Nonparametric Inferences for Ramp Stress Tests under Random Censoring

Abstract

This paper considers nonparametric estimation of lifetime distribution of a product under ramp stress accelerated life tests in which the stress on an item increases linearly with time and observations are randomly censored. Assuming that a cumulative exposure model holds, the lifetime distribution of an item under ramp stress is derived. Three nonparametric estimators of the lifetime distribution at use condition stress are obtained for the situation where the time transformation function relating stress to lifetime distributions of a test item is a version of the inverse power law. The proposed estimators are robust to underlying lifetime distribution and are computed in closed form. They are compared with maximum likelihood estimator for small samples under exponential lifetime distribution. The method is extended to the case of competing risks.