A Markov Chain model for the performance evaluation of manufacturing lines with general processing times

Abstract

This paper presents a Markov Chain approximation to model stations in manufacturing lines with general distributed processing times. The proposed Markov Chain approximation enables the use of continuous flow models for the performance evaluation of serial lines with finite buffers and mixed manual – automated operations. Each station in the line can consist of a highly automated machine with deterministic processing times, or of a human operator performing manual operations with general distributed processing times. Stations with random processing times are modelled through a continuous time – discrete state Markov Chain characterized by an operational state with a deterministic processing time, and by an auxiliary down state used to stochastically dilate the overall completion time of a part on the station. The Markov Chain parameters are defined through moments fitting of the probability distribution of the processing time of the original station. The resulting Markov Chain represents the behavior of the station in isolation and is then used as input in the decomposition techniques, based on continuous flow models, for the performance evaluation of serial lines. The model has been applied in the analysis of the production performances of a real assembly line.