Comparing the Economic Effectiveness of Various Adaptive Schemes for the c Chart

In an attempt to improve the effectiveness of statistical process control (SPC) procedures, a variety of adaptive schemes has been developed in the last decades. However, considering control charts for attributes, relatively few works about adaptive schemes have been proposed, and most of them were proposed only recently. The common characteristic of those schemes is that one or more chart parameters are allowed to adaptively vary during the SPC operations according to the sampling information history, typically the current point plotted on the chart. In this way, the adaptive schemes are smarter than the related static ones, but they are also more complicated in terms of implementation. The purpose of the present work is to evaluate and compare the economic performance of the main adaptive schemes of a control chart for attributes, in order to derive conclusions on their relative effectiveness. In particular, the analysis is focused on the c chart that is used to monitor the total nonconformities number in an inspection unit. A numerical comparative study, based on a 2V5−1 fractional factorial design scheme, to investigate on the influence of several operating and costs parameters, is carried out, and the related considerations are given. The obtained results show that the chart parameter having the most impact on the economic performance is the sampling interval. Therefore, in most cases, the use of a c chart with adaptive sampling intervals is the better choice than other adaptive schemes, which are also more complicated in terms of implementation.