The number of failures and repairs of a repairable system in interval (0,T) can be seen to be a point process N(t). Under the assumptions of instantaneous and minimal repair, a reasonable model for it is the Nonhomogeneous Poisson Process (NHPP). The intensity function of s(t) of the NHPP completely determines the probability structure of N(t). It is therefore interesting to test the goodness of fit hypothesis H_o: s(t) = s_o(t), 0 < t < T . Such tests exist in the literature since Cox (1955) and Crow (1974). Several such tests have been studied and compared in Bain, et al. (1985), and Cohen and Sackrowitz (1993). All of these tests are conditional tests given that N(T)=n . Only recently Pena (1998), Pena and Augustin (1999), and Deshpande, Mukhopadhyay and Naik-Nimbalkar (2002) have considered testing H_o unconditionally with N(T) being random which it is if the design is to truncate observation at a predetermined time T. In this talk we review the two approaches and their respective powers for certain relevant alternatives.
Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.