Use of independent runs for the improvement of the response of Shewhart control charts

Abstract

The paper deals with an extension of standard Shewhart charts witch provide independent runs of given length, or IR-charts, with the purpose of improving the performance of the former by allowing a faster detection of small and medium shifts in a process mean. The author purposely chooses to remain in the field of indipendent sample observations, which are much more frequently used in SPC compared to other types of charts due to their simplicity, and shows how careful choice of independent runs, formed by the same sample means used in a standard X-chart, can be adopted in order to reduce ARL values and, therefore, the expected time of detection of out-of-control situations. The result is obtained without the main drawback of dependent runs procedures as summarised in the Western Electric Company runs rules and others recalled in the paper, with lies in the fact that their in-control ARL is too low, thus providing a too short expected time before a false out-of control alarm occurs.