On testing for repair effect and time trend in repairable mechanical units

The Modulated Power Law process (MPLP) has been recently used to analyse repairable mechanical units whose failure pattern incorporates both renewal-type behaviour and time trend. In this paper, a Bayes approach is used to develop significance tests for testing for a reduction of the MPLP to simpler models, namely the Gamma Renewal and the Power Law processes, which are special cases of the MPLP model. Furthermore, significance tests to compare the effect of the repair actions on the future reliability or the time trend in two independent MPLP samples are proposed. Large simulation studies have been carried out, both to measure the exact size of the proposed tests and to investigate their power in a largely repeated use of each test. Finally, numerical examples are given to illustrate the proposed procedure.