The on-going PALFA survey at the Arecibo Observatory began in 2004 and is searching for radio pulsars in the Galactic plane at 1.4 GHz. Observations since 2009 have been made with new wider-bandwidth spectrometers than were previously employed in this survey. A new data reduction pipeline has been in place since mid-2011 which consists of standard methods using dedispersion, searches for accelerated periodic sources, and search for single pulses, as well as new interference-excision strategies and candidate selection heuristics. This pipeline has been used to discover 41 pulsars, including 8 millisecond pulsars (MSPs; P < 10 ms), bringing the PALFA surveys discovery totals to 145 pulsars, including 17 MSPs, and one Fast Radio Burst (FRB). The pipeline presented here has also re-detected 188 previously known pulsars including 60 found in PALFA data by re-analyzing observations previously searched by other pipelines. A comprehensive description of the survey sensitivity, including the effect of interference and red noise, has been determined using synthetic pulsar signals with various parameters and amplitudes injected into real survey observations and subsequently recovered with the data reduction pipeline. We have confirmed that the PALFA survey achieves the sensitivity to MSPs predicted by theoretical models. However, we also find that compared to theoretical survey sensitivity models commonly used there is a degradation in sensitivity to pulsars with periods P >= 100 ms that gradually becomes up to a factor of ~10 worse for P > 4 s at DM < 150 pc/cc. This degradation of sensitivity at long periods is largely due to red noise. We find that 35 +- 3% of pulsars are missed despite being bright enough to be detected in the absence of red noise. This reduced sensitivity could have implications on estimates of the number of long-period pulsars in the Galaxy.
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