摘要：The power law process (PLP) (i.e., the nonhomogeneous Poissonprocess with power intensity law) is perhaps the most widely used modelfor analyzing failure data from reliability growth studies. Statistical inferencesand prediction analyses for the PLP with left-truncated data withclassical methods were extensively studied by Yu et al. (2008) recently.However, the topics discussed in Yu et al. (2008) only included maximumlikelihood estimates and con dence intervals for parameters of interest, hypothesistesting and goodness-of- t test. In addition, the prediction limitsof future failure times for failure-truncated case were also discussed. In thispaper, with Bayesian method we consider seven totally di erent predicitonissues besides point estimates and prediction limits for xn+k. Speci cally,we develop estimation and prediction methods for the PLP in the presenceof left-truncated data by using the Bayesian method. Bayesian point andcredible interval estimates for the parameters of interest are derived. Weshow how ve single-sample and three two-sample issues are addressed bythe proposed Bayesian method. Two real examples from an engine developmentprogram and a repairable system are used to illustrate the proposedmethodologies.
