Nonparametric Bayes estimation of the survival function and failure rate from record-breaking data
Abstract Record-breaking data is data in which only successive minimums are recorded. A nonparemetric Bayes approach is used to derive an estimator of the survival function and failure rate for this data. A Dirichlet distribution is assumed to be the prior distribution for the failure probabilities assigned to the intervals defined by the consecutive ordered data values. When the parameters of the prior distribution are unknown, an empirical Bayes approach is used to find an estimator for the survival function and failure rate. Using the successive failure times data of air conditioning units on Boeing aircraft introduced by Proschan[6], the nonparametric Bayes estimators of the survival function are plotted against the empirical Bayes estimators and the nonparametric and parametric maximum likelihood estimators of Samaniego and Whitaker ([8], [9]). The results show that the nonparametric Bayes estimator is smoother than the other estimators.