Throughput and Flow-Time in a Production Line with Partial Machine Availability and Imperfect Quality Processing  

Machine availability and quality can significantly constraint production systems. This work investigates the throughput and flow-time of a serial production line, considering partial availability and imperfect quality processing of machines. It assumes a line with two or more stations each with a single machine, and a buffer between every two consequent stations. Each item is inspected for quality post processing, resulting in either: good item continuing to the consequent station, defected item requiring rework in the current station, or bad item which is scrapped.

It is assumed that the demand is unlimited (i.e. system’s arrivals), the machine’s process times are deterministic, and the machine availability follows known probability. Inspection results also follow known probabilities: Pr(good)+Pr(defected)+Pr(scrap)=1. The study develops analytical models of the production system based on Markov chains and Queuing Theory, and verifies the results using simulation. It investigates the production line throughput and the items flow-time, determines the most throughput-constrained station, and priorities the corresponding most throughput-limiting factors (i.e. machine’s availability, and the item’s good, defected or scrap rate).

Two main cases are investigated in the steady state: (I) production line with n stations and unlimited buffers size, and (II) production line with two stations and a limited buffer size. The steady state requirement is developed for both cases, showing interesting analogy to the traffic intensity requirement in the Queuing Theory (i.e. less than unity). It is also shown that the stations throughput-limiting factors are bounded by the steady state requirement. Preliminary results of Case I exhibit that the most throughput-constrained station is the first one. Also, that increasing the “traffic intensity equivalent” drives larger buffer on average, and reduces the probability of an idle machine. Preliminary results of Case II illustrate that it is always preferred to improve the throughput-limiting factors of stations closer to beginning of the line than closer to its end.

Future research will demonstrate the effect of the station throughput-limiting factors improvement in a production line of more than two stations with limited buffers size.

Keywords: availability; inspection; production systems; quality control; throughput.