Evaluation of the similarity index

Abstract

In this thesis, we evaluate the statistical procedure based on the similarity index proposed by Ypma and Ross in 'Determing the similarity between expected and observed ageing behavior'. The function for the similarity index is defined based on the inner product of two probability density functions, assumed to be related to the Weibull distribution. The evaluated statistical test aims to verify whether an observation of censored lifetime data is compliant with a given reference distribution. The test is compared to both the likelihood ratio test and a test using a variation of the similarity index. The comparison between these tests is based on their power function. First, a clear explanation of the complete statistical procedure using the similarity index is provided. Then the observations for which the test can be used are explained further. Its application and small limitations are shown using an example. Then, the two alternative tests are introduced. This will be followed by a theoretical overview of the power comparison method. Finally, the simulation for the power comparison is conducted. The power function is estimated for multiple relevant base cases along a few alternative parameter lines. It can then be concluded that the likelihood ratio test has consistently higher power than the similarity index test. However, the variation of the similarity index demonstrates a varying power, with instances of both higher and lower values than the original similarity index test.