Data Analysis and Related Applications 3

6Restricted Minimum Density Power Divergence Estimator for Step-stress ALT with Nondestructive One-shot Devices

One-shot device data represent an extreme case of interval censoring. Some kinds of one-shot units do not get destroyed when tested, and so, survival units can continue within the test, providing extra information about their lifetime. Moreover, one-shot devices may last for long times under normal operating conditions, so accelerated life tests (ALTs) may be used for inference. ALTs relate the lifetime distribution of a unit to the stress level at which it is tested via a log-linear relationship. In particular, the step-stress ALT model gradually increases the stress level at which units are submitted to at pre-fixed times during the life-testing experiment. However, when the number of units under test is small, the outlying data may greatly influence the parameter estimation. In this chapter, we develop robust restricted estimators based on the density power divergence (DPD) under linearly restricted subspaces, for nondestructive one-shot devices under the step-stress ALTs with exponential lifetime distributions. We theoretically study the asymptotic and robustness properties of the restricted estimators and we empirically illustrate such properties through a simulation study.

6.1. Introduction

One-shot devices can be only tested at some discrete inspection times, and so we can only know whether a test unit has failed or not before certain fixed times. Inference ...