Probability masses fitting in the analysis of manufacturing flow lines

The analysis of manufacturing systems with finite capacity and with general service time distributions is made of two steps: the distributions have first to be transformed into tractable phase-type distributions, and then the modified system can be analytically modelled. In this paper, we propose a new alternative in order to build tractable phase-type distributions, and study its effects on the global modelling process. Called ‘probability masses fitting’ (PMF), the approach is quite simple: the probability masses on regular intervals are computed and aggregated on a single value in the corresponding interval, leading to a discrete distribution. PMF shows some interesting properties: it is bounding, monotonic, refinable, it approximates distributions with finite support and it conserves the shape of the distribution. With the resulting discrete distributions, the evolution of the system is then exactly modelled by a Markov chain. Here, we focus on flow lines and show that the method allows us to compute upper and lower bounds on the throughput as well as good approximations of the cycle time distributions. Finally, the global modelling method is shown, by numerical experiments, to compute accurate estimations of the throughput and of various performance measures, reaching accuracy levels of a few tenths of a percent.