Design of the statistical control of low fraction nonconforming processes restricted to small samples

Abstract

We present the non-conventional design of no charts used for the surveillance of processes characterized by a very low fraction nonconforming, with a costly and/or time-consuming inspection procedure. which makes the inspection of large samples prohibitive. Under these circumstances, the trade-off between the false-alarm rate and the speed with which the chart signals process deteriorations is the basis to design the control chart, once [depending on the sample size) the conventional np chart with three-sigma limits offers little protection against false alarms or is slow in detecting process disturbances. The study was motivated by the real case of a newspapers packaging process. The nominal number of newspapers in the package depends on the newspaper's breadth, and packages with a number of newspapers different from nominal are considered nonconforming.