Maximum algebra of random variables with its applications in discrete event systems

A maximum algebra of random variables, which can be used to analyse the manufacturing processes in discrete event stochastic dynamic systems, is presented. A kind of series-parallel production line systems in which the work durations of all tasks are random variables with exponential distributions is discussed. By means of the maximum algebra of random variables the statistical characteristics of total manufacturing time are obtained in order to estimate its production performance. An example is given for confirming the validity of the method by comparing it with the result of simulation.