The unstable conveying zone has been recognized by many authors in their attempts to define the minimum conveying velocity on the dilute phase side of this zone. It was found that the gas flow rate influences the magnitude and frequency of the pressure fluctuations experienced during this type of flow. Generally a reduction of gas flow rate will reduce both the intensity and frequency of the fluctuations. During the measurement of data for the previous experiments, it was recognized that the pressure fluctuations of dilute and strand flow can serve as simple indicators of the flow stability. An analysis of these fluctuations is presented, which suggests that simple statistical factors can be used to estimate the system condition of operation with respect to the pressure minimum or unstable zone. These elementary trends in the data can be useful for one attempting to optimize a system. This analysis lead to a more intensive approach using Hurst＇s rescaled range analysis, to examine the changes in pressure fluctuations, which occur when a system undergoes a simulated optimization procedure. The analysis suggested that Hurst＇s exponent may be used as an indicator of the onset of instability.