parameters is considered. In this way, ChRE can be applied to analyze outcomes produced in occurrences with multiple events, such as failures, queuing, automobile accidents, telephone calls, and accidents in a factory. The original ChRE is extended to analyze the total number of outcomes in which a given total number of occurrences of different multiplicity occur. The model can be analyzed as a compound Poisson distribution where the compounding distribution is Poisson truncated at zero. Applications to reliability and queuing processes data are presented. The results compare favorably with those from other models