Abstract

Suppose that l different kinds of arrivals are identified. Let N i (t) be the number of arrivals of type i that occur up to time t. Then\(N\left( t \right) = {N_1}\left( t \right) + \cdots + {N_l}\left( t \right) \), the summary process, is the total number of arrivals of all types that occur up to time t. Arrival types may, for instance, be failures of l components of a series system. N(t) would then count the system failures. Or in an application to reactor safety, N i (t) might be the number of accidents due to the ith cause and N(t) would be the total number of accidents due to all causes. WritingM(t)=EN(t) and M i (t)=EN i (t), then of courseM(t)=M 1 (t)+⋯+M l (t) and \(\mu \left( t \right) = \mu \left( t \right) + \cdots + {\mu _l}\left( t \right) \).

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Copyright information

© Chapman and Hall 1988

Authors and Affiliations

  • W. A. ThompsonJr
    • 1
  1. 1.University of MissouriColumbiaUSA

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