Assignable causes of variation and statistical models: another approach to an old topic

This paper presents a fresh approach to the analysis of Shewhart control chart's performance. We consider two different types of assignable causes of variation. One–called type I–affects only the parameters of a model of the underlying distribution. The other–called type X–impacts the type of the original distribution. We analyze cases when the underlying normal distribution transforms into a uniform and log-normal distribution after the intervention of an assignable cause of variation. It is shown that the Power Functions for control charts for individual measurements and control charts for means differ significantly from the well-known traditional studies. We believe that this approach may open up new areas of research in the field of Statistical Process Control (SPC) and extend the spheres of SPC applications in practice.