Efficient Determination of Sampling Rate and Sample Size in Statistical Process Control

Abstract

We propose a simple method for the determination of minimum efficacious sampling rate and sample size in Shewhart-like control charts, a controversial topic both in the academic and industrial fields dealing with Statistical Process Control (SPC). By modeling the control procedure as the sampling of a stochastic process and analyzing data in the frequency realm, it is possible to identify meaningful system time scales and apply the well-known Nyquist-Shannon sampling theorem in order to define conditions for an efficient quality control practice. Such conditions express the minimal requirements for an efficacious monitoring of quality indices, indicating the minimal efficacious sampling rate and the minimal effective size of rational subgroups in Xbar and R (or S) charts, which are useful both in the setup phase and in the on-line control phase of the Shewhart's control charts. Results can be applied also to I-MR charts. No statistical assumptions are made on the monitored data; in particular neither statistical independence nor Gaussianity is assumed in the derivation of the results. We focus on continuous processes like those typical in, but not limited to, e.g. refining, chemical processing and mining.