Density and Failure Rate Estimation

Abstract

Density and failure rate estimation are valuable tools to assess and explore the occurrence and timing of failures in reliability and quality control. This article focuses on nonparametric approaches such as histograms, the kernel method, and other smoothing procedures. Nonparametric density and failure rate estimation is particularly valuable for exploratory data analysis and in situations where available information is insufficient to specify a parametric model, as these methods “let the data speak for themselves”, and no assumptions are needed beyond smoothness of the functions to be estimated. Issues specific for nonparametric approaches are finite bias behavior and choice of the necessary smoothing parameter. For failure rate estimation, available data are sometimes incompletely observed (censored) or available in aggregated form only, necessitating appropriate adjustments. Shape restrictions such as increasing failure rate (IFR) are also occasionally of interest in reliability.