Smooth Nonparametric Estimation of the Failure Rate Function and its First Two Derivatives

Abstract

The class of nonparametric estimators of kernel type is considered for the unknown failure rate function and its derivatives. The convergence of the suggested estimations in distribution and in the mean square sense to the unknown failure rate function and its derivatives is proved. The interval estimator of the failure rate function is constructed. Advantages of the nonparametric estimators in comparison with the parametric algorithms are discussed. The suggested estimators of the failure rate function can be used to solve problems of exploitation reliability of complex physical, technical, and software systems under uncertainty conditions.