AN ECONOMIC DESIGN-MODEL FOR (X)OVER-BAR CHARTS WITH RANDOM SAMPLING POLICIES

Recent literature contains many papers on the study of variable (but d eterministic) sampling interval (VSI) policies for (X) over bar contro l charts. VSI policies perform better than their corresponding classic al fixed-sampling-interval (FSI) policies. Results are also available in the literature for an adaptive VSI policy, an enhancement of the VS I policy, where the sample size also changes with the sampling interva l. However, for many industrial (especially continuous) processes wher e (X) over bar charts are used, maintaining deterministic time interva ls between samples is not possible owing to inherent randomness of the processes. In this paper we propose a new variable sampling policy, n amed random sampling policy (RSP), for (X) over bar charts in which th e sampling intervals and the sample sizes (considered a function of th e sampling intervals) are treated as random variables. An economic mod eling 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 ap plication of the economic model is demonstrated through design of RSP parameters for two numerical example problems.