Filter effect in the use of control charts for productive process control

Abstract

In this paper the author analyses the reduction of product nonconformity obtainable through the use of Shewhart control charts during the operative phase of a productive process. This result can be called "filter effect" of control charts. The author supplies a quantification of this effect by defining , in correspondence with a nonconformity input of the process, an approximate measure of the expected proportion of nonconforming units resulting from the use of control charts. The study is conducted both under the classic hypothesis of a single shift,which is constant over time, in the observed process parameter, and under the hypothesis of a uniformly progressive shift. The result obtained show that, at a given level of nonconformity input, the filter effect is more pronounced in the case of a progressive shift, and above all, that it is possible to quantify this effect at assigned levels of risk. It can be observed that the filter effect of a control chart increases when the nonconformity level of the process decreases. Therefore the filter effect is particularly remarkable when more time is needed to detect the process parameter and, consequently, there is a longer exposure to the resulting nonconformity.