Economic design of cumulative count of conforming control charts based on average number of inspected items

Nowadays, continuous improvement can be regarded as the essence of survival and growth in order to not only increase the competition in global market, but also requirement for ever-decreasing defect levels in processes. therefore, new statistical analysis techniques and decision-making procedures have been continuously evolved, both to handle high quality processes and to look for process improvement opportunities. ccc-r chart, or extended approach of ccc charts, is generally a technique for high quality processes, when nonconforming items are rarely observed. this study develops a mathematical model based on the average number of inspected items for the economic design of ccc-r chart, so that the average cost per item is minimized. the optimal designed parameters for different nonconforming fractions and different parameters in each iteration are calculated. in addition, with respect to type i error (α) and type ii error (β) in the process, sensitivity analysis of the model is carried out.