In this paper, authors apply a double sampling procedure for the improved np chart and provided
the designs that minimize the ARL1 against increases of 50%, 100% and 200% in the process
non-conforming rate. This procedure was applied to processes with in-control non-conforming fraction
p0 equal to 0.005, 0.010 and 0.020 and for ARL0 ≥200 and for ARL0 ≥ 370.4. The optimal designs
were given for average sample sizes such that np0 = 0.5, 1.0, 2.0 and 4.0. In all these cases it was
found that the double sampling minimizes the number of samples needed until the detection of one
item out of control in the process.