Abstract
Tests are considered for the hypothesis of a constant intensity against the alternative of an intensity which increases with time in a nonhomogeneous Poisson process. Attention is focused on step-function alternatives and tests designed for such alternatives. One application is testing for abrupt changes in equipment following scheduled overhauls. The authors recommend the order-restricted likelihood-ratio test over an ordered chi-square test for such situations, provided the points at which jumps can occur are known. Otherwise, they recommend the test based on the Laplace statistic. The performance of these tests is evaluated for smooth alternatives, with the result that the smallest relative power of the order-restricted likelihood-ratio test is 73%, while for the Laplace test it is 82%. A numerical example based on failure times for a main-propulsion diesel engine is presented. The result is that the order-restricted likelihood-ratio test corresponds to the lowest statistical significance level.
Recommended Citation
M. Engelhardt et al., "Tests For Positive Jumps In The Intensity Of A Poisson Process: A Power Study," IEEE Transactions on Reliability, vol. 39, no. 3, pp. 356 - 360, Institute of Electrical and Electronics Engineers, Aug 1990.
The definitive version is available at https://doi.org/10.1109/24.103018
Department(s)
Geosciences and Geological and Petroleum Engineering
International Standard Serial Number (ISSN)
0018-9529
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2023 Institute of Electrical and Electronics Engineers, All rights reserved.
Publication Date
01 Aug 1990
Comments
Office of Naval Research, Grant AFOSR-84-0164