On the Effect of Random Alternating Perturbations on Hazard Rates

TL;DR

This paper investigates how dichotomous noise, modeled by the telegraph process, affects hazard rates in systems, providing new stochastic models and statistical tools for survival analysis and reliability data interpretation.

Contribution

It introduces a novel stochastic process for hazard rates under alternating perturbations and derives its distribution, mean, and variance, with applications to survival analysis.

Findings

Derived explicit probability distribution, mean, and variance of the process.

Provided confidence bands for hazard rate estimates in survival analysis.

Demonstrated applicability to reliability data sets.

Abstract

We consider a model for systems perturbed by dichotomous noise, in which the hazard rate function of a random lifetime is subject to additive time-alternating perturbations described by the telegraph process. This leads us to define a real-valued continuous-time stochastic process of alternating type expressed in terms of the integrated telegraph process for which we obtain the probability distribution, mean and variance. An application to survival analysis and reliability data sets based on confidence bands for estimated hazard rate functions is also provided.