On the performance of the conditional decision procedure in geometric charts

To improve the performance of control charts the conditional decision procedure (CDP) incorporates a number of previous observations into the chart’s decision rule. It is expected that charts with this runs rule are more sensitive to shifts in the process parameter. To signal an out-of-control condition more quickly some charts use a headstart feature. They are referred as charts with fast initial response (FIR). The CDP chart can also be used with FIR. In this article we analyze and compare the performance of geometric CDP charts with and with no FIR. To do it we model the CDP charts with a Markov chain and find closed-form ARL expressions. We find the conditional decision procedure useful when the fraction p of nonconforming units deteriorates. However the CDP chart is not very effective for signaling decreases in p.

► The clarification of an apparent contradiction in two expressions of the chart’s ARL.
► The need of an assumption of the number of subgroups within limits at start up which lead us to introduce the FIR concept in a CDP chart.
► The Markov chain model that allows us to derive a general ARL expression for the CDP chart and to compute its run length distribution.
► The claim that the run length is not a geometric random variable as it may be suggested.
► The corrected design of the CDP chart.