Transient Behavior of Two-Machine Geometric Production Lines

Production system transients characterize the process of reaching the steady state throughput. Reducing transients' duration is important in a number of applications. This technical note is intended to analyze transients in serial production lines with machines obeying the geometric reliability model. The Markov chain approach is used, and the second largest eigenvalue of the transition matrices is utilized to characterize the transients. Due to large dimensionality of the transition matrices, only two-machine systems are addressed, and the second largest eigenvalue is investigated as a function of the breakdown and repair probabilities. Conditions under which shorter up- and downtimes lead to faster transients are provided.