We present a proportional hazards model (PHM) that establishes a framework suitable for performing reliability estimates and risk prognostics on complex multi-component systems which are transferred at arbitrary times among a discrete set of non-stationary stochastic environments. Such a scenario is not at all uncommon for portable and mobile systems. It is assumed that survival data, possibly interval censored, is available at several “typical” environments. This collection of empirical survival data forms the foundation upon which the basic effects of selected covariates are incorporated via the proportional hazards model. Proportional hazards models are well known in medical statistics, and can provide a variety of data-driven risk models which effectively capture the effects of the covariates. The paper describes three modifications we have found most suitable for this class of systems: development of suitable survival estimators that function well under realistic censoring scenarios, our modifications to the PHM which accommodate time-varying stochastic covariates, and implementation of said model in a non-linear network context which is itself model-free. Our baseline hazard is a parameterized reliability model developed from the empirical reliability estimates. Development of the risk score for arbitrary covariates arising from movement among different random environments is through interaction of the non-linear network and training data obtained from a Markov chain simulation based on stochastic environmental responses generated from Karhunen-Loe`ve models.
Equivalence of cell survival data for radiation dose and thermal dose in ablative treatments: analysis applied to essential tremor thalamotomy by focused ultrasound and gamma knife
