Template:Goodness-of-fit test camsaa

Goodness-of-Fit Tests
While using the Crow-AMSAA model in the RGA 7 software, there are four goodness-of-fit tests which may become available depending on their applicability. The Cramér-von Mises goodness-of-fit test tests the hypothesis that the data follows a nonhomogeneous Poisson process with failure intensity equal to $$u(t)=\lambda \beta {{t}^{\beta -1}}$$. This test can be applied when the failure data is complete over the continuous interval $$[0,{{T}_{q}}]$$  with no gaps in the data. The Chi-Squared test is a goodness-of-fit test that can be applied under more general circumstances, particularly when the data set is grouped. In addition, for multiple system data the Common Beta Hypothesis (CBH) test also can be used to compare the intensity functions of the individual systems by comparing the $${{\beta }_{q}}$$  results for each system. Lastly, the Laplace Trend test checks for trends within the data. Due to their general application to multiple models, the Common Beta Hypothesis test and the Laplace Trend test are both presented in Appendix B. The Cramér-von Mises and Chi-Squared tests are described here since they apply to the Crow-AMSAA model only.