Stochastic System Modeling Applied to an Industrial Production System

This paper demonstrates the application of two stochastic methods for calculating system availability, reliability and downtime for an industrial system. The first method utilized is taken from the Markov process theory of system reliability modeling which allows the states of the system at any point in time to be modeled as a stochastic process. This procedure of stochastic system modeling is quite general and can be applied to many different system configurations, including series, standby redundant, parallel-redundant, maintained or nonmaintained. The method is applied to an industrial system consisting of subsystems in a series configuration together with a standby spare subsystem with repair maintenance. A critical requirement of the system studied is high availability, since it would eventually be placed in series in an automotive production line. The paper also includes the description of a stochastic failure rate method which allows the reliability analyst to determine the reliability of a system in the face of uncertainty in the component failure rates. Failure rates of the components are combined in a Monte Carlo scheme by postulating an exponential life conditional distribution with a log normal prior distribution of the failure rates for all components. An example is included in which stochastic failure rate modeling is applied to a subsystem.