Optimal properties of the Laplace trend test for soft-reliability models

The author studies the Laplace trend test when it is used to detect software reliability growth, and proves its optimality in the frame of the most famous software reliability models. Its intuitive importance is explained, and its statistical properties are established for the five models: Goel-Okumoto, Crow, Musa-Okumoto, Littlewood-Verral, and Moranda. The Laplace test has excellent optimality properties for several models, particularly for nonhomogeneous Poisson processes (NHPPs). It is good in the Moranda model, which is not an NHPP; this justifies entirely the use of this test as a trend test. Nevertheless, the Laplace test is not completely satisfactory because neither its exact statistical-significance level, nor its power are calculable, and nothing can be said about its properties for the Littlewood-Verral method. Consequently, the author suggests that it is always better to check if it has good properties in the model, and to search for other tests whose statistical-significance level and power are calculable