Comparisons of standby and parallel systems for processing times

Two types of redundant systems subject to stochastic failures during the continuous production process are investigated for the best performance with minimum costs. This paper studies the optimal redundant units for parallel systems and standby systems when processing jobs with random working times. First, the reliability and mean time to failure for both redundant systems are derived and compared. Next, the expected cost functions and the optimal numbers of units are obtained for the two redundant systems. Subsequently, availabilities of parallel and standby systems are defined. Finally, the expected cost functions of the parallel and standby systems are discussed under the case of N tandem works with random processing times.