Summary: Power law process (PLP) or Weibull process is used to model reliability growth and is usually characterized by the intensity function $λ(x)$. Some computationally simple tests for shape parameter based on conditional likelihood are proposed in the presence of nuisance parameter. The large sample tests based on Fisher information and Score test are also derived. A simulation study is performed to compare the tests in terms of power. Few examples are also discussed at the end of the paper.