  In this paper, the average achievable rate of a re-configurable intelligent
surface (RIS) aided factory automation is investigated in finite blocklength
(FBL) regime. First, the composite channel containing the direct path plus the
product of reflected paths through the RIS is characterized. Then, the
distribution of the received signal-to-noise ratio (SNR) is matched to a Gamma
random variable whose parameters depend on the total number of RIS elements as
well as the channel pathloss. Next, by assuming FBL model, the achievable rate
expression is identified and the corresponding average rate is elaborated based
on the proposed SNR distribution. The phase error due to quantizing the phase
shifts is considered in the simulation. The numerical results show that Monte
Carlo simulations conform to the matched Gamma distribution for the received
SNR for large number of RIS elements. In addition, the system reliability
indicated by the tightness of the SNR distribution increases when RIS is
leveraged particularly when only the reflected channel exists. This highlights
the advantages of RIS-aided communications for ultra-reliable low-latency
communications (URLLC) systems. The reduction of average achievable rate due to
working in FBL regime with respect to Shannon capacity is also investigated as
a function of total RIS elements.
