A simple goodness-of-fit test for the power-law process, based on the Duane plot

The PLP (power-law process) or the Duane model is a simple model that can be used for both reliability growth and reliability deterioration. GOF (goodness-of-fit) tests for the PLP have attracted much attention. However, the practical use of the PLP model is its graphical analysis or the Duane plot, which is a log-log plot of the cumulative number of failures versus time. This has been commonly used for model validation and parameter estimation. When a plot is made, and the coefficient of determination, R², of the regression line is computed, the model can be tested based on this value. This paper introduces a statistical test, based on this simple procedure. The distribution of R² under the PLP hypothesis is shown not to depend on the true model parameters. Hence, it is possible to build a statistical GOF test for the PLP. The critical values of the test depend only on the sample size. Simulations show that this test is reasonably powerful compared with the usual PLP GOF tests. It is sometimes more powerful, especially for deteriorating systems. Implementing this test needs only the computation of a coefficient of determination. It is much easier than, for example, computing an Anderson-Darling statistic. Further study is needed to compare more precisely this new test with the existing ones. But the R² test provides a very simple and useful objective approach for decision making with regard to model validation.