Multi-sample simple step-stress experiment under time constraints

In the context of accelerated life testing, a step-stress model allows for testing under different conditions at various intermediate stages of the experiment. The goal is to develop inference for the mean lifetime at each stress level. The maximum likelihood estimates (MLEs) exist only when some (at least one) failures are observed at each stress level. This limitation can be tackled by a multi-sample step-stress model, which imposes a weaker condition for the existence of the MLEs, i.e. at each stress level, some failures (at least one) must be observed in at least one of the samples. The step-stress experiment with multiple samples at the same stress levels was introduced by Kateri et al. ( Journal of Statistical Planning and Inference, 139 , 2009a ). In this article, we focus on the likelihood inference under such a multi-sample set-up for the case of a simple step-stress experiment under exponentially distributed lifetimes when time constraints are in place in the experimentation.