Use of the Kolmogorov–Smirnov test for gamma process

Abstract

This article deals with the use of the Kolmogorov–Smirnov test for comparing an observed gamma process with a reference process or for comparing two observed gamma processes. In the case of observed processes with periodic inspections, the Kolmogorov–Smirnov test can be applied directly. It is pointed out that, from the power of test point of view, the length of monitoring is more important than the number of observations. In the case of observed processes with aperiodic inspections, a method for building an empirical cumulative distribution required for the test is proposed. It consists of generating equal time increment observations from the original sample thanks to the gamma bridge. A sort of the original observations for improving the power of the test is proposed. Simulations have proved the feasibility of the approach and shown that when the variance of the time increments increases, the power of the test decreases only a little. An illustrative example showing the interest of such a test for maintenance is described.