A New Goodness-of-Fit Test for Censored Data with an Application in Monitoring Processes

In this article, we propose a new goodness-of-fit test for Type I or Type II censored samples from a completely specified distribution. This test is a generalization of Michael's test for censored data, which is based on the empirical distribution and a variance stabilizing transformation. Using Monte Carlo methods, the distributions of the test statistics are analyzed under the null hypothesis. Tables of quantiles of these statistics are also provided. The power of the proposed test is studied and compared to that of other well-known tests also using simulation. The proposed test is more powerful in most of the considered cases. Acceptance regions for the PP, QQ, and Michael's stabilized probability plots are derived, which enable one to visualize which data contribute to the decision of rejecting the null hypothesis. Finally, an application in quality control is presented as illustration.