The geometric distribution based on the inverse binomial method of sampling is used to defineQstatistics for the case when the process falloutpis known and when it is not known in advance of sampling. The effectiveness to detect shifts inpof four tests made on ShewhartQcharts of these statistics as well as both exponentially weighted moving average and cumulative sumQcharts computed from these statistics is studied. The classic test of one point outside 3-sigma control limits is found to have poor sensitivity to detect a one-step permanent shift inp.The test consisting of four-out-of-five points beyond one standard deviation is found to be a good general omnibus test on a ShewhartQchart to detect an increase or decrease inp.