Performance Evaluation of Production Lines with Random Processing Times, Multiple Failure Modes and Finite Buffer Capacity — Part I: The Building Block

Abstract

The paper presents an exact analytical method for the performance evaluation of two-machine lines with random processing times, multiple failure modes and finite buffer capacity. Unlike previous works on this subject, machines can fail in different modes, each one characterized by exponentially distributed time to failure and time to repair. The steady state probabilities of the Markov chain of the system is obtained in a compact form with a computational effort that depends only on the number of failure modes considered and not on the capacity of the buffer. Finally, the improvements provided by the proposed method over existing techniques are discussed and quantified. The method has been derived to be used as a building block within the development of a new set of decomposition equations for the analysis of larger systems, such long transfer lines and assembly/disassembly systems.