Variate Generation in Reliability

This chapter considers (1) the generation of random lifetimes via density-based and hazard-based methods, (2) the generation of certain stochastic processes that are useful in reliability and availability analysis, and (3) the generation of random lifetimes for the accelerated life and proportional hazards models. The accurate modeling of failure time distributions is critical for the development of valid Monte Carlo and discrete-event simulation models for applications in reliability and survival analysis. Once an accurate model has been established, it is oftentimes the case that the complexity of the model requires an analysis by simulation. The associated variate generation algorithms for common stochastic models are introduced here. Although the generation of random lifetimes is typically applied to reliability and survival analysis in a simulation setting, their use is widespread in other disciplines as well. The more diverse wider literature on generating random objects includes generating random combinatorial objects, generating random matrices, generating random polynomials, generating random colors, generating random geometric objects, and generating random spawning trees.