It is suggested that problems in a reliability context may be handled by a Bayesian nonparametric approach. A stochastic process is defined whose sample paths may be assumed to be increasing hazard rates by properly choosing the parameter functions of the process. The posterior distribution of the hazard rates is derived for both exact and censored data. Bayes estimates of hazard rates and $\operatorname{cdf's}$ are found under squared error type loss functions. Some simulation is done and estimates graphed to better understand the estimators. Finally, estimates of the hazard rate from some data in a paper by Kaplan and Meier are constructed.
@article{1176345401,
author = {Dykstra, R. L. and Laud, Purushottam},
title = {A Bayesian Nonparametric Approach to Reliability},
journal = {Ann. Statist.},
volume = {9},
number = {1},
year = {1981},
pages = { 356-367},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345401}
}
Dykstra, R. L.; Laud, Purushottam. A Bayesian Nonparametric Approach to Reliability. Ann. Statist., Tome 9 (1981) no. 1, pp. 356-367. http://gdmltest.u-ga.fr/item/1176345401/