26. Non-parametric Bootstrap Confidence Limits for Age-Dependent Failure Tendency Using Incomplete Data

This paper addresses modeling of age-dependent failure tendency. The field data of an aircraft device record the follow-up start and end of the units and the failures in chronological order. The data are incomplete since they lack the exact age of the unit at some failures in a way that seems to be random. We construct a non-parametric point estimate of the nonlinear cumulative failure rate, and we model the failure point process behind. Firstly, we point out how effectively the quantiles of the distance to next failure capture and interpret the information in real data. Further, since the characteristics of the actual field data are recognizable enough, it is possible to generate artificial (bootstrap) data sets that imitate the field data set. Each simulated data set determines a nonparametric estimate of the cumulative failure rate, and these estimates together provide fully nonparametric bootstrap confidence bounds for the cumulative failure rate. For practical purposes, we carry out some computational demonstrations on how the data set size and the censoring rate affect the confidence bounds.