Shewhart control charts have previously been suggested as a process control tool for use in routine linear accelerator (linac) output verifications. However, a comprehensive approach to process control has not been investigated for linac output verifications. The purpose of this work is to investigate a comprehensive process control approach to linac output constancy quality assurance (QA). The RBA-3 dose constancy check was used to verify outputs of photon beams and electron beams delivered by a Varian Clinac 21EX linac. The data were collected during 2009 to 2010. Shewhart-type control charts, exponentially weighted moving average (EWMA) charts, and capability indices were applied to these processes. The Shewhart-type individuals chart (X-chart) was used and the number of data points used to calculate the control limits was varied. The parameters tested for the EWMA charts (smoothing parameter (λ) and the control limit width (L)) were λ = 0.05, L = 2.492; λ = 0.10, L = 2.703; and λ = 0.20, L = 2.860, as well as the number of points used to estimate the initial process mean and variation. Lastly, the number of in-control data points used to determine process capability (C(p)) and acceptability (C(pk)) were investigated, comparing the first in-control run to the longest in-control run of the process data. C(p) and C(pk) values greater than 1.0 were considered acceptable. The 95% confidence intervals were reported. The X-charts detected systematic errors (e.g., device setup errors). In-control run lengths on the X-charts varied from 5 to 30 output measurements (about one to seven months). EWMA charts showed in-control runs ranging from 9 to 33 output measurements (about two to eight months). The C(p) and C(pk) ratios are higher than 1.0 for all energies, except 12 and 20 MeV. However, 10 MV and 6, 9, and 16 MeV were in question when considering the 95% confidence limits. The X-chart should be calculated using 8-12 data points. For EWMA chart, using 4 data points is sufficient to calculate the initial mean and variance of the process. The EWMA limits should be calculated with λ = 0.10, L = 2.703. At least 25-30 in-control data points should be used to calculate the C(p) and C(pk) indices.