Recent literature contains many papers on the study of variable (but deterministic) sampling interval (VSI) policies for &Xmacr; control charts. VSI policies perform better than their corresponding classical fixed-sampling-interval (FSI) policies. Results are also available in the literature for an adaptive VSI policy, an enhancement of the VSI policy, where the sample size also changes with the sampling interval. However, for many industrial (especially continuous) processes where &Xmacr; charts are used, maintaining deterministic time intervals between samples is not possible owing to inherent randomness of the processes. In this paper we propose a new variable sampling policy, named random sampling policy (RSP), for &Xmacr; charts in which the sampling intervals and the sample sizes (considered a function of the sampling intervals) are treated as random variables. An economic modeling framework for design of RSP with run rules is developed. Within the proposed modeling framework, special cases of RSP, such as VSI and FSI policies with and without run rules, can also be evaluated. An application of the economic model is demonstrated through design of RSP parameters for two numerical example problems.
