Abstract
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.
Highlights
We consider a class of point and interval prediction problems for stochastic models determined by the trend-renewal process (TRP) which is defined to be a time-transformed renewal process (RP), where the time transformation is given by a trend function λ(·)
The main purpose of the simulation study is to examine how much the predicted failure times and the prediction intervals constructed by the constrained least squares (CLS) method for a TRP(F, λ(·)) model with an unknown distribution function F differ from the predictors constructed by the ML method in the TRP(F, λ(·)) with known F and the same trend function λ(·)
According to our knowledge the problem of prediction in a TRP has not been engaged a good deal of the literature
Summary
We consider a class of point and interval prediction problems for stochastic models determined by the trend-renewal process (TRP) which is defined to be a time-transformed renewal process (RP), where the time transformation is given by a trend function λ(·). The method proposed allows to predict the failure time and construct the prediction interval for the failure time in the case when the renewal distribution of the process is completely unknown. Using the prediction methods proposed, the predicted times and prediction intervals for a TRP with completely unknown renewal distribution are compared in a simulation study with the corresponding results for the TRP with a Weibull renewal distribution and power law type trend function. The predicted failure times and the prediction intervals constructed for a TRP with completely unknown renewal distribution function F and power law trend function (power law TRP) are compared with the predictors in the reference to the TRP models with F corresponding to the Weibull
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
