Stochastic System Modeling Applied to an Industrial Production System

Abstract

Two stochastic methods for calculating system availability, reliability, and downtime for an industrial system are the stochastic system modeling approach and the stochastic failure rate model. The former method is applicable when the underlying component or subsystem failure and repair-time distributions are exponential. The method provides system state probability expressions which can be used to compute system reliability and availability. The system differential equations which yield the system state probabilities in the steady state can be derived intuitively as long as the analyst can model the manner in which the system can migrate to adjacent states. The method was demonstrated in detail for a system of four identical subsystems in series with one identical standby spare. Three simultaneous linear equations for the state probabilities were derived and used to derive system availability. Subsystem exponential failure and repair rates were used as parameters. The second method, the stochastic failure rate model, makes the assumption that component failure rates are log-normally distributed while component life is conditionally exponentially distributed. The method is based on a Monte Carlo procedure for sampling from the component failure rate distributions, resulting in a probability distribution for system reliability. The step-by-step procedure is described, with its implementing computer program. Results are shown for a system with 210 components.