By default, Minitab provides five trend tests: MIL-Hdbk-189 (pooled), MIL-Hdbk-189 (TTT-based), Laplace (pooled), Laplace (TTT-based), and Anderson-Darling. For more information, go to Trend tests (also called goodness-of-fit tests).
For the air conditioning data, the p-values for the goodness-of-fit tests are 0.107, 0.448, 0.388, 0.688, and 0.389. Because all p-values are greater than α = 0.05, the engineer can conclude that there is not enough evidence that a trend exists in the data. This result is consistent with a shape of 1 for the power-law process.
Although the power-law process provides an adequate fit, using a two-parameter model is not necessary when there is no trend in the data. Therefore, the engineer may want to consider using the simpler homogeneous Poisson process to model these data.