Bayes inference for repairable mechanical units with imperfect or hazardous maintenance

The Modulated Power Law process (MPLP) has been recently proposed as a suitable model to describe the failure pattern of repairable mechanical units subject to imperfect or hazardous maintenance. In this paper, an informative Bayes procedure is proposed to analyze failure data arising from a MPLP sample, which allows prior information on the failure/repair process to be incorporated into the inferential procedure. Inference both of the MPLP parameters and of some functions thereof (such as the unconditional mean number of failures and the unconditional failure intensity), as well as prediction on failure times in a future sample, is developed. Finally, a numerical example is given to illustrate the proposed procedure.