In this paper, we carry out queuing analysis to examine and integrate a quality control (inspection) process into a multi-stage flexible flow shop configured in an $M/M/1$ queue system. Our main concern is to improve the performance of multi-stage flexible flow shop production. Besides, this work aims to help managers in improving their efficiency and effectiveness, and in selecting a joint inspection, being the most suitable policy for minimizing inspection and queueing related costs. We adopt an analytical approach based on real-life data from a Kach company that produces disposable appliances. Queuing analysis reported in this work provides a basis for estimating and analyzing production systems by measures such as utilization, the percentage of the idle workstation, number of batches in the system, number of batches in the queue, expected time spent in the queue, and expected time spent in the system. The results indicate the performance of the company in relation to inspection and expected time.