Use the tests for trend to determine whether a homogeneous Poisson process or a nonhomogeneous Poisson process is the appropriate model.
If you reject the null hypothesis, you can conclude that there is some trend in your data and you should model your data with a nonhomogeneous Poisson process such as the power-law process.
If you fail to reject the null hypothesis, there is not enough evidence to reject the homogeneous Poisson process model. Although the power-law process may still be appropriate, the homogeneous Poisson process is a simpler model and thus a better choice.
With interval data, Minitab provides only the MIL-Hdbk-189 test. Minitab uses the pooled version of the MIL-Hdbk-189 test when the data for different systems are in one column and another column provides system identifiers. When the data are in one column, Minitab assumes that the different systems are from identical processes. Minitab uses the TTT-based version of the MIL-Hdbk-189 test when the data for different systems are in different columns. When the data are in different columns, Minitab assumes that different systems are from different processes.
If the times change in a systematic way, a trend exists in the pattern of times between failures. Trends can be monotonic or non-monotonic.
|Test||Null hypothesis||Rejecting H0 means|
| MIL-Hdbk-189 (Pooled)
|HPP (possibly different MTBFs)||Monotonic trend|
| MIL-Hdbk-189 (TTT-based)
|HPP (same MTBFs)||Monotonic trend or systems are heterogeneous|
|Anderson-Darling||HPP (possibly different MTBFs)||Monotonic or non-monotonic trend or systems are heterogeneous|