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The power-law process (PLP) plays an important role in studying and modeling the failure process of repairable systems. This study proposes the modified signed log-likelihood ratio test for the scale parameter ( γ ) of the PLP, which is essential for the system’s reliability prediction. The accuracy of the proposed method is evaluated and compared to other existing methods in terms of empirical type I error rates and empirical powers. The simulation results show that the proposed method is very satisfactory and superior to other methods in controlling the probability of type I error and has the highest powers for most situations, even for small numbers of failures  n . Additionally, the performance of the proposed method is also illustrated using two real examples.

Modified signed log-likelihood ratio test for the scale parameter of the power-law process with applications to repairable systems