Prediction in trend-renewal processes for repairable systems

Some problems of point and interval prediction in a trend-renewal process (TRP) are considered. TRP’s, whose realizations depend on a renewal distribution as well as on a trend function, comprise the non-homogeneous Poisson and renewal processes and serve as useful reliability models for repairable systems. For these processes, some possible ideas and methods for constructing the predicted next failure time and the prediction interval for the next failure time are presented. A method of constructing the predictors is also presented in the case when the renewal distribution of a TRP is unknown (and consequently, the likelihood function of this process is unknown). Using the prediction methods proposed, simulations are conducted to compare the predicted times and prediction intervals for a TRP with completely unknown renewal distribution with the corresponding results for the TRP with a Weibull renewal distribution and power law type trend function. The prediction methods are also applied to some real data.